An LMI Approach to Robust Controller Design for AVR System

• Published in: 2008 40th Southeastern Symposium on System Theory (SSST) pp. 17 - 24
• Main Authors: Aghaie, Z., Amirifar, R.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.03.2008
• Subjects: Control systems; Cost function; Error correction; Frequency conversion; H infinity control; Linear matrix inequalities; Robust control; Stability; Three-term control; Transfer functions
• ISBN: 9781424418060; 1424418062
• ISSN: 0094-2898
• DOI: 10.1109/SSST.2008.4480182

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.