A Control System Design Method Using Real Order Phase Lead-Lag Compensator

Abstract

The new type of the design method proposed in this paper is similar to the one using phase lead-lag compensator and has two particular characteristics. First, the approximate system described real order lag element with a dead time element is specially adopted to identify the controlled object. The principle of the identification derived from the frequency characteristics is presented. Secondly, the compensator is composed by an integral element and phase lead-lag elements having multiple zeros and multiple poles. The order of phase lead-lag elements is, in general, an integer but in this design it will be treated as a real number. In order to use practically the compensator, the impulse response function of the compensator is obtained in the form of a series expansion of a gamma function and it can be performed by the convolution method between the impulse response function of the compensator and a deviation error signal.The compensator parameters are determined by a rule of trial and error in order to obtain a quick response using manipulating variable under the maximum value assigned in advance. Since the order of the compensator can be adjusted finely through numerical treatment as to a real, the quick response by a relatively small manipulating variable has been performed. Then, the selection of the sampling time in the case of practical digital control is considered in detail. The effectiveness of this control design method is shown by examples.

A Design Method for the Real Order Phase Lead-Lag Compensator with a Reference Model

“…(1) (5) (6) (7) (13) Ke −Ls (1 + T s) ν · · · · · · · · · · · · · · · · ·(1) K T L ν (14) case 2 : G p (s) = K · N (s) M (s) · · · · · · · · · · · · · · · · · ·(2) M (s) s N (s) G c (s) (14) G c (s) = K c (1 + T d s) µ s 1 + T d n s ρ · · · · · · · · · · · · · · · · · · · · · ·(3)…”