MODELING, DIAGNOSIS AND CONTROL OF COMPLEX NONLINEAR UNCERTAIN DYNAMICAL SYSTEMS: FROM ALGORITHM DESIGN TO PHYSICAL EXPERIMENT
Date of Award
Doctor of Philosophy in Mechanical Engineering and Applied Mechanics
Mechanical, Industrial and Systems Engineering
Complex systems with uncertain and nonlinear dynamics are a large class of very important systems in modern engineering. Typical examples include automatic robots, aeroengines, chemical processes, manufacturing systems, and power networks. In this dissertation, we focus on the problems of dynamics modeling, tracking control, and fault diagnosis of complex nonlinear uncertain dynamical systems (NUDSs), in terms of both algorithm design and physical experiment. The studied NUDSs include: (i) discrete-time lumped parameter systems that are modeled by discrete difference equations; (ii) continuous-time distributed parameter systems modeled by partial differential equations; and (ii) soft robots with a highly nonlinear and uncertain dynamical model.
We first study the modeling, diagnosis and control problems of discrete-time lumped parameter systems (DTLPSs). Specifically,
- the dynamics modeling/identification problem of DTLPSs is solved based on the Deterministic Learning (DL) technique - a typical tool for nonlinear system identification and dynamical pattern recognition. An adaptive radial basis function neural network (RBF NN) based scheme is proposed to achieve locally-accurate identification of the uncertain nonlinear dynamics of DTLPS;
- the precise tracking control problem of DTLPSs is then investigated by using the above-proposed dynamics modeling/identification approach. An adaptive RBF NN learning-based tracking control scheme is developed, which can not only achieve stable and accurate tracking control for the system’s states/outputs, but also realize accurate identification of the system’s nonlinear uncertain dynamics through the online control process;
- the accurate fault diagnosis problem of DTLPSs is also investigated based on the proposed dynamics modeling/identification approach. An adaptive RBF NN dynamics modeling-based fault detection scheme is developed, which can effectively handle the effect of system uncertainty on fault detection process, such that the occurring faults can be accurately captured and detected. This scheme can be used to guarantee desired reliability and safety of the system’s real-time operation.
By extending the above research works, we further investigate the modeling, diagnosis, and control problems of continuous-time distributed parameter systems (CTDPSs). Different from lumped parameter system, distributed parameter system involves an infinite number of state variables and has spatiotemporal nature, which is usually modeled by partial differential equations, thus its modeling and control problems are more complicated and challenging. In view of this, a novel adaptive dynamics learning-based framework for CTDPSs is proposed by using the combination of the Galerkin method and the DL technique. Particularly, the Galerkin method is employed for model order reduction purpose, i.e., to derive a low-order model to capture the system’s dominant dynamics, so as to deal with the infinite-dimensional and spatiotemporal nature of the CTDPS’s dynamics. The DL technique is to deal with the nonlinear and uncertain nature of the system’s dynamics, which can achieve accurate identification/modeling of system’s uncertain dynamics and obtain the associated knowledge for reutilization. Using these techniques, the dynamics modeling/learning, fault diagnosis, and tracking control problems of CTDPSs can be solved by extending the existing results of lumped parameter systems. Lyapunov stability theory and singular perturbation theory are used to analytically guarantee system stability, control accuracy, and operation reliability when extending the existing approaches to CTDPSs.
Finally, we perform physical experiments on a real soft trunk robot to validate the above-designed algorithms. Soft robots have deformable structures, complex geometry and excessive degrees of freedom, which is a typical example of distributed parameter systems with highly nonlinear and uncertain dynamics. Specifically, model order reduction process of the soft robot’s dynamics is first performed by using the finite element method and proper orthogonal decomposition technique, to derive a low-order model to capture the soft robot’s dominant dynamics. A novel adaptive RBF NN learning-based framework is then developed for the soft robot’s dynamics modeling, fault diagnosis, and tracking control problems, by extending the existing results of CTDPSs. Through both theoretical analysis and physical experiments, it is demonstrated that the proposed approaches are generic and usable for general soft robots, guaranteeing desired applicability and practicality.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Zhang, Jingting, "MODELING, DIAGNOSIS AND CONTROL OF COMPLEX NONLINEAR UNCERTAIN DYNAMICAL SYSTEMS: FROM ALGORITHM DESIGN TO PHYSICAL EXPERIMENT" (2023). Open Access Dissertations. Paper 1541.
Available for download on Friday, April 17, 2026