Design, Modeling, and Implementation of an Environmental Control Chamber

This thesis goes over the details of humidification and temperature modeling for an enclosed, non-hermetically sealed space. Review of common methods of thermal and humidification design was performed to detail which method is suitable for any given application. For the application of designing an enclosure for the preparation of Cryo-TEM sample grids, it was determined that system design via lumped capacitance methods was the best option. A detailed and practical analysis of the application of the lumped capacitance method is described. A detailed overview of how to apply control of relative humidity and temperature in an enclosed space is also included. It was required to build the entire system from the ground up to implement a control scheme for the preparation of Cryo-TEM grids. This includes the design of heaters, a humidifier, an enclosure, electronics, and programming. Heating of the enclosure was accomplished through the utilization of cartridge heaters in an application to take advantage of the benefits of forced convection. Humidification was accomplished with a closed loop design where moist air is fed to the enclosure and the dry air of the enclosure is returned to the humidifier. Water vapour was produced through an ultrasonic piezoelectric transducer. Control of these elements was established via PC and electronic control. Work has shown the effectiveness of the lumped methods for developing accurate higher order models for thermal systems. Experiments had to be performed to determine the thermodynamic parameters associated with convection required to develop the state space equations to represent the system. This is due to the many unknowns present without the use of CFD simulations. For portions of the system relying on thermal conduction, the predictive model calculated shows excellent agreement with real world data. Once the thermal model for the overall system was developed, experimentation of various inputs and changes in thermodynamics were used to verify the effectiveness of the model. There was also a need to develop a model for humidification based on direct measurements of relative humidity. The model is based on pressure driven mass flow in terms of partial pressures and conservation of mass. This leads to a system where the active input is water vapour and the passive input being the ambient water vapour partial pressure. Since relative humidity is based off of dry bulb temperature, there was a need to develop a model to take temperature into consideration. A model was developed to consider all of these factors in a first-order system. ACKNOWLEDGMENTS I would like to thank all of the staff in the University of Rhode Island’s Department of Mechanical, Industrial and Systems Engineering for their unwavering support throughout my time here at the University of Rhode Island. I want to specifically thank my advisor, Professor Musa Jouaneh, for supporting my education and providing great advice and wisdom throughout my research. In addition, I would like to acknowledge Jim Byrnes and Joe Gomez for their practical and technical expertise in their respective fields of electronics and manufacturing. Special thanks goes to the sponsor of my research, NanoSoft LLC., not only for their funding, but for their expertise and assistance in the project. Last but not least, I would like to thank my family and friends for supporting me throughout my undergraduate and graduate career at the University of Rhode Island. Between their personal and academic support, I was able to persevere and succeed in graduate school.

A detailed overview of how to apply control of relative humidity and temperature in an enclosed space is also included. It was required to build the entire system from the ground up to implement a control scheme for the preparation of Cryo-TEM grids. This includes the design of heaters, a humidifier, an enclosure, electronics, and programming. Heating of the enclosure was accomplished through the utilization of cartridge heaters in an application to take advantage of the benefits of forced convection. Humidification was accomplished with a closed loop design where moist air is fed to the enclosure and the dry air of the enclosure is returned to the humidifier. Water vapour was produced through an ultrasonic piezoelectric transducer. Control of these elements was established via PC and electronic control.
Work has shown the effectiveness of the lumped methods for developing accurate higher order models for thermal systems. Experiments had to be performed to determine the thermodynamic parameters associated with convection required to develop the state space equations to represent the system. This is due to the many unknowns present without the use of CFD simulations. For portions of the system relying on thermal conduction, the predictive model calculated shows excellent agreement with real world data. Once the thermal model for the overall system was developed, experimentation of various inputs and changes in thermodynamics were used to verify the effectiveness of the model.
There was also a need to develop a model for humidification based on direct measurements of relative humidity. The model is based on pressure driven mass flow in terms of partial pressures and conservation of mass. This leads to a system where the active input is water vapour and the passive input being the ambient water vapour partial pressure. Since relative humidity is based off of dry bulb temperature, there was a need to develop a model to take temperature into consideration. A model was developed to consider all of these factors in a first-order system.  Graphic of EM grid with a carbon film overlayed on a copper grid [9]. Grids are typically 3 mm in diameter. . . . . . . . . . . 3

1.2
Picture of a FEI Vitrobot machine, a commonly found Cryo-TEM grid preparation system. A dewar is filled with liquid ethane for sample vitrification (A) located below the temperature and humidity controlled chamber (B). A pair of tweezers with a Cryo-TEM grid (C) is mounted onto the machine's plunger inside the environmental control chamber [11]. . . . . . 4

1.3
Graphic of EM grid after preparation. Starting from the left, a macro-view of the EM grid, a close up of the porous carbon film within one grid square, top view of specimen suspended in the carbon film, cross-sectional view of specimen suspended in carbon film [12] Environmental control is an important aspect of many industrial and scientific applications. Such applications require the accurate control of temperature and relative humidity in a confined space and allows for processes that need such control. Examples of where temperature and humidity control are implemented are in incubators for bacteria as well as Cryogenic Electron Microscopy (Cryo-EM) along with a myriad of other applications [1] [2]. The reason for why temperature and humidity control are needed varies upon the application and parameters needed for certain processes. Temperature control for biological applications are important in order to preserve proteins as too high of a temperature can cause proteins to denature [3]. Humidity regulates processes where there is a system comprising of water. Anything that is water-based and exposed to air can lead to water evaporation dependent upon the humidity of the surrounding air [4]. Control of humidity allows for the control of evaporation or condensation in an enclosed environment [5]. The objective of this thesis is to study the mechanics of temperature and humidity control and implement a control system for a Cryo-EM sample preparation system.

Electron Microscopy Technologies
There are two distinct EM technologies that are widely used today; the Scanning Electron Microscope (SEM) and the Transmission Electron Microscope (TEM) [6]. The TEM is analogous to a light microscope where the electrons are transmitted from the electron gun through a thin specimen and the electrons that are able to pass through the specimen are detected on an imaging plate. SEM on the other hand relies on the reflection of electrons off of a surface which is great for three-dimensional specimens but at a resolution that is one order of magnitude less than TEM [7].
A subset of electron microscopy is the use of cryogens to prepare EM samples. Cryogenically frozen specimens can be used in both TEM and SEM systems which are respectively named Cryo-TEM and Cryo-SEM or Cryo-EM for general cryogenic electron microscopy. One of the main reasons that Cryo-EM is utilized in the scientific world is that Cryo-EM allows for the imaging of a specimen in its native aqueous environment as opposed to negative staining where the specimen is subjected to heavy metal salts and dehydration [8]. The freezing of an aqueous specimen allows for the specimen to be subjected to the vacuum present in the electron microscope where the specimen would otherwise be damaged due to water or other liquids evaporating out of the sample.

Cryo-TEM Sample Grid Preparation
Careful preparation of EM specimens is required for high quality imaging.
TEM requires the specimen to be thin enough for electrons to pass through without the appearance of visual aberrations on the image or where the signal to noise ratio is satisfactory [8]. For the scope of this research, the system being implemented will focus on the preparation of samples that are suspended in carbon on an EM grid. An example of an EM grid is depicted in Figure 1.1. Graphic of EM grid with a carbon film overlayed on a copper grid [9]. Grids are typically 3 mm in diameter.
The preparation of Cryo-TEM grids is a highly involved process. In short, the process can be summarized into a few steps. The selection of the proper sample grid is the first step and is dependent upon the desired application of the grid. There are various carbon pore sizes as well as grid mesh sizes to consider. Grid mesh material can be a limiting factor depending on how the user wants to prepare their specimen. Copper is the most common material but it is not recommended if the user wants to grow a biological specimen on the grid itself since copper is a known biocide [8]. Once the grid type is known, the user mounts the grid onto a pair of tweezers mounted on a plunger located in an environmentally controlled chamber as shown in Figure 1.2. Next, about 5 µL of aqueous sample is pipetted onto the grid. Then, the loaded EM grid is blotted with filter paper to remove excess liquid and to achieve a uniformly thin sample. The EM grid is then plunged into a dewar, located outside of the environmentally controlled chamber, filled with liquid ethane where the specimen is vitrified. The specimen must be carefully maintained at a temperature below -137°C at all times until the specimen is imaged in the electron microscope per the satisfaction of the user. If the specimen reaches a temperature above -137°C, then it will become devitrified and the image of the specimen will contain aberrations due to ice crystal formation. For a more detailed step by step procedure in preparing EM grids, refer to [10]. A graphical representation of the specimen in the prepared EM grid is shown in Figure 1.3. Picture of a FEI Vitrobot machine, a commonly found Cryo-TEM grid preparation system. A dewar is filled with liquid ethane for sample vitrification (A) located below the temperature and humidity controlled chamber (B). A pair of tweezers with a Cryo-TEM grid (C) is mounted onto the machine's plunger inside the environmental control chamber [11]. Graphic of EM grid after preparation. Starting from the left, a macroview of the EM grid, a close up of the porous carbon film within one grid square, top view of specimen suspended in the carbon film, cross-sectional view of specimen suspended in carbon film [12].
All of the preceding steps need to be followed for proper vitrification of the specimen. Any deviations can lead to non-uniformities in the specimen, nonvitreous ice, or other complications when the specimen is ultimately imaged with an electron microscope. Some visual examples of how poor vitrification can adversely affect image quality is shown in Figure 1.4. For the scope of this research, the temperature and humidity control of the system is the most important aspect being addressed. Improper temperature and/or humidity control can adversely affect the specimen being prepared. Improper humidity control, as discussed earlier, will cause an increase in evaporation in the specimen causing it to be dehydrated prior to vitrification [13]. Temperature control will affect the humidity in the enclosure as well since the saturation pressure or density of air is dependent upon the temperature of air [14]. Therefore, to ensure that there is not excessive evaporation in the specimen, the temperature needs to be held at a steady state so that the relative humidity in air is not affected and can maintain a desired set point.  [8].
In addition to the environment encountered by the specimen, the blotting process itself has been known to cause specimens to be poorly imaged or imaged in a non-native state. Conventionally, the use of blotting paper or filter paper is used to wick excess specimen solution off of the EM grid to ensure a uniform thin thickness of sample on the grid. This can cause shear rates in the specimen that are approximately 10 3 to 10 5 s -1 where shear rates as low as 600 s -1 can cause worm-like micelles [15] [16]. A new method presented by [15] utilizes capillary tubes replacing blotting paper. Results have shown that capillary tubes are able to reduce the shear rates in the specimen by one to three order of magnitude on average when compared to blotting. This allows for the wider application of Cryo-TEM to produce specimen images of nano-scale objects in its native morphology that may not have been feasible with conventional blotting.

Objective
The primary objective in this research is to develop an environmental control chamber that is able to perform the processes needed for a proper Cryo-TEM sample preparation system similar to the process developed in [15]. The chamber must be able to control the temperature and humidity to conform to the user's specified settings and to enable the proper preparation of EM sample grids. The control of the operation is governed by a PC program with a graphical user interface (GUI) which communicates with the sample preparation system via a custom control board. Temperature and humidity is controlled via two separate control loops and is implemented in software. Any auxiliary equipment needed for the process, such as actuators, are also controlled by the software along with supporting hardware with user specified inputs.
To accomplish this, modeling of the system is required to determine the design parameters for the system. Such modeling includes determining the temperature's transient response to a user specified desired temperature input and the input of the ambient air temperature. The humidity response of the system is based off of the dry bulb temperature of the enclosure's air and the mass flow rate of water vapour in the control volume. Knowing this, it is possible to model the humidity of the system as a function of the physical characteristics of the system, dry bulb temperature, and the mass flow rate of water vapor into the system. Therefore, to properly design the system, a model of the system's thermal properties needs to be developed to govern the thermal and humidity performance of the environment chamber.
In addition to the thermal and humidity design, the development of control hardware is necessary for the system to function. This will be accomplished by designing a printed circuit board (PCB) that will effectively act as an intermediate piece of the system between the PC and the EM sample preparation instrument.
The PCB has to be able to direct power to individual components in the system in concert with the digital commands given by the PC via a data acquisition card.
The PCB is also responsible for connecting various sensors to the system. The sensors that are to be used in the system utilize an analog voltage signal that represents a state variable. These analog signals have to be processed before being read by the PC by using various analog signal processing hardware which includes op-amps, wheatstone bridges, and electrical filters. This is necessary to prevent any analog noise that may be present in the system to not reach the PC and cause inaccurate readings. The control of temperature, as mentioned earlier, is an important factor during the design stage of this product. To accurately design a temperature control system, one must know the parameters and mechanics associated with the plant dynamics for the enclosure. Several methods of analyzing the thermodynamics of a system exist each with their own advantages and disadvantages. This includes the use of a priori methods such as analytical and numerical methods, as well as methods utilizing experimental data to determine the system dynamics. This section will go over the variety of methods that are most commonly used for thermal design.

Heat Transfer Mechanics
Temperature control is governed by the mechanics of heat transfer. Heat transfer can be broken down into three basic mechanisms; conduction, convection, and radiation [1]. These mechanisms can be used to determine the temperature values at different points in the system during the steady-state portion of its dynamics.
Thermal conduction is the most basic form of heat transfer mechanics but it is generally limited to heat transfer in solids. It is defined as the energy transfer between adjacent parts of a solid body [2]. This generally limits the use of thermal conduction calculations to solid-solid interfaces and is not applicable for fluids as heat transfer at solid-fluid interfaces are defined under convection. Thermal conduction can be mathematically defined in Equation 2.1 where q is heat rate, k is known as the thermal conductivity and is a constant dependent on the material used, A is the area associated with the heat transfer in question, T i is the temperature associated with a point in the solid body, and x i is the position associated with the temperature T i [3]. This equation is limited to heat transfer in one-dimension but it is extremely useful for design as there are various applications in which an assumption can be made to model a system as one-dimensional. For scenarios where heat transfer cannot be looked at with one-dimensional models, there exist theories for steady-state and transient analysis of thermal systems in [4].
For heat transfer boundary conditions where there is a solid-fluid interface, there exists the heat transfer mechanism of convection. The mathematics behind convection is similar to heat transfer through conduction and is stated in Equation 2.2 below. The convective heat transfer coefficient, h, is a parameter that is dependent upon the specific convection boundary conditions that is related to the Nusselt number of the fluid in the heat transfer problem. The Nusselt number of a fluid is a dimensionless term that characterizes the ratio between the convective and conductive heat transfer in a fluid and its formulation is dependent upon the geometry of the solid-fluid interface as well as the flow's thermodynamic conditions [5]. Therefore, the convective heat transfer coefficient will also depend upon these factors. Specifically, it is a function of the steam velocity U , body length L, wall roughness height γ, wall temperature T w , freestream temperature T ∞ , density ρ o , viscosity µ, fluid thermal conductivity k, fluid specific heat c p , buoyant specific weight g∆ρ, and the overall shape or geometry of the object that is immersed in fluid [6]. This relationship is better expressed visually in the form of a function in Equation 2.3. Various scenarios of heat transfer with forced, free, and combined convection with laminar and turbulent fluid conditions are covered in [7]. Once the Nusselt number of the boundary condition of a specific problem is known, the convective heat transfer coefficient can be calculated using Equation 2.4 where N u is the average Nusselt number and L is the length or effective length of the heat transfer boundary [8].
The other form of heat transfer is the mechanism of radiation. Radiation is a specialized case where thermal energy is emitted from an object via electromagnetic radiation and does not require a medium to travel through. J. Stefan and L. Boltzmann determined that the thermal power radiated from an object is proportional to the absolute temperature of the object to the fourth power. For real surfaces, this relation is scaled by the surface's emissivity, , which is a value ranging between zero and one [9]. This relationship is shown in Equation 2.5 where T is the surface temperature of the object in absolute units, σ is the Boltzmann constant, and A is the surface area associated with the origin of emitted radiation.
Every object emits thermal radiation into space, but it can potentially be ignored in the overall thermal system performance calculations if the absolute temperature of the object and the application of the object deems that it is a small percentage of the overall heat transfer. There are numerous other factors at play when dealing with radiative heat transfer and it can get fairly complex when looking at the details. To learn more about the intricacies associated with radiative heat transfer, [10] goes over the details from a physics perspective and covers heat transfer from a single body as well as heat transfer between two or more bodies within line of sight of each other.
The previously discussed heat transfer mechanics covers the extent of steadystate analysis of thermal systems. If it is desired to understand the transient response of the system, then the thermal energy storage capabilities of materials needs to be taken into consideration. Otherwise known as thermal capacitance, the transient response of an object is dependent upon the mass of the object, m, and its specific heat, c p . Using these parameters, the heat flow going into an object can be characterized into a lumped thermal capacitance formulation shown in Equation 2.6 as a first order ordinary differential equation. For systems with a fixed mass, the product of the mass and specific heat of the object can be represented as a thermal capacitance, C [11].

System analysis and design
There exist a few methods for the design and analysis of physical thermal systems. For simple systems that consist of a few parts, or that have a simple geometry, it may be advantageous to utilize an analytical approach to modeling such a system as it will reduce the amount of computing time necessary during the design phase of a project [12].  [14]. This methodology could also be used for calculating variables over a plane or 3-D space. There is also a method that combines experimentally derived data with that of an analytical model to simulate the thermal response for certain inputs that is used for complex problems or for those with larger physical scale.
All of these approaches are touched upon in the following sections.

Numerical methods
To solve problems that consist of complex geometries, many intricate factors, or boundary conditions that may be extremely difficult to generate a priori, numerical analysis can be performed. This is especially valuable for models that contain convective boundary conditions for geometries that are not covered by readily available resources on heat transfer. Cylinders, flat plates, spheres, and other simple geometries are covered by formulations in [15] or other available literature in the subject and the convective heat transfer coefficient can be determined using these formulations if the velocity, material properties of the fluid surrounding the object, and the object's geometry is known. However, this calculation is rarely used by itself in practical design of common devices due to the limitations of simplifying the design problem. Therefore, to practically design complex thermal systems without having to do many experiments in the early parts of the design phase, it is recommended to use numerical analysis. Unlike analytical methods, numerical analysis can only determine an approximation of variables where analytical can provide exact solutions to define the values of variables across a geometry.
For practical design, it is usually not necessary to have perfect results as there will most likely be error in variable values due to real-world implementation.
As described earlier, numerical methods provide an approximation to a flow property such as flow velocity, density, pressure, and temperature. To accomplish this calculation, the use of finite-difference methods (FDM) or finite-element methods (FEM) are utilized where each node or element represents a flow property. A finite-difference methodology explained by [16] goes into great detail of how flow properties can be determined by having defined the boundary conditions and initial conditions of the problem and then approximating the numerical quantity at adjacent nodes for a certain parameter. FEM is similar to FDM where a system is discretized but instead of having a mesh of discrete nodes and approximating solutions for neighboring nodes, FEM uses discrete elements where the flow problem is modeled between nodes. Determining an FEM solution will require more computing power than its FDM counterpart since there is greater detail to the data between nodes needed to be calculated [16].
In order to solve for a discretized system in an FEM of FDM application, the governing fluid flow equations need to be evaluated to get an accurate solution.
There are three governing partial differential equations that fully model the prop-

Lumped capacitance method
To analyze and design systems with the discussed steady state and transient response formulation, it is common to reorganize the equations to reflect that of components of an electrical circuit. The construction of such an electrical analog, known as the lumped capacitance method, can be used to simulate the response of a thermal system as done by [19] with the use of a resistor-capacitor network.
This method has also been used by design engineers for analyzing a convection oven and comparing it to its real world thermal performance over time with temperature control with little error between the analytical model and real world data [12]. The use of such a method eliminates the need for complex partial differential equations for cases where the need for such detail is not required and is seen as a more practical approach to thermal system design. It replaces these partial differential equations with algebraic relationships which reduces the needed com- This relationship is shown in Equation 2.14 and results in a single resistance value R [21]. 14) The thermal resistance due to convection can be characterized if the average convective heat transfer coefficient (h) and the surface area where heat flux is traveling through is known. The equivalent thermal resistance can then be expressed as the inverse of the product of these two characteristics as shown in Equation 2.15 [21]. Unlike the coefficient of thermal conductivity, the average heat transfer coefficient is not entirely based upon the properties of the materials involved in the heat transfer. As previously discussed in the heat transfer mechanics section, the coefficient is a function of flow properties, flow and object thermodynamics, and the overall geometry of the problem and is determined via the Nusselt number.
Work has been performed on the determination of thermodynamic properties for the design process of an oven. Tapia et. al. did a study on determining a single oven resistance and capacitance for the walls of an oven of various geometries and determined the equations below [22]. Equations 2.18 through 2.21 presents the functions of thermal resistances and capacitances in terms of geometry and thermodynamic properties for ovens that are in the form of cubes and rectangular prisms where l is the length of a side, δ is the wall thickness, and C x is the capacitance of the air within the oven or heated enclosure.
R rectangular = δh + k kh[2(l 1 l 2 + l 2 l 3 + l 1 l 3 ) + 4(l 1 + l 2 + l 3 )δ + 12δ 2 ] (2.18) The use of the lumped capacitance method has seen extensive use in academia and industry alike. As the conversation on applied numerical analysis was limited to temperature modeling of an oven, this discussion will also be restricted to kitchen ovens. An application of where the transient analysis of a professional oven is performed with the lumped capacitance method is in [12]. A model is shown where the author discretized the oven into several elements of equivalent thermal resistances and capacitances and the results of this model matches well with the experimental values of air temperature that were obtained to validate the model.
The one portion of their analysis where it stepped outside the bounds of modeling solely using the equations produced from analysis, was when the average convective heat transfer coefficient of the oven walls had to be determined. To do this, they performed a CFD analysis of the oven cavity to study the air flow characteristics of the oven and find the convective heat transfer coefficient that way. The author also had to tune the coefficient after the CFD analysis by comparing the thermodynamic properties with the results of the model. It was successfully tuned once the values converged with satisfactory error.
Other work on the topic was performed by Ramirez-Laboreo et. al. who studied and developed an eighth-order discrete lumped capacitance model of a commercial electric oven [23]. In addition to modeling the temperatures in the oven, the work also focused on modeling the cooking process of food which includes mass transfer associated with the evaporation of water from the cooking food. The authors obtained the thermal model by first discretizing the oven into individual components and arranging the electrical analog accordingly. Due to the complexities associated with obtaining the particular thermodynamic properties of the individual components, system identification was performed by using a large array of thermocouples on every component as well as measuring the room temperature with a thermocouple. Knowing the heat flux flowing through the system as well as the heat associated with vaporizing the water out of the food sample, which was represented by a porous material saturated with water for experimental controllability and repeatability, the thermal resistances and capacitances can be determined experimentally.
Experiments were also performed by Abraham et. al. for the determination of a general model for a load situated in an electrically heated oven via natural convection and radiation [24]. Various geometries, materials, and surface finish emissivities were experimented with to validate the model. Like Ramirez-Laboreo, the oven temperature profiles were determined by using thermocouples throughout the oven cavity with the only difference being a larger array of thermocouples were utilized. There was only a theoretical analysis to determine the temperature response of the thermal load in the oven with only the oven cavity temperature acting as an input. The rest of the data, including the oven air and wall temperatures, were determined experimentally. This follows the same trend as most authors on the subject due to the complexity of oven modeling or any other modeling associated with a heated and enclosed space. Generally, it is only practical to try to theoretically model an isolated single component as complexities associated with heat transfer creates great difficulty in modeling without any experimental data to base the model on.

Experimental modeling
In addition to modeling the temperature within an enclosed space using theoretical analysis or numerical simulation, there exists the widespread use of determining the thermodynamics of the system utilizing experimental data. As mentioned in the previous sections, it is a challenge to find an accurate theoretical or numerical model mainly due to aspects that fall under mass flow characterization of the system, such as the average convective heat transfer coefficient inside a heated enclosure. These models had to be tuned with the use of experimental data and later verified to prove accuracy. Unklesbay et. al. analyzed a convection oven solely through the use of experimental data and statistical methods to determine the transfer function and the dynamics of the thermal response [25]. The model that was determined from the experimental data was measured against actual data from further tests to determine the accuracy and repeatability of this method and it was concluded to accurately track and predict the temperature within the oven.

Humidity Control
Humidity control is the area of study concerning the control of moisture in air and is often defined as psychrometrics. Moist air is a homogeneous mixture of water vapour and dry air and is important for the application of this environmental control chamber. This section goes over the factors and mechanisms pertinent to this project.

Mechanics of Humidification
The mechanics of humidity is essentially based on the ratio of water vapour in air compared to how much water vapour the volume of air in interest can handle before precipitating. The amount of water vapour in air is typically expressed in terms of the partial pressure of water vapour but can also be expressed as the mass of water vapour per unit volume of air. Humidity of air can be expressed as specific humidity ω which is the mass ratio of water vapour m v per unit of dry air m a or relative humidity φ where the ratio is expressed as a ratio of the partial pressure of water vapour p v and the saturation vapour pressure of water p s in air for a given dry bulb temperature. These relationships are expressed in Equations 2.22 and 2.23 respectively where the additional variable p is the total pressure of the gaseous mixture [26]. In regards to Equation 2.22, the right-most formulation was derived using the ideal gas law and 0.622 is solely the ratio of the molecular weight of water vapour to the molecular weight of dry air.
When analyzing systems that manipulate the physical properties of a mixture, it is important to obey the theories of conservation of mass and the conservation of energy to determine the thermodynamics of humidification. The addition of water vapour at a given temperature to a stream of dry air will alter the humidity and temperature of air depending on the humidification mechanism utilized. Such mechanisms are thermally driven methods such as steam or mechanically driven methods, both of which are described more in detail in later sections. For analyzing the energy of the system, the mixture enthalpy is determined and is defined as the sum of the enthalpy of dry air and water vapour as shown in Equation 2.24 where H is defined as enthalpy and h is enthalpy per unit mass [26]. Subscripts a labels the parameter for dry air and subscript v is for parameters associated with the water vapour. Another useful formulation is the energy balance equation for humidification and dehumidification systems is illustrated in Equation 2.25 where the subscript w indicates a value associated with liquid water, 1 for one end of the humidifier and 2 represents the opposite end. This equation is used for mass flow problems where there is an inlet and outlet involved such as a duct and the goal of the analysis is to determine the thermodynamics at the inlet and outlet of the control volume [26].
The modeling of temperature, relative, humidity, and even light was expressed in [27]. Focusing on humidity modeling, the authors took the modeling approach by modeling the absolute humidity in the chamber in order to decouple the response from the dry bulb temperature. State variables used in this approach were temperatures of important components and the air as well as the absolute humidity of the air. Ignoring the effects of condensation yields a linear control scheme. The system analyzed in [27] used on-off control through the use of relays of various components. Upon validating the models after system identification was performed, the comparison between experimental data and the predictive model resulted in a fit between approximately 62-73% for each state variable including temperatures and absolute humidity.
In addition to solving a relative humidity problem analytically, one can use CFD to solve for relative humidity inside of a control volume numerically. There exists a myriad of complex humidification systems that involve sources and sinks of water vapour which are best modeled through the use of CFD. Teodosiu et.
al. utilized CFD to model relative humidity, air velocity, and temperature profiles in offices which included aspects that affect a room's relative humidity such as climate control and the transpiration of human workers [28]. Although this was a highly inclusive model of relative humidity, the general theories behind the modeling reflected the theoretical formulations based upon conservation of mass and energy principals stated previously. Therefore, CFD can be used as an additional tool in the analysis and/or design of control systems aimed at manipulating and controlling relative humidity systems.
The modeling of saturation vapour density or pressure is based off of empirical data for various dry bulb temperatures. A fitted polynomial curve of this data was used to predict this metric and there exists several polynomial fits for various air dry bulb temperature ranges. If it is desired to measure the saturation vapour content in terms of partial pressures, the formulation by [29] gives a few eighth-order approximations of the saturation vapour pressure for various temperature ranges as well as whether the air in question is over liquid water or ice.
The approximation stated in [29] allows for the determination of saturation vapour pressure in terms of Pascals and is presented as Equation 2.26. This eighth-order polynomial approximation is used for the dry bulb temperature range of 0 to 100°C and is plotted versus dry bulb temperature in Figure  In addition to studying the saturation vapour pressure for humidification analysis, there exists psychrometric charts for the determination of various thermodynamic variables for moist air including dry bulb temperature, wet bulb temperature, specific humidity, relative humidity, specific volume, and specific enthalpy.
Knowing any two values of these properties in addition to knowing the constant pressure of the mixture enables for the determination of the other variables. An example of a psychrometric chart for atmospheric pressure is featured in [30] and [26] goes over the use of psychrometric charts as well as including specific examples. The use of these charts are widely used in industry for an approximation of variables pertinent to heating, ventilation, and air conditioning applications and has a use for analyzing an environmental control chamber.

Humidification Methods Steam
One of the most common humidification methods is to heat and vaporize liquid water into steam. This method increases the specific humidity and the dry bulb temperature of air since both thermal energy and mass of water vapour in air are introduced to the virgin air [26]. Utilizing steam in this manner is simple but for design, it may not be favorable for applications that involve the control of temperatures elevated above the zero-input temperature as this method may increase the temperature above a desired threshold.

Evaporative
Another method to increase the specific humidity of air is to utilize the natural evaporation of water without the need to add external energy to the system. This method capitalizes on the natural tendency for water to evaporate in low relative humidity environments [31]. This is due to the state between liquid water and air not being in equilibrium with each other. The water is evaporated through random molecular collisions where some molecules gain enough energy to escape the bulk of liquid water and mix with the dry air. Equilibrium is established once the water vapour pressure reaches saturation. Implementation and enhancement of this mechanic is produced by employing a wick and a fan that introduces a stream of air to the moist wick. The wick increases the surface area of water to air as well as positioning the water into the stream of air. Exposing the moist wick to the flowing air increases the rate of humidification [32]. This method offers humidification without introducing unwanted heat to the system and produces fine and filtered water molecules. However, this method does have a limiting factor for use since at higher relative humidity as it is more difficult for the water to be evaporated from the wick. If it is desired to have a cool humidifier that does not need to produce high levels of humidity in the surrounding air without increasing temperature, then this method may be superior.

Ultrasonic
In addition to the previous methods, there is a way to mechanically introduce atomized water to air in order to increase humidity via the use of an ultrasonic humidifier. Ultrasonic humidifiers consist of a piezoelectric vibrating plate submerged in a reservoir of liquid water. The piezoelectric plate emits vibrations into the surrounding water a high ultrasonic frequency which displaces and disrupts the surface tension of the water. This process atomizes the liquid water into water vapour during this displacement without the need to heat the water to promote evaporation [33]. Just like evaporative humidifiers, ultrasonic humidifiers will produce a cool mist for humidification. A drawback of this method is that it naturally does not have a filter for filtering out minerals within the water which causes a more translucent mist compared to other humidifiers [32].

Electronics and Software Design
The electrical system for the prototype was designed in coordination with the other sub-systems involved in the prototype, including the temperature and humidity control sub-systems. Since the combination of software and electronics affects other portions of the prototype, the overall design is first discussed to give a better understanding of how each sub-system was melded together for a complete system design.

Firmware
Another portion of the project that required coding is the microcontroller that was used in the system's electronics which will be talked about in a later section. The utilized microcontroller is the ATMEGA328P-PU and this particular microcontroller was chosen due to it's compatibility with the open-source Arduino IDE and its ease of programming with a dedicated programmer.
The purpose of this microcontroller is solely for fan control of the humidifier and heater. Although it is not required to use PWM fans for these sub-systems, this architecture allows for greater hardware flexibility for these sub-systems. The microcontroller receives an analog signal from the data acquisition card's digital to analog output pins for control of the heater and humidifier fans and translates the analog voltage to a PWM duty cycle of a set frequency specified in the firmware's code. It also receives feedback from the tachometers of the heater fans to determine the rotational speed of the fans for the purpose of optional safety protocols for heater failure. The firmware generated for this project only variably controls PWM duty cycle and measures heater fan rotational speeds. Besides reading the frequency of tachometers, the reason why this method of PWM control was used instead of using the more traditional PWM generator circuit that consists of a triangular wave generator and a comparator was due to being able to set the frequency via programming.
The firmware code was generated in the Arduino IDE environment and can be programmed with the in system programmer of the later discussed circuit board.
Since the microcontroller and the base Arduino environment can only support a few specified PWM frequencies, there needed to be a solution to set any frequency for the PWM signals. Luckily, an open-source solution for this problem was found at [1]. By adding this code to the Arduino IDE library, this enabled for greater flexibility and functionality for the previously discussed application. The complete firmware code is found in Appendix A.1.

Software
The overall control of the system is governed by a PC with software coded in Visual Basic. Users are able to operate the software to specify a desired set point for the temperature and the relative humidity of the enclosure as well as monitor these parameters over time. This is accomplished by discretizing analog voltage signals from hardware and storing the data in established data arrays in the Visual Basic source code. The GUI shows the data arrays for air temperature and relative humidity in the enclosure through the use of line graphs where the vertical axis represents the parameter value and the horizontal axis represents time in seconds.
The status of heater temperature and ambient air temperature are also shown in the GUI but does not visually record that information in a plot. The user can also tune fan speeds to a specified duty cycle if there is a need to limit air speed in the enclosure as well as set a specified duration of time for the control task after which the system's hardware will turn off. A graphic of the GUI is shown in Figure 3 In addition to viewing this information live, the user can also save the data to a .txt file for additional analysis or for any other reason that requires system data to be recorded. This function not only records the temperature and relative humidity, but also records other parameters that are valuable for looking at the data at a later date. This data includes logical values that specify whether the heater and/or humidifier was active and the PWM duty cycles of the fans in addition to the previously mentioned temperature and relative humidity data. For further details of the Visual Basic source code used in this project, please refer to Appendix A.2.
In order to interface the software with the required hardware, all communications were accomplished with the use of a data acquisition card. Specifically, the USB-1408FS-Plus was employed as the intermediate component between system hardware and the PC and occupies a single USB port on the computer. It has 8bit digital input, 8 channels of 13-bit resolution analog to digital converters, 8-bit digital output and 2 digital to analog converters. The analog pins are capable of recording or transmitting signals at 50000 samples per second [2].

Electronics
In addition to the development of software and firmware for the system, there was a need to design and build electrical hardware for proper application of the software. A printed circuit board (PCB) was used to provide the necessary signal processing and power delivery for all of the sub-systems involved. The large problem the PCB solved was the generation of accurate and low noise analog signals that were free from any loading effects from the sub-systems that draw a large amount of electrical power. Therefore, the design of the PCB allowed for proper measurement of state variables, power delivery that does not affect sensor measurements, control of all electrical parts, and communication to the PC's software.
To better follow along with the discussion of the electronics of this section, refer to the provided schematics located in Appendix B.1.
The measurement of all state variables was accomplished by employing analog sensors to measure parameters. These analog sensors consist of sensors measuring state properties such as temperature, relative humidity, and position of numerous components. Temperature of the air inside the enclosure as well as the ambient air temperature was measured using LM35 temperature sensors which are a silicon-based integrated circuit that produces a linear analog voltage signal that scales with temperature and has an overall temperature response range from -55 to 150 Centigrade depending on the particular sensor [3]. The LM35 sensors used in the prototype have a range from 0 to 110 Centigrade. Adafruit PT100 platinum RTD sensors were used for monitoring the temperature in the heaters since this sensor has a wide temperature operating range and a maximum measurable temperature of 550 Centigrade [4]. Relative humidity was measured with a Honeywell HIH-4021 relative humidity sensor in the initial prototype. This sensor operates similarly to the LM35 temperature sensor since it is also a silicon based device that produces an analog voltage signal that scales with the measured relative humidity [5]. This sensor was replaced in the final design with a Vaisala HMP110 temperature and relative humidity sensor probe due to better relative humidity accuracy for the most-often used case where the enclosure will be operated below 40 Centigrade [6].
The Actuonix L12-50-50-12-P linear actuator that was used in the final application contains a potentiometer that measured the extension by producing an analog voltage signal [7]. The actuator was used in the final Cryo-TEM prototype for controlling a door that separates the enclosure from the dewar and was used to protect the thermodynamics of the system.
All of the circuits containing the previously mentioned analog circuits as well as any other analog sensors the user would like to use are in series with analog signal processing components. The LM35 temperature sensors' analog output pin are directly connected to the input of a non-inverting operational amplifier with an output gain of 10 in order for the data acquisition card to read the signal and be outside its uncertainty error range of about ± 11 mV [2]. Taking into consideration that the LM35's analog voltage signal scales at 10 mV per degree centigrade, the gain was necessary in order to prevent any signal noise caused by measurement uncertainty [3]. The RTDs were placed as a resistor in a wheatstone bridge in order to take the difference of the voltage between two fixed 1 kilohm resistors and the voltage between the RTD and another 1 kilohm resistor. This technique reduces the effect of any problems that may occur due to fluctuations in the 5 VDC power rail. The outputs of the wheatstone bridge are connected to an active low-pass filter prior to the two signals being processed by a differential operational amplifier in an effort to reduce the number of pins needed for the data acquisition card to read. There are also two customizable analog sensor circuits that can utilize either 24 VDC or 5 VDC analog sensors and contain a non-inverting operational amplifier with trim potentiometers located between the inverting input and the output of the amplifier for hardware control of the amplifier gain. In parallel with the potentiometer, a SPST switch is used to short the potentiometer in case the user decides to not have any gain on these sensor signals. This is the case for the HIH-4021 relative humidity sensor due to its voltage output range. As for the circuit designed for the HMP110 sensor, it does not contain any components to manipulate the output signal save for some buffering due to circuitry inboard of the sensor. All of the aforementioned circuits contain active low-pass filters at or near the input to the data acquisition card which all have a cutoff frequency of about 23 Hz which was chosen in conjunction with the sampling frequency of the software. These active filters also have the benefit of having the sensors not subject to any loading effects due to the operational amplifier's low impedance output. The analog outputs of the circuitboard is connected to a DC-37 female D-sub connector which is connected to the data acquisition card.
In an effort to decrease the noise in measurement signals, a linear power supply is used for the measurement circuits. Linear power supplies offer low output voltage ripple as opposed to switching power supplies which often generate high frequency noise without filtering. The only downside with linear power supplies is that they are not ideal for high power circuits. To get the benefits of both of these power supplies, a circuitboard that utilize both a linear and a switching power supply for specific applications will be able to have both a noiseless voltage supply for sensitive components and enough power to drive high power components such as heaters. To achieve this, the power supplies and their respective components need to be electrically isolated from one another and can only communicate with each other through the use of optocouplers. Specifically, the switching power supply used for the heaters, humidifiers, and other high power components is a 350 Watt power supply built by Delta [8]. The linear power supply for measurements and system logic can be a fixed output power supply or a lab bench linear power supply that is capable of supplying 24 VDC. In order to bridge the gap between the circuits powered by the separate power supplies, LTV-847 optocouplers are used to communicate digital logic, PWM, and other square waves from individual sub-systems back to the PC or the microcontroller.
As mentioned earlier, an ATMEGA328P-PU microcontroller was used for fan control and fan monitoring of the heaters and humidifier as their control and monitoring is based on square waves. The foundation of utilizing this microcontroller in the circuitboard is based off of the open-source Arduino Uno Rev 3 platform whose schematic is found at [9]. This design was altered to better serve the application at hand. Besides the fans, the microcontroller is able to communicate with the PC through an 8-bit parallel connection to the data acquisition card's digital input pins via the aforementioned D-sub connector. The motivation behind this was that the microcontroller is in a good position for being utilized as both a controller and a safety mechanism by having the option of telling the computer any warnings that the firmware can be coded for this application.
For controlling the numerous high-power components in the total system, it was determined that transistors were the better choice for switching instead of relays. The main consideration in this decision was that transistors are capable of switching at a higher frequency whereas electromechanical relays would quickly wear out for this application. There exists high frequency switching due to the narrow deadband of the on-off control of temperature. The narrow deadband was deemed necessary to keep the temperature close to the desired temperature. Normally the reason why on-off control is used is to prevent wear on components, however since the heaters do not have any mechanical components, excluding the fans, there will not be any significant wear due to the high-frequency switching.
The fans themselves are PWM controlled fans and were designed for such high frequency therefore, the entire heater system with the transistors allow for a narrow deadband control. The same logic can also be extended to the humidifier since it is also controlled by a transistor in an on-off control system and has a similar fan in terms of operation and an ultrasonic humidifier that operates at high frequencies. The transistor used for this application is a Vishay IRL540 MOSFET which has the capacity of handling up to 20 Amps of electrical current when the die is at 100 degrees Centigrade. When the transistor is saturated, the drain-source on-state resistance between the drain and the source is 0.077 Ohms [10]. These characteristics make these transistors suitable for controlling the high-power devices in the system. An array of six of these transistors are utilized in the final circuit board. Cooling for the heater's transistor is needed due to approximately 10 Amps of current flowing through it causes the transistor to dissipate about 8 Watts of heat. Therefore a heat sink capable of dissipating this amount of heat with natural convection was used to preserve the transistor.

Prototype Enclosure Design
The prototype enclosure built for preliminary evaluations is simply put, a cube with 10 inch sides built with 7/32 inch thick polycarbonate sheets. To form the enclosure, the polycarbonate was machined and assembled into two pieces, one being the lid and the other piece being the main body of the enclosure that consists of five pieces of polycarbonate glued together with plastic cement. The interior of the enclosure was sealed with a bead of silicone sealant along the interior edges to mitigate the escape of hot and humid air. The panels consists of machined features to facilitate the addition of hardware necessary for properly sealing the enclosure which includes but is not limited to holes for tube fittings, gaskets, and sealed cord grips.
Heating and humidifying the enclosure necessitates features for interfacing the heaters and humidifier. The enclosure has two tube fittings for fitting a closedloop humidifier outside of it. This allows for one fitting to act as an inlet to the enclosure and the other to be the return. In addition to the tube fittings, two sealed cord grips were installed into one of the walls of the enclosure in order to feed electrical wires into the interior of the enclosure without compromising the sealing of the enclosure. An additional hole is used to fit a probe that contains sensors for measuring relative humidity and temperature of the enclosure's cavity. Gaskets were also installed in portions of the enclosure where there is a possibility for significant air to escape the inside of the enclosure including the lid, tube fittings, and the sensor probe. Additional details of the construction of the enclosure can be found in Appendix B.2 and a 3-D rendering of the enclosure assembly is shown in Figure 3

Temperature Control
This section goes over the theoretical analysis of the thermal system and goes over the design process of the necessary components.

Heater Design
The first step in the design phase is to design and build adequate heaters for the system. It was decided that the heater has to conform to a size envelope, to use electric heaters that run on 24 VDC for power delivery, and to be relatively safe for its application. Prior to doing any sort of analysis, a proof of concept prototype was designed with the knowledge that forced convection was to be employed to have a compact heater size and with the idea that the prototype should be easily altered as far as modifying the properties of heat transfer. This section goes over the design process of the heater.
To conform with the size and electrical requirements, the decision was made to use ceramic cartridge heaters for the heat source. Specifically, the cartridge heaters used were designed for and utilized in 3-D printer nozzle heater assemblies and an example of such a cartridge heater is shown in [11]. These heaters are 20 millimeters long with a 6 millimeters diameter and are capable of producing a heat rate of 40 Watts per unit which allows for the potential of a compact array of these heaters connected in parallel to deliver sufficient heat for the enclosure. When using these heaters it is important to note the thermal limitations of the cartridges. Although a thorough internet search did not yield any readily available documentation for these heaters directly, an observation of an exhibit of where these heaters are used such as in [12], it is stated that the maximum temperature for the extruder is 260°C so this will be the metric to analyze the heater temperature against. Measuring the temperature of the heaters will be performed by an RTD temperature sensor which outputs an analog voltage signal that can be measured by a PC.
The previously mentioned cartridge heaters may be able to deliver a heat rate of 40 Watts each, however it is required to have them implemented in a manner to not overheat and destroy the heaters or at the very least, have them implemented in a safe way. To do this, the cartridge heaters were embedded into a metallic piece to draw heat away from the heaters themselves. The style of this design was inspired by how CPUs are cooled in computers. Typically CPUs are cooled using a heat exchanger or some form of a heat sink both of which are enhanced with force convection induced by a fan that is mounted directly or near the heat sink itself. With this in mind, the cartridge heaters and RTD were installed inbetween two metallic plates with grooves that match the diameter of these parts in order to provide the best interface for heat conduction. The assembled plates with heaters and RTD are to be referred to as the heater block. The material used for these plates was determined to be copper due to its high thermal conductivity and relatively low specific heat. The heat transfer performance was enhanced through the use of a heat sink and a PWM controlled 24 VDC brushless fan that directs air towards the heater. A detailed drawing is provided in Appendix B.3 which includes all of the parts used in the design. A cross section of the design is provided for in  The previously discussed heater sub-assembly was utilized in a modular fashion for the ease of manufacturability and scalability. To keep the heaters together and to provide a platform for eliminating excess wiring within the enclosure, the sub-assemblies were mounted onto a 3-D printed mounting bracket. Also included on the mounting bracket is a fixture for mating a prototype PCB for connecting the fans, cartridge heaters, sensors, and any other auxiliary electrical components.
For this enclosure, two heater blocks were to be used to provide up to 240 Watts of heat rate or more. A 3-D CAD model of the finished assembly is depicted in  Theoretical analysis was performed on the previously mentioned heater design.
The steady state analysis is done first to determine a maximum operating heater wattage that will not damage the system. This is a simple analysis for the heaters since it can be accurately modeled by a first-order system. The heater's equivalent thermal resistance is determined by the sum of the thermal resistances of the heat sink and the heater block. For this analysis, the heat transfer properties will be determined with the heater's fan set to a 25% duty cycle as this was to be used in the final system. At this duty cycle, the air velocity against the heat sink was determined to be 7.05 m/s which was determined by referring to the datasheet included in Appendix D.2 to find the volumetric flow rate for this duty cycle as well as using the cross sectional area of the fan's duct from the manufacturer's CAD file. Cross referencing this velocity to the heat sink's datasheet in Appendix D.1, it can be found via interpolation that the thermal resistance at this velocity is approximately 1.10 K/W. For the heater block, it is assumed that the majority of the heat transfer is through the heat sink. Assuming this, the thermal resistance through the block is calculated using Equation 2.14 with the thermal conductivity of copper being 400 W/mK as found in [13] and was calculated to be 0.00530 K/W.
Summing the heat sink thermal resistance and the heater block thermal resistance adds up to the total thermal resistance of the heater which is 1.10 K/W. The data for the specific heats of the mentioned materials were gathered from [14] where the specific heat of copper was 0.39 kJ/kgK and 0.91 kJ/kgK for aluminum.
With this information, the total theoretical capacitance was found to be 85 J/K.
A model for the heater was developed with the previously determined thermal resistance and capacitance of the heater. By treating the ambient temperature and heat dissipation rate through the heaters as inputs to this system, a first-order differential equation can be used to model the heater's behavior. An electrical analog for this system is visually represented in Figure 3.5 and its mathematical form is presented in Equation 3.1 below. Being a linear equation, it lends itself to be suitably simulated in Matlab with the lsim function, details of the simulation are shown in the Matlab function script located in Appendix C.1. The results of this simulation for a single heater, not the whole dual-heater assembly, with an actual input of 116 Watts and the heater exposed to ambient room temperature air are shown in Figure 3.6 with temperature change versus time. This heat rate input represents the use of three 40 Watt cartridge heaters in the heater block and the reason for why this does not lead to a heat rate input of 120 Watts is due to electric power dissipation through the IRL540 MOSFET used to control the heater. The transistor's drain-source on-state resistance is 0.077 Ω at 5 VDC and this value was used to determine power loss in the heater circuit due to a lack of information for the transistor at 24 VDC. The Matlab script was written to take the transistor's resistance into consideration and effectively models the dynamics with a heat input as a function of the equivalent electrical resistance of the heaters and is only meant for use in a 24 VDC system.

Thermal State Space Representation
As discussed in the former section, the best way to model the entire system's thermal performance is To identify the various parameters of the state-space equation, measurements of the transient and steady-state response of each separate component must be performed. By running an experiment or several experiments to collect data reflecting the state variables, the parameters of thermal resistances and capacitances can be identified. Specifically, by using the data for a certain temperature node as an input and isolating the system prior to the node, it is possible to tune the system parameters to yield the proper transient and steady-state response for each component. For example, since it is known what the thermal resistance and capacitance of the heater are and that there was an experiment to measure each of the temperature nodes, the adjacent resistance-capacitance element can be determined. Using the state-space equation associated with element 1 and 2 in Figure   3.7 and treating the enclosure air temperature as an input along with heat flow, the thermal parameters can be found. The thermal resistance is the first item to be determined since the steady state response needs to be determined prior to the transient response which is affected by thermal capacitance. Tuning the thermal resistance to get the model to match the measured data to a satisfactory error allows for the thermal resistance determination of each component. The same can be done for determining the thermal capacitance of the system or if the scenario allows for it, typical system dynamic formulations can be used for characterizing the transient response.
The first element of the thermal system has already been theoretically modeled earlier for this application due to its simplicity. Since there are two heater blocks in the constructed prototype, the thermodynamic parameters R 1 and C 1 can be determined for the dual heaters by treating the heater blocks to be in parallel with one another. In other words, the heat rate input to the system is shared by the two heater blocks symmetrically. The thermodynamic properties have already been determined in Section 3.3.1 earlier therefore, to determine the thermodynamic values needed for the previously state state-space equation, the previously determined heater thermal resistance was reduced by half and the heater capacitance doubles in value.
Another consideration for this modeling application is the heat rate loss due to the IRL540 transistor since this will result in an error in the calculation. To account for this, the model in Matlab was coded to take this into account. This was easily done by knowing that the heat rate input is a function of the number This formulation allows for an easy conversion of datasheet heat dissipation rate solely with the heaters to the actual heat dissipation rate in an application with a MOSFET transistor controlling the actuation of heat rate.
The experiments for the identification of the thermal state-space system utilize the previously discussed LM35 and platinum RTD sensors in Section 3.1.3. To enhance thermal conduction between the critical surfaces of the cartridge heaters and various temperature sensors, Arctic MX-4 thermal compound was utilized [15].
This allows for a proper mating of thermal components to maximize heat flow to associated components without having to worry about the surface conditions of the various sensor and heater mating surfaces and allows for more accurate temperature readings from the temperature sensors. Temperature readings from the enclosure walls, heaters, humidifier, and air were read every second for the duration of the experiments to records the temperature state-variables.

Humidity Control
This section is dedicated to going over the design and analysis of humidification.

Humidifier Design
The humidifier used in the prototype is a closed-loop design where air is drawn from the enclosure to be humidified and is returned to the enclosure. 3/4 in. innerdiameter tubes were used to transport the water vapour-air mixture between the humidifier and the enclosure. The entire humidifier assembly consists of a 3-D printed cover with ports and fixtures for fans, cabling, and the aforementioned tubing, a reservoir for distilled water, and an ultrasonic humidifying head. Tech-nical drawings of the humidifier cover are shown in Appendix B.4. The reservoir is a stainless steel food container that is roughly 4 and 13/16 inch diameter and includes a latch to secure the cover in place. A CAD rendering of the humidifier assembly is shown in Figure 3.8. The ultrasonic humidifying head used in the system is similar to the humidifier found in [16]. This particular humidifier is said to be able to atomize 400 milliliters of water per hour under normal operating conditions. Given that this is an unknown parameter for the application it is used in, the average amount of water atomized will be measured on a mass basis. The fan utilized is a 40 millimeter Mechatronics MD4028V24B-FSR-PC capable of delivering 24.3 CFM of air.
The fan was installed on the intake side of the humidifier to reduce the ingress of water to the electrically controlled fan. The humidifier head was loosely installed on the floor of the water reservoir with wiring passing through the cover of the humidifier. A cross section is available in Figure 3.9 to show the placement of the the ultrasonic humidifier.

Humidifier Characterization
The characterization of the humidification process was done through massflow analysis of the water vapour in the system. Utilizing conservation of mass principles allows for the determination of the mass of water vapour in the system over a given amount of time. In addition to mass-flow analysis of the system, the temperature dependent variable of saturation vapour pressure for water vapour in air was performed to calculate relative humidity with known vapour pressures.
Since relative humidity operates on a pressure driven basis of the water vapour partial pressure in the moist air mixture, transient and steady-state parameters were used to generate a first-order predictive model for relative humidity for a known dry-bulb temperature input. The model is shown in Equation 3.4 where P v is the water vapour partial pressure in the enclosure, P a is the ambient water vapour pressure of the ambient environment,ṁ is the mass flow rate of water vapour from the humidifier, R n is the pneumatic resistance between the enclosure and the ambient environment, and C n is the pneumatic capacitance of the enclosure, if the volume and pressure of the gas mixture remains unchanged, there must be mass flow directed outside of the control volume to have equalized gas pressure [17]. As with all applications of fluid flow, there is a resistance to flow due to drag associated with the fluid coming into contact with the enclosure surfaces. A transient term also exists since the enclosure acts as the sole storage element of water vapour. Due to the combination of the complexity of the system and the scarce amount of information on the transient modeling of relative humidity, both the pneumatic resistance and the pneumatic capacitance had to be empirically To fully characterize the humidification system, measurements of the partial pressures and the mass flow rate of water vapour were performed. Two Honeywell HIH-4021 relative humidity sensors and two LM35 temperature sensors were employed in this exercise to measure the relative humidity and dry bulb temperatures of the air in the enclosure as well as the air of the ambient environment simultaneously. Mass flow rate of water vapour was determined by measuring the mass loss of the humidifier's water reservoir over the duration of an experiment. The measurements from the temperature and relative humidity sensors allows for the calculation of the saturation vapour pressure and the instantaneous water vapour pressure for both points with Equations 2.23 and 2.26 under the valid assumption that the air pressure of the enclosure's interior is equal to the air pressure of the ambient environment. After an experiment was performed to generate data for the water vapour partial pressures of the enclosure and the ambient air, steadystate analysis followed by transient analysis of the observed response led to the determination of the values for pneumatic resistance and capacitance. Pneumatic resistance is equivalent to the quotient of the water vapour's partial pressure difference between the enclosure and the ambient environment, and the humidifier's water vapour mass flow rate. Pneumatic capacitance was calculated via the knowledge of the time it took for the water vapour partial pressure to reach steady state which is equivalent to five time constants. The quotient of the experimentally derived time constant and the earlier determined pneumatic resistance yielded the experimentally determined pneumatic capacitance [17].

System Performance
The following chapter covers the experiments and analysis performed on the preliminary prototype. Experiments were performed for system identification and model validation for the systems relating to thermal control and relative humidity.

Thermal Performance
As stated previously in Section 3.3.1, the accuracy of the heater models allows for the initial formation of the state-space equations. Utilizing the parameters found in the aforementioned section allows for the simulation of the thermal response of the heaters for a given heat rate input and ambient temperature. Testing the heaters was done with three cartridge heaters in each heater block, totaling 116 Watts of heat rate, while the enclosure's exterior was subjected to room temperature and using a fan PWM duty cycle of 25%. The temperature measurement of the heater blocks was done for approximately 13 minutes where the heaters reached steady state. The two temperatures associated with the two heater blocks of the heater assembly are plotted against the model in  For greater detail, two thermal models for the system were produced for conditions consisting of when the humidifier is not connected to the enclosure and one for when the humidifier is attached and the only the humidifier fan is on. In the tests with the humidifier attached, the humidifier element was not powered resulting in only dry air circulating through the humidifier and returning to the enclosure with its specific humidity unchanged. The reason for this is due to noticeable differences in thermal resistance and capacitance between the two conditions. Plots of the experimental results and the model's simulation for both cases are depicted in

Humidity Performance
As previously mentioned in Section 3.       Viewing the dynamics of the humidifying system under the constraint of change over time allows for typical system analysis as was performed. Since relative humidity is both a function of partial pressure or mass of water vapour and dry bulb temperature, observing relative humidity versus dry bulb temperature allows for a different perspective for the underlying mechanics. Figure 4.13 shows the relationship of relative humidity and temperature over the range of a typical temperature profile from the tests. The resulting swan shape in this depiction is due to a change in control inputs. The first portion of the plot where relative humidity is decreasing while dry bulb temperature is increasing resulted from purely heating the air in the enclosure. As expected, the relative humidity decreases with temperature if the water vapour content of the air remains constant due to the saturation pressure increasing with the increase in temperature. The other portion where humidity is increasing and temperature is decreasing is the result of the same heat rate input as well as having the humidifier turned on for the remaining duration of the plot. Temperature decreases with the increase in humidity due to the inclusion of cold water vapour and reaches a steady state condition once the relative humidity reaches steady state. The increase in humidity at the first portion of the plot is caused by an unknown factor inherent in the prototype.
Probable causes are the fact that more humid air is less dense than dry air causing the moist air to settle at the top of the enclosure and forced passed the humidity sensor when the heater's fans are turned on, or cooler air being forced passed the sensors which has higher relative humidity due to having a smaller water vapour saturation partial pressure [1].  Table 4.4 below whereṁ refers to the mass flow of water vapour caused by the humidifier, φ a is the relative humidity of the ambient environment, T a is the temperature of the ambient air, φ o is the initial condition for relative humidity inside the enclosure, T is the resulting temperature profile of the enclosure's air for a given heat rate input, and t delay is the programmed time for humidification to begin. All of the table entries containing "From data" are an array of values that was measured from real world testing in an effort to isolate any issues of the humidity model to only be caused by humidity factors. This includes barring any temperature modeling that is also dependent on the humidification of the system. The temperature profiles chosen are respective of their defined constant heat rate step inputs over the duration of the model and test. Initial conditions for relative humidity inside the enclosure were chosen on a basis to reflect that of the data collected from tests. Specifically, the relative humidity initial condition was chosen at the peak of the first leg of the plot in an effort to ignore the anomaly causing the initial jump in relative humidity.  Figure  4.14. Comparing the data and the models' results found in Figure 4.14 shows how the model parallels actual data. If the hump at the first leg of the measured results are ignored, then it can be seen that both the model and the real world values have a similar relationship to one another in terms of being proportionate to one another.
The first leg consists of an exponential decay of relative humidity as temperature increases which both the model and the measured values agree with. They also agree with the relative humidity and temperature converging to a similar contour regardless of the initial conditions or heat rate input to the system. Agreement also exists for the second leg of the plot where humidification is occurring resulting in a polynomial pattern for all cases. The model also converges to the same final value after the three hour simulation. Another experiment was in order to sort out the issue of the beginning hump.
In an effort to notice how the model behaves without the hump, the enclosure  It is important to note that while utilizing this model for design, the user must be aware that once the relative humidity reaches 100%, the water vapour partial pressure will no longer increase assuming the dry bulb temperature does not change. Any additional water vapour added to the control volume will result in condensation which this model does not cover. Therefore, the model for Figure   4.15 was performed in a step-wise fashion due to the model being outside of its scope during condensing conditions. The initial step from point A to point B in Figure 4. However, there are cases where this lumped capacitance method excels at in thermal systems. Predictive models prior to experimentation are possible for thermal systems where the heat transfer mechanic is through thermal conduction.
As shown in Section 4.1.1, the predictive model for the heaters was nearly an exact fit to the real world performance. It is likely that the same method can be applied to hermetically sealed humidification systems only to study the humidity model by itself. Therefore, for systems that are isolated from the ambient environment or where the parameters that are easily calculated from textbook values, the lumped systems method is a good tool.

Future Work
Future work consists of further efforts in modeling and applying said models.
The goal of all of this modeling is not only to study the methods of how it is accomplished, but for application in actual devices. This future work should be done in parallel with one another to achieve the best result.
To further work on the relative humidity model, a new rig needs to be designed and built. It is suspected that leakage paths from the system may negatively affect the predictive model. To rectify this, it is proposed to construct a new enclosure design that is hermetically sealed and allows for the interior to be subjected to positive air pressures. This removes any possibility for mass flow, and any energy flow associated with said flow, into the surrounding environment. A known and isolated control volume would be the best path forward for more analysis into the humidity model where more literature on the subject is needed.
In addition, work needs to be performed on generating a humidity model which includes the mechanic of condensation. Condensation was noticeable during the previous experiments which may have had a considerable effect on the performance of the humidification system. Not only is this an important factor to know for control design, knowing the condensation mechanic allows for knowledge of how to control this potentially damaging effect of humidification. Water collection in an enclosed space if not drained can cause damage to electrical components or the enclosure itself if improper materials are used.