LMI-Based Robust Control Of Uncertain Hamilton System And Application

In real working conditions,there are uncertainties in any system.These uncertainties often cause deterioration of the system performance,or even lead to instability.The generalized Hamilton system is a kind of more generalized open system which integrates energy generation,dissipation and external energy exchange.Because the Hamilton system method shows strong robustness for improving system parameter perturbation and external disturbance,it is shown in stability research,robust control design and so on.Strong superiority is essentially a nonlinear control strategy.The Hamilton function(the generalized energy:kinetic energy + potential energy)effectively avoids the difficult process of constructing the Lyapunov function directly,and the stability of the closed loop system is effectively ensured in the theoretical sense.In addition,most of the research results based on the Hamilton method are concentrated on state feedback,but the state variables of uncertain systems are usually not easily measured.In order to obtain system state information,the research and design of the observer have important practical significance and application value.In this paper,the robust control and application of uncertain Hamilton systems are studied.The main contents are as follows:(1)For uncertain Hamilton system,using LMI processing technology to study the problem of guaranteed performance control(guaranteed cost control),the existence condition and design method of the guaranteed performance controller for the uncertain Hamilton system are given to satisfy the closed-loop stability of the system,and there is a performance index upper bound for all permissible uncertainties.The feasibility of the method is verified by numerical simulation.(2)For the uncertainty and state uncertainty of a class of Hamilton systems,based on the LMI processing method,using the cross control idea,the H? control method is combined with the adaptive control method,and the observer is introduced through the method of state reconstruction.On the one hand,the existence condition and design method of H? adaptive controller for uncertain Hamilton systems are given,it can not only overcome the shortcomings of the classical control theory,but also realize the real-time adjustment of the control method through system identification and maximize the control efficiency.On the other hand,the H? adaptive controller based on the observer is proposed to obtain the state quantity of the system while guaranteeing the robust stability of the controlled system,and provide the state feedback.The precondition.The effectiveness of the proposed method is verified by comparing the simulation results.(3)For the permanent magnet synchronous motor speed control system in the form of Hamilton system,based on the LMI processing technology and the Lyapunov stability theory,some methods and conclusions proposed in this paper are applied to the speed tracking control of permanent magnet synchronous motor,an observer based of H? adaptive controller for PMSM speed regulation system in Hamilton form is given.The feasibility and effectiveness of the proposed method are verified by background simulation,and it is further realized in the speed control experiment of permanent magnet synchronous motor experimental platform.