SELECTION OF NOISY SENSORS AND ACTUATORS FOR REGULATION OF LINEAR SYSTEMS

MICHAEL LAWRENCE DELORENZO, Purdue University

Abstract

This research has developed and tested an algorithm which aids the controls engineer in placing sensors and actuators in a linear system to 'best achieve' a set of variance specifications on the outputs and inputs of the system. The term 'best achieve' has been defined to be the sensor and actuator configuration which enables a controller to do either of the following: Meet the input specifications while minimizing a sum of output variances normalized by their specification (i.e. input-constrained solution), or meet the output specifications while minimizing a sum of input variances normalized by their specification (i.e., output-constrained solution). The approach taken to solve this sensor and actuator selection (SAS) problem was to use LQG theory to specify a structure for the controller, and then develop an algorithm (SASLQG) that places sensors and actuators in this controller structure to achieve either the input-constrained or output-constrained solution. The main advantage of this approach is the mathematical ease with which LQG theory addresses variance constraints, and the main disadvantage is that there may be other controller structures which do better. In applying LQG theory to solve the SAS problem two specific extensions of the theory resulted. The first was development of sensor and actuator effectiveness values (V(,i)('sen) and V(,i)('act)) which determine the importance of each sensor and actuator to the LQG controller when both the sensors and actuators are assumed noisy. The second extension was the development of the algorithm LQGWTS which provides a systematic method for adjusting the weighting matrices in the LQG cost functional V so that the controller which minimizes V also satisfies either the input-constrained or output-constrained variance requirements. These two extensions were combined to form a sensor and actuator selection algorithm (SASLQG). The algorithm was applied to two substantial models of large space structures and the resulting configurations although not guaranteed to be optimal achieved better performance than any alternative configuration tested. The algorithm also provides insight into the sensitivity of the controller design to sensor and actuator deletions and therefore, insight into an optimal number for both sensors and actuators. Lastly, the algorithm provides information which identifies the most demanding outputs and the critical actuators for the final sensor and actuator configuration.

Degree

Ph.D.

Subject Area

Aerospace materials

COinS