An Analysis of Observed-System Sensitivity to Plant Parameter Variations.

State-variable feedback is a modern control theory technique that is employed in system design to place closed-loop poles to achieve desired performance characteristics. Two problems associated with state-variable feedback are physical inaccessibility to plant states and output sensitivity to plant parameter variations. In this report an observer is employed to reconstruct all plant states. The plant-observer system is investigated with respect to sensitivity aspects of the following three areas state-variable representation, extent of pole placement, and observer dynamics design. A comparison between physical, phase, and Jordan canonical variables indicated physical and phase variable representations yield identical sensitivity functions Jordan canonical variables result in greater sensitivity than physical and phase variables. Placing plant poles close together creates a high system sensitivity to plant parameter variations separation of poles reduces sensitivity. As a minimal requirement for low system sensitivity, observer poles should be placed to the left of dominant plant poles further reductions in sensitivity are achieved by placing observer poles to the left of all plant poles. Author