Optimization and invariance in control systems with constant and variable structure

Abstract

The paper considers invariancy in the automatic control systems subject to external disturbances with known statistics. Invariancy conditions established by means of K(D) transform theory are generalized for systems with known disturbance statistics. A new design principle for the systems invariant to any continuous control function is developed.Usually error signal is independent of control action only if the right-hand side of the system's non-homo-genious differential equation vanishes. To meet this requirement one must use control action derivatives in the control algorithm. In this case any variation of system parameters would make these invariancy conditions invalid. It is shown that with the aid of open-loop variable structure systems one can perform a wide range of control functions without static errors. In this case there is no need to meet this classical invariancy condition. Note that combined servo systems with variable open-loop structure are insensitive to certain variations of the system parameters.