The Symmetry Principle Usage to Design the Previously Disturbed Linear Control Systems

Abstract

The paper deals with developing backgrounds to design the control systems for electrical motors and actuators. We offer to design controllers by using the known approach based on the control systems symmetry principle. This principle similar to the feedback linearization approach allows us to fully compensate for the inner dynamic of a plant but contrary to feedback linearization it forms the system’s desired motion by defining desired transfer function of the open-loop control system. Since the used approach operates with the transfer functions apparatus we offer to generalize these functions by taking into account the plant’s non-zero initial state while performing the Laplace-Carson’s transformation. Such an approach gives us the possibility to consider the generalized transfer function as some matrix differential operator which defines free and perturbed system’s motions. We study this operator in our paper and show the patterns of its determination and implementation. Our study allows us to supplement the definition of direct and inverse dynamic problems and consider the last one as the problem with the two solutions which define the plant’s control signal and its initial conditions. We use them to define the generalized inverse transfer function and, in conjunction with the desired transfer function for an open-loop system, find the controller transfer function. This method is applied to design a control system for the angular position of a DC electric drive. Our results show that the designed control system is an asymptotically stable one for various initial conditions.