Reaserch On State-frequency Method Of Satisfactory Control

The state-frequency method of satisfactory control put forward in this thesis is a new tool for control system design. The key to this method consists in the following aspects: based on the state-space representation of linear systems, the idea of the satisfactory control and the toolbox of linear matrix inequality(LMI) of MATLAB Software are employed to find a controller that ensure some given frequency response characteristics(maximum singular value, bandwidth, area, zero frequency characteristic ) simulataneously.This dissertation deals mainly with the multi-objective controller design problem .The desired specifications include: steady state covariance, steady output covariance, H_∞ performance, opportunity-awaiting indices, steady-state error coefficients, controller gain constraints, and other frequency domain characteristics.Throughout this thesis, the following methods are adopted to solve the above problem: a matrix decomposition based on generalized inverse method, linear matrux inequality (LMI) method, iterative linear matrix inequality method for solving the bilinear matrix inequality (BMI), and the nonlinear optimization method.The contributions of this dissertation lie in the following aspects: extending existing satisfactory control by including new frequency domain specifications, taking into consideration of controller fragility introducing some new solving technics. So the research of this dissertation further promotes the practical applications of satisfactory control. The main contents of this dissertation are as follows:(1)Some detailed account of the characteristics of closed-loop amplitude-frequency is given. Also, the mathematical description and physical significance are presented. (2)A controller design method to achieve closed-loop amplitude-frequency characteristics and additional specifications is proposed(3)The consistent analysis of desired specifications under PID control (4)A satisfactory decoupling control is given(5)The design of satisfactory non-fragile controller for linear stochastic systems with admissible perturbations in model and controller, and the consistency analysis for the desired specifications are presented.