Quenching of Adaptive Control System Response to Test Signal

Abstract

In adaptive control a test signal may be used to identify the parameters of the system to be controlled. A test signal disturbs the system. Therefore it is desirable to eliminate the effects of this signal as soon as the identification has been completed. After identification a quenching signal may be introduced to eliminate the system response to the test signal. The systems treated here are described by linear differential equations with slowly varying coefficients. The nature of the quenching signal depends on whether or not it is bounded or unbounded. The unbounded quenching signal is a linear combination of a properly weighted impulse and derivatives of an impulse. The weights are determined by the initial conditions on the system at the instant of quenching, and the system parameters. Unbounded quenching is considered to be optimum if the response to the test signal is eliminated with minimum integral squared error. The bounded quenching signal is obtained by scheduling the lengths of time that its value is either at the upper or lower bound. The quenching signal is determined by the test signal and the system to be controlled. Therefore, as soon as the system is identified, quenching can be accomplished by scheduling regardless of the other disturbances to which the system is subject. The method applies to the quenching of system response whether or not adaptive control is involved.