Adaptive Time Optimum Control of a Purely Inertial System

Abstract

This paper describes a purely inertial system whose attitude around its axis is controlled with air jet, and gives the results of the adaptive optimum control of the system. It is well known that the time optimum control of the purely inertial system can be accomplished by appling positive and negative maximum torques according to the parabolic switching curve in the phase plane.
In order to realize the desired switching curve, a nonlinear resistor, called the “varistor”, is used in the control system. Keeping the time optimum control loop closed, the small perturbation signal is applied to the system and the inertial moment of the controlled subject is measured by the correlation method. The measured moment is fed into the adaptive control system to determine the optimum switching curve in the phase plane automatically. By changing the moment, it is experimentally verified that the switching curve is optimally set.
The response of the moment measuring system to the sudden change of the moment is described. Also the effects of the test signal on the time optimum control and on the error of the measured moment are stated.