مرکز منطقه ای اطلاع رساني علوم و فناوري - On-off limit-cycle controllers for reaction-jet-controlled systems

Abstract :

Analytical expressions have been obtained by Mendel [1] for performance cost functions that describe the behavior of a reaction-jet-controlled system during an on-off limit cycle. The cost functions are expressed in terms of the amplitudes of the limit-cycle switch states $\\theta_{s}$ and $\\dot{\\theta}_{s}$ . No structure is assumed for $u(t)$ in [1]. In this paper, $u(t)$ is chosen to be an asymmetrical deadzone function that is proceeded by a $T$ -second time delay. Contained within $u(t)$ are three design variables: control gains $K_{\\theta}$ and $K_{\\dot\\theta}$ , and asymmetry $l$ . This paper shows how $\\theta_{s}$ and $\\dot{\\theta}_{s}$ can be obtained from prespecified values of $K_{\\theta}$ and $K_{\\dot{\\theta}}$ , and how $K_{\\theta}$ and $K_{\\dot{\\theta}}$ can be obtained from prespecified values of $\\theta_{s}$ and $\\dot{\\theta}_{s}$ ; thus, it provides one with the means for utilizing the results in [1] for a specified controller. In addition, conditions are obtained for the existence of an on-off limit cycle. These conditions are interpreted in the phase plane; that is to say, each condition is viewed as a phase-plane constraint or constraints between $\\theta_{s}$ and $\\dot{\\theta}_{s}$ . It is shown how to construct the admissible regions for $\\theta_{s}$ and $\\dot{\\theta}_{s}$ ahead of time. It is also shown how to choose the asymmetry variable $l$ so that limit-cycle existence is assured. All of the results are brought together first as a synthesis procedure, and then as an analysis procedure. Details of both procedures are given. This paper provides the control system designer with new tools for: 1) better understanding the limitations of a fixed controller for the reaction-jet-controlled vehicle; 2) more efficient ways to analyze choices of the controller\´s parameters on system performance; and 3) more efficient ways to choose these parameters.