Research And Application Of Tracking Control Methods Based On Discrete Polynomial Fuzzy Models

Stability analysis and controller design of nonlinear systems have always been the research focus in the control field at home and abroad.Due to the advantages of sum of squares(Sum of Squares,SOS)based on convex optimization theory and numerical solution,there are many achievements in the study of polynomial nonlinear systems.Takagi-Sugeno(T-S)fuzzy models,which can approximate the real complex nonlinear systems with arbitrary precision by fuzzy membership functions,plays an important role in the research of nonlinear system.As a generalization of T-S fuzzy models,polynomial fuzzy models combine the advantages of T-S fuzzy models and polynomials.It has fewer fuzzy rules than T-S fuzzy models,but it can represent nonlinear systems more effectively.At the same time,most of the research problems related to polynomial fuzzy models can be easily solved by SOS tools.It is the emergence of polynomial fuzzy models that pushes the research of fuzzy logic system analysis and controller design to a new stage.With the diversity and complexity of real dynamic system,the analysis and design based on polynomial fuzzy systems will face new challenges.In this dissertation,the inherent SOS design framework is broken out,and the tracking control problem of discrete nonlinear systems is studied based on the feedback nonlinearization,a classical nonlinear control method,and the novel reinforcement learning method.The corresponding polynomial fuzzy controllers are designed to achieve different tracking control objectives.The research in this dissertation will cover the following aspects:To solve the complete tracking problem of a class of discrete polynomial fuzzy systems,a design method of feedback linearization control law is proposed,which makes the output of the closed-loop system achieve the perfect tracking of the given reference signal.The design method is analytical.The local stability of the system at the origin is analyzed,which can be used as a qualitative method to test the quality of the discrete polynomial fuzzy model.More importantly,for a given discrete polynomial fuzzy system,a sufficient decision condition is established to analyze the feasibility of designing a perfect tracking controller based on feedback linearization.Besides,in order to analyze the boundedness of controller output,a sufficient and necessary condition is established.To solve the asymptotical tracking problem of a class of discrete polynomial fuzzy systems,a design method of partial feedback linearization control law is proposed,which enables the closed-loop system to asymptotically track the step reference signal and effectively overcome the constant disturbance problem.What's more,to establish a more relaxed condition to analyze the feasibility of tracking controller design for a given discrete polynomial fuzzy system based on feedback linearization,a nonconvex matrix inequality problem is transformed into a convex linear matrix inequality problem by using the full block S-procedure method.The proposed method has a wider application space.To make the parameter adjustment of the designed polynomial fuzzy controller intelligent and the system have the optimal performance index,the optimal tracking control problem of a class of discrete nonlinear systems is solved in this dissertation,based on the relationship between the optimal control and the optimal tracking control problem,as well as the policy iteration algorithm of reinforcement learning.The policy iteration algorithm is firstly combined with the polynomial fuzzy models to establish an actor-critic structure based on the polynomial fuzzy models,which can adjust the parameters of the controller and achieve the performance index of minimizing the value function.In this dissertation,theoretical analysis and experimental verification are carried out based on the two degrees of freedom(2-DOF)rotor flight simulator system independently developed by the laboratory.The simulator provides a good experimental platform for the research of control problems.Theoretical analysis stage: Based on its physical structure and motion mechanism,the complex vector combined with the Lagrange equation method is used to establish its dynamic model.In addition,the modeling method of polynomial fuzzy model based on Talor series is used to obtain its polynomial fuzzy model,which is verified and compared with the traditional T-S fuzzy model.Experimental verification stage: The parameters of the actual system model are obtained by fitting the measured input and output data of the system.On this basis,the polynomial fuzzy tracking control law is designed based on the optimal tracking control method proposed in Chapter 4.The tracking ability to different desired trajectories of the pitch angle of the 2-DOF rotor flight simulator under the action of the controller is verified through the experiments.The disturbance experiments indicate that the controller has certain anti-disturbance ability and robustness.The experimental results show that the designed polynomial fuzzy controller is correct and effective.