1983 Volume 19 Issue 7 Pages 526-530
Exact model matching is considered to be the most reasonable design method for the control systems. As the means of exact model matching, two approaches have been developed; one is the time domain method and the other is the frequency domain method. The latter is more general than the former in that it can be applied to multivariable systems. Furthermore, the required calculations are far simpler for the frequency domain method. It has been recognized that the resultant control system consists of input dynamics and linear state variable feedback part in general. In the first half part of this paper, it is pointed out that the resultant control system for the scalar plant can always be transformed into the complete feedback control system.
It is well known that two conditions are necessary and sufficient to the achievement of exact model matching; (1) the plant is of minimum phase, and (2) the relative degree of the desired transfer function is not less than that of the plant. It is the fact that there are many nonminimum phase plants. Furthermore, the plant of minimum phase in continuous time turns to the nonminimum phase plants in discrete time often. The adaptive control of nonminimum phase plant is the recent important subject, and it should be noted that the basic concept for the adaptive control links firmly to the exact model matching theory.
The method to achieve exact model matching for the nonminimum phase plant is presented in the second half of this paper. The basic idea relies on the fact that any transfer function can be represented as the difference of two minimum phase transfer functions. The problem can be reduced to the ordinary exact model matching one by setting up a compensator in parallel with the plant to be controlled. The design method is illustrated by an example.
