Robust H_? Control Of Uncertain Double Inverted Pendulum System With Time Delay Based On LMI

Time delay and uncertainties are important factors that have to be considered in the design of control systems.In the design of controller,it is necessary to ensure a certain robustness to resist the external uncertain disturbance;in the study of time-delay system,on the basis of ensuring the internal stability of the system,the design of controller should make the system as less conservative as possible.The main content of this paper is to study the stability and H_?robust controller of uncertain systems with time-delay according to the classical theory and methods of dealing with time-delay systems,and to design the H_?robust controller based on LMI algorithm combined with the double inverted pendulum model,and further verify its rationality.In this paper,robust stability analysis is carried out based on the double inverted pendulum system with time-delay uncertainty.Firstly,the mathematical model of the inverted pendulum system is established by Lagrange equation method,and linearized at the equilibrium state to obtain the state space description with uncertain disturbance.On this basis,the controller is designed according to the time-delay stability treatment method studied.In the process of the research on the treatment of uncertain systems with time delay,the classical free weight matrix method is improved to deal with the quadratic integral term.By discussing the stability of nominal systems with time delay,the stability condition of nominal systems with time delay in LMI form is proposed.Based on the time-varying delay dependent functional,the time-varying delay dependent uncertain systems can be dealt with The influence of the construction of Lyapunov Krasovskii functional and the selection of the bound inequality on the conservative type of the conclusion is discussed in detail.Then,a suitable functional is constructed and the H_?controller design problem is studied according to the bounded real with time delay.The rationality of the conclusion is verified by numerical calculation and singular value analysis.Then,based on the inverted pendulum model,the simulation design is carried out from two aspects of input delay and state delay to verify the rationality of the H_?robust controller based on LMI algorithm.In this paper,the H_?controller based on the stability theory and LMI algorithm is compared with the controller based on LQR algorithm.When the time delay is uncertain,the H_?controller based on LMI algorithm has better stability effect,shorter time to achieve stability and larger range of time delay.In addition,when the BRL condition is extended to the controller design,several solutions to the nonlinear term are discussed,and the principle and process of the iterative algorithm used in this paper are described in detail.