Controller Design Of A Class Of Hybrid Systems

With the more increasing complicated and monumental industry control systems, the more increasing control precision and the coupling relationship between continuous variable system(CVS) and discrete event dynamic system(DEDS) in engineering practice increasingly is prominent, the coupling relationship between the continuous and the discrete processes, and the dynamics characteristic they show increasingly is valued, the study of hybrid system(HS) theory has aroused the Chinese and foreign control community's widespread interest. Hybrid systems are composed of discrete event dynamic subsystems and continuous time dynamic subsystems, which interact on each other. Due to the different requirements of different subjects for systematic study, there are many different models for hybrid system, such as hierarchical structure model, mixed logical dynamics model(MLD), piecewise affine system model(PWA), hybrid automaton model(HA), linear complementarity model (LC), abstract time and space model and so on.PWA's extended state space are divided into polyhedron areas. The state space expression is defined in each area. Piecewise affine system can approximate a large class of nonlinear systems, and can be equivalent transformation with many types of hybrid systems under certain conditions. Because the arbitrary approximation characteristics, piecewise affine system's arbitrary subsystem in its corresponding division are linear or affine, we can use a known linear system theory to explore the characteristics of nonlinear system. So this thesis focuses on the stability and control of the hybrid system based on piecewise affine system model, and some conclusions are drawn.This thesis introduces a class of discrete PWA systems whose subsystems contain nonlinear disturbance and parameter perturbation, and designed a state feedback controller for given model. The simulation results show the effectiveness of the algorithm by LMI toolbox. Then, further research was carried out on the given system, the effective output feedback controller is designed to ensure the closed-loop system is stable under the condition of certain interference. Solving the convex optimization problem could find the method of designing the robust controller. The conclusion makes sense to solve problems for piecewise affine system. Finally, the effective passive state feedback controller was designed for a class of discrete-time PWA systems with parameter perturbation and the robust controller ensured that the system is strictly passive. The simulation example is given to illustrate the feasibility of this method.