Adapative Control for a Deployable Optical Telescope

Abstract

In this paper a novel Direct Model Reference Adaptive Control, (DMRAC) and Direct Adaptive Disturbance Rejection, (DADR) controller design process is applied to a Deployable Optical Telescope, (DOT). First the DMRAC and DADR theory for discrete time systems is presented and the stability of the DMRAC and DADR control system is proved for Strictly Positive Real dynamic systems. The design process is used to explore the DMRAC and DADR controller design space for the high order flexible space structure. It is shown in this paper that the DOT system is not Strictly Positive Real. However, through Reduced Order Modeling and non-linear optimization the DOT system can be cast in a form with filtering so that the DOT system is Strictly Positive Real. The difference between the new Strictly Positive Real system and the original DOT system and performance metrics for DMRAC and DADR metrics are discussed. Three performance metrics are proposed to determine the performance of the DMRAC and DADR controller. First the integrated error signal between the Reference Model and the Plant output is evaluated and discussed. Second, the ability of the controller to track the output of the reference model is evaluated by determining when the error signal falls below a given threshold set by the designer of the DMRAC and DADR controller. The time at which the error signal falls below the user defined threshold also has an associated confidence that is dependant on the DMRAC and DADR controller simulation. Finally, the Maximum Error Variance is used as a DMRAC and DADR controller performance metric. The DMRAC and DADR controller is shown to meet the given set of performance requirements for step and sine wave inputs even in the face of input disturbances of known frequency but unknown magnitude and phase. The DMRAC and DADR controller design process and controller performance are discussed. The novel design process is also used to empirically understand what characteristics of the DMRAC and DADR controller significantly affect the dynamic system. For example, it has been shown that a high order reference model does not enhance performance of the system.