Abstract
A number of synthesis methods of optimal robust servosystems have been proposed. In most of those, however, the optimality is not necessarily well-defined. For example, the initial state of the servocompensator to be decided is not naturally derived from the viewpoint of optimality criterion. For the case of stepwise reference, Ikeda and Suda clarified that the optimal servosystems cannot be obtained till the performance index is minimized in terms of not only control input but undefined initial state of the servocompensator. Although their results are reasonable and interesting, some of those are available only to the stepwise reference case.
This paper considers the problem of synthesising the optimal robust servosystems of which reference is generated by a linear dynamical system, and generalizes their results. We first introduce the ideal trajectories for state and input variables of the augmented system, such that the resulting output completely coincides with the reference. Using the deviation variables from those ideal trajectories, we define the augmented error system and the corresponding quadratic performance index. The optimal control law can be then obtained by minimizing the performance index in terms of both control input and undefined initial state of the servocompensator, which consists of feedback control to stabilize the augmented system, feedforward control from the reference generator, and some outer signals including the same mode with the servocompensator. The outer signals are not needed if the state variables of servocompensator can be suitably adjusted at the moment of changing in reference input. It is also shown that when reference changes only in a steady state, in the case that the reference is of single-mode such as stepwise signal the optimal control law can be constituted of only state feedback and feedforward control, and in the multi-modes case it cannot generally be constituted without the outer signals.
