Parameter Plane Analysis for Large Flexible Spacecraft

Abstract

The parameter plane technique for stability analysis and system design has been modified to obviate the sometimes cumbersome (particularly for high-order systems) derivation of the system characteristic equation. Instead, it is proposed to implement this technique by manipulating the matrices of the original equations. The objective is to keep the concepts simple and leave the tedious tasks to the computer. Using this technique, it is shown how a system may be designed by pole placement. This is implemented by mapping selected contours from the complex plane onto a selected two-parameter plane. Two primary advantages over existing frequencydomain techniques are: 1) system dynamics are portrayed in terms of two parameters, rather than a single parameter, thereby increasing the power of the designer's tool; and 2) the original system equations may be used without having to obtain the openor closed-loop transfer functions or the characteristic equation.