Control for LPV Systems with Nested Saturation and Its Applications to Flight Control Systems
|Course||Navigation,Guidance and Control|
|Keywords||Actuator nested saturation Linear parameter-varying systems (LPV) Domain of Attraction Linear matrix inequalities (LMI) Parameter Dependent Lyapunov Function Quad Rotor control|
Saturation is the most commonly encountered nonlinearities in control systems. Input saturation constraints exist in various physical systems, such as chemical plants, mechanical systems, and even communication networks. More often than not, the occurrence of actuator saturation can greatly deteriorate the performance of the systems, and even drive the systems to be unstable. On the other hand, the requirement of the systems’ performance is higher and higher in the fields of Astronautics and Aeronautics now, which need to solve the saturation problem as soon as possible. Therefore, due to the important theoretical and practical significance, the research on the system subject to actuator saturation has attracted tremendous attention in the control theory field. Linear parameter-varying systems are typical time-varying control systems of very importance, and it is characterized as a linear system that depends on time-varying smooth parameters that are unknown but measurable. The measurement of these parameters provides real-time information on the variation of the plant’s characteristics.Based on Lyapunov stability theory and linear matrix inequality technique, the estimation of domain of attraction and controller designing for linear parameter-varying system with nested saturation are studied in this thesis. At the same time, the problem of robust control is considered. The main contents of this paper are outlined as following:(1) Under the given feedback gains, based on descriptor system approach and parameter dependent Lyapunov function approach, the domain of attraction for the linear parameter-varying system with nested saturation is estimated and the local asymptotical stability conditions are given. Then the problem can be solved by an optimization problem with some linear matrix inequalities (LMI) constrains, which can maximize the estimation of the domain of attraction of the LPV systems. A gain-scheduling controller has been designed. At last, a Four-rotor helicopter control example is given to illustrate the effectiveness of the proposed method.(2) The domain of LPV system with nested saturation and disturbance is estimated by parameter dependent Lyapunov function approach. The problem is formulated and solved by a LMI optimization problem, which can maximize the estimation of the domain of attraction of the LPV system. The feedback matrixes design is solved as an iterative optimization problem with LMI constraints. At last a helicopter system control example is given to illustrate the effectiveness of the proposed method.The conclusion and perspectives are given in the end of the thesis.