Fixed Order L <sub> 1 </ Sub> Controller Optimization Design,

Robust control theory is an important subject in feedback control theory. L₁-control theory has attracted much attention as the complement of H∞_-control theory, but the research on L₁ -control is not mature. On the other hand, research on singular system has pratical significance because it has more extensive form than normal system.This dissertation makes research on optimizing design of fixed-order L₁-controller, and extends the problem to singular system. The main contents are outlined as follows:(1) A method is derived to approximate the L₁-norm of given transfer function for continuous-time linear time-invariant systems. Using Matlab Control Engineering Toolbox and the strong calculating ability of PC;this method can approximate the L₁-norm conveniently and rapidly.(2) The optimization problem is formulated to design fixed-order L₁ -controller. The method of approach and Simulated Annealing Algorithm are utilized to solve the problem. Comparing with other methods indicates this method can design optimal L₁-controller which is low-order, rational and fit for multi-block problem.(3) A new method to design fixed-order L₁-controller is presented using Youla parametrization approach and Genetic Algorithm. Numerical example shows the method is simple and the optimal solution is good.(4) The optimization method of fixed-order L₁-controller is extended to singular system. Similarities and differences of fixed-order L₁-controller design are investigated for the two kinds of system. Numerical example shows the validity of the method.The last part is summary and perspective.