An LMI Approach to Robust Controller Design for AVR System

This paper develops stability and performance preserving H
₂
and H
_infin
controller reduction methods to a PID controller for linear continuous time-invariant single-input, single-output systems. Several cost functions such as the two and infinity norms of the error between complementary sensitivity functions, input sensitivity functions and loop gain functions of nominal closed-loop system and the system using reduced-order controller are considered for the optimization problem. The error between these transfer functions are converted to a frequency weighted error between the Youla parameters of the full-order and reduced-order controllers. Then, the H
₂
and H
_infin
norm of this error, subject to a set of linear matrix inequality constraints, is minimized. The main ideas of order reduction to a PID controller and stability preservation are contained in the constraints of the optimization problem. However, since this minimization problem is nonconvex, the Youla parameter of the reduced-order controller is obtained by solving a suboptimal linear matrix inequality problem that is convex and readily solved using existing semi-definite programming solvers. The method is tested for an uncertain model of an AVR system. A robust controller is designed for the AVR system and it is reduced to a low-order controller using the proposed controller order reduction methods.