Number and placement of control system components considering possible failures

One of the first questions facing the designer of the control system for a large space structure is how many components actuators and sensors - to specify and where to place them on the structure. This paper presents a methodology which is intended to assist the designer in making these choices. A measure of controllability is defined which is a quantitative indication of how well the system can be controlled with a given set of actuators. Similarly, a measure of observability is defined which is a quantitative indication of how well the system can be observed with a given set of sensors. Then the effect of component unreliability is introduced by computing the average expected degree of controllability (observability) over the operating lifetime of the system accounting for the likelihood of various combinations of component failures. The problem of component location is resolved by optimizing this performance measure over the admissible set of locations. The variation of this optimized performance measure with number of actuators (sensors) is helpful in deciding how many components to use.