Abstract
Designing method of linear control systems by means of the theory of optimal regulator problem with a quadratic performance index has many advantages compared with conventional design methods. For example, under reasonable restrictions this method always assures a stable control system by straightforward computations.
However, if some characteristics (overshoot, settling time, etc.) of the system to be constructed are previously required, there are no general rules to reflect these requirements on the parameters of the quadratic performance index.
One shortcoming of the regulator problem is that signals from outside are only considered as impulsive disturbances added to each integrator, since reference or command is not assumed to exist in the regulator problem. This is not convenient to desigh servosystem.
This paper discusses an extended regulator problem effectively applicable to the case where design requirements are given and a stepwise reference exists in addition to the impulsive disturbances. In this problem there are introduced a model fulfilling the required characteristics and a modified quadratic performance index containing the value of control function necessary to keep the plant at a steady-state.
The optimal system constructed by this method consists of the both of a feedback controller and a feedforward controller, and its step response can satisfactorily be kept close to that of the model without offset.
An illustrative example is also presented.
