Perfect and subperfect regulation in linear multivariable control systems

Abstract

This paper is concerned with the synthesis of a high-gain feedback control, called perfect regulation (p.r.), for linear multivariable systems with external signals. The existence condition for p.r. is derived, in which the minimum phase property plays an essential role. The use of an observer is discussed for achieving p.r. under restricted state observation. Some asymptotically ideal feedback properties are demonstrated, such as the complete desensitization, the complete servo performance with decoupling and the complete disturbance rejection, which formulate the loop-tightness for multivariable systems. A design method for applying p.r. to non-minimum phase systems, called subperfect regulation (s.p.r.), is proposed based on the factorization of the plant transfer function matrix into the minimum phase part and the totally non-minimum phase part. It is a multivariable extension of a well-known design technique for scalar systems to overcome the difficulty of phase non-minimality. Computational procedures for p.r. and s.p.r. are discussed. An illustrative example is shown.