Research And Application Of Robust Gain-Scheduling Based On LPV System

Gain-Scheduling (GS) is one of the most famous methods in the engineering and is applied in many fields, especially for flight control systems. Due to lack of stability theory prove within operation range and burdensome process, the traditional GS is not compatible for modern system gradually, Linear Parameter-Varying (LPV) system is an important time-varying system, GS based on LPV system can overcome the shortcomings of the traditional GS, because it can describe nonlinear and time-varying characteristics of a class of dynamic systems.The robust GS theory based on LPV system is investigated, and the conservatism of current methods is analyzed and studied, some new methods which have smaller conservatism are obtained. And partial results are applied to the flight control system of a class of tailless aircraft. The main research contents and contributions are listed as follows:(1) Model problems of robust GS, LPV system modeling, are studied. The transformation methods of nonlinear system to LPV system are introduced, and aim at the conservatism of these methods, an improved method is proposed. The performance of models got by different methods is evaluated using reachable set and the results testify the proposed method has smaller conservatism. At the same time, method of polytope representation of the general LPV system based on high-dimensional singular value decomposition is studied, and the implementation steps are given.(2) Robust GS based on quadratic Lyapunov functions is studied and a new GS strategy is proposed because of the conservatism of the current GS strategy which based on parameter geometry distance. Aim at polytope, the new strategy based on Gap-Metric does convex decomposition through generalized distance between the system and its vertex systems. The simulation result testifies the new one has smaller conservatism.(3) In order to reduce the conservatism of the quadratic Lyapunov function method, the parameter dependent Lyapunov function method is studied from two aspects. Firstly, aim at the polytope, a multi-slack variables parameter dependent Lyapunov function method is proposed, this new method can decouple the Lyapunov function and system matrix and the conservatism is reduced. Secondly, aim at the affine parameter dependent LPV system, an affine parameter dependent Lyapunov function method is proposed. The variations of the variable parameter are considered and the conservatism is reduced.(4) The robust GS based on linear fractional transformation (LFT) is studied and the basic idea of this method is introduced. The LFT representation of polynomial LPV and the dimensionality reduction methods and steps are given. A less conservative analysis and synthesis method based on S-procedure is proposed. The bilinear matrix inequality is used in this method because less constraint on full block scaling matrix and the iterative LMI algorithm to the BMI is given.(5) The multi-objective robust GS based on LPV system is studied, the extended LMI and parameter dependent Lyapunov function, which can reduce the conservatism of the multi-channel single Lyapunov function method, are applied into LPV system multi-objective control using multi-channel principle. A class of BMI problem is studied, a new simple and effective iterative LMI algorithm is proposed which can further reduce the conservatism.(6) The results obtained in the dissertation are applied to flight control system of a class of tailless aircraft. The LPV model of the aircraft is developed, the robust GS controllers of longitudinal and lateral are designed using Lyapunov function method and LFT method respectively, and in accordance with system uncertainty the robustness of the controller is verified. The simulation results prove the feasibility and efficiency of the methods.In a word, the dissertation is focus on the robust GS control based on LPV system, and some new results are obtaied, and then the results are applied to flight control system. The meaningful attempt of robust GS to the high-performance aircraft is done.