AAS 97-650
LINEAR QUADRATIC REGULATOR CONTROL OF DYNAMIC SYSTEMS DESCRIBED BY MATHIEU EQUATIONS
D. Mackison - University of Colorado
Abstract
Differential equations with periodic coefficients, such as the Mathieu equation, occur frequently in satellite orbit and attitude dynamics problem. Stable parameter ranges for these equations are determined by the Floquet method- to repeatedly integrate the differential equation for the state transition matrix over the period of the coefficients and examining the eigenvalues of . If the equations, as in the case of the Mathieu equation, can be separated into a part with an explicit time dependence, and a part with a constant coefficient, then a modified linear quadratic optimization method, Guaranteed Cost Control (GCC) may be used to compute a constant gain, state variable feedback control, which will guarantee stability of the closed loop system for all allowed variations of the coefficients.