Minimum effort dead‐beat control of linear servomechanisms with ripple‐free response

Abstract

A new and systematic approach to the problem of minimum effort ripple-free dead-beat (EFRFDB) control of the step response of a linear servomechanism is presented. There is specified a set of admissible discrete error feedback controllers, complying with general conditions for the design of ripple-free dead-beat (RFDB) controllers, regardless of the introduced degree of freedom, defined as the number of steps exceeding their minimum number. The solution is unique for the minimum number of steps, while their increase enables one to make an optimal choice from a competitive set of controllers via their parametrization in a finite-dimensional space. As an objective function, Chebyshev's norm of an arbitrarily chosen linear projection of the control variable was chosen. There has been elaborated a new, efficient algorithm for all stable systems of the given class with an arbitrary degree of freedom. A parametrized solution in a finite space of polynomials is obtained through the solution of a standard problem of mathematical programming which simultaneously yields the solution of a total position change maximization of servomechanism provided that a required number of steps and control effort limitation are given. A problem formulated in this way is consecutively used in solving the time-optimal (minimum-step) control of a servomechanism to a given steady-state position with a specified limitation on control effort. The effect of EFRFDB control on the example of a linear servomechanism with torsion spring shaft, with the criterions of control effort and control difference effort, is illustrated and analysed. Copyright © 2001 John Wiley & Sons, Ltd.