Discrete Time Noncollocated Control of Flexible Mechanical Systems Using Time Delay

This paper studies discrete time noncollocated control of flexible mechanical systems. A sampled data system with one sensor and one actuator is formulated. Specific time delay is introduced in the feedback loop to eliminate the destabilizing effect of noncollocation of the sensor and actuator. A stability criterion that explicitly relates the closed-loop stability to the sampling frequency, time delay, and sensor and actuator locations, is derived. Based on the criterion, particular noncollocated controllers are designed for a simply supported beam. A sensitivity analysis yields a robust control condition in terms of the sampling frequency, system parameter uncertainties, and inherent delays. In addition, the relationship between frequency folding in data sampling and spill-over instability is discussed.