Research On Robust Control And Fault Detection For A Class Of Discrete-time Conic-type Nonlinear Systems

In this thesis,the issues of robust control and fault detection for a class of discrete-time systems with conic-type nonlinearities are deeply studied.Since Zames proposed conic-type nonlinearity in 1966,many researchers have taken great interest in it.In recent years,the results on conic-type nonlinear systems have also emerged.As a special class of nonlinear factor,the conic-type nonlinearity lies in one hyper-sphere,the center of which is a linear system,and the radius is another norm constrained by a linear system.In fact,the conic-type nonlinear systems are embodied in many nonlinear dynamics,such as the nonlinearities of dead zone and saturation,the nonlinearities of hardening spring and softening spring,the sinusoidal nonlinearities in a single pendulum system and inverted pendulum system,etc.With the promotion of science and technology,the transformation of China's industry tends to be knowledge-intensive.The traditional continuous-time control has faced severe challenges,the main reasons are caused by two aspects:On the one hand,compared with the traditional industry,the modern industrial producers put forward higher requirements for the control standard of the digital system.On the other hand,there are many characteristics of complex nonlinearities,multivariable and strong coupling in modern industrial control.In the modern control systems,the calculation of the computer based on discrete sampling system is widely used.However,the limitation of the sampling process makes the implementation of the discrete algorithm can not be deduced by a continuous system.With the rapid development of the computer control theory,most control problems of complex systems can be solved by discrete-time nonlinear systems.Therefore,when we design the system controller,a discrete-time model of the system is necessary,then study the performance of the system by the difference equation approach,and finally get the control algorithm of the discrete system.On the basis of the above discussion,a class of discrete-time conic-type nonlinear systems models is presented in this thesis.The parameters satisfying the system performance index can be easily obtained according to the developed Lyapunov function and LMI method.The concrete research ideas and conclusions are as follows:(1)The robust H_?controller design problem for a class of discrete-time conic-type nonlinear systems with uncertainties and time delays is studied.Firstly,utilizing conic-type definition constraints and mathematical transformation,the conic-type nonlinearity is transformed into a linear form with a nonlinear term.Secondly,the idea of feedback is applied to design a robust H_?controller such that the closed-loop augmented system asymptotically stable and satisfies a certain performance index of the H_?disturbance suppression.Thirdly,an appropriate Lyapunov function is selected,and the Lyapunov stability criterion and LMI technology are applied.Sufficient conditions for the systems'stabilization are obtained.Finally,a simulation example is given to demonstrate the feasibility of the robust control method.(2)The observer-based finite time l₂-l_?control for a class of discrete-time Markov jump systems with conic-type nonlinearities is studied.The general state-space model is obtained by linearizing the conic-type nonlinearity.Based on the finite-time bounded theory and l₂-l_?control approach,an observer-based robust controller is designed in the form of feedback such that the augmented system finite-time bounded and satisfies the specific l₂-l_?performance index.The effectiveness of the developed method is illustrated by two simulation examples.(3)The designed filter of fault detection for a class of discrete-time Markov jump system with conic-type nonlinearities is discussed.The approach in this chapter is to summarize the robust fault detection problem as the H_?filtering problem.Combing the Lyapunov function and LMI technique,sufficient conditions exist for a feasible solution of the fault detection filter are proved.The designed filter guarantee augmented Markov jump systems with H_?disturbance rejection performance index are stochastically stable.Finally,a circuit model simulation is employed to verify the feasibility of the proposed method.Finally,a general summary of the designed control scheme and fault detection problems in this thesis is given,the improvement approach of follow-up work and the future research direction are also pointed out.