Control of a flexible beam for optimum step response

The objective of this paper is to examine the end-point control of a flexible beam using the stable factorization approach. We begin with a description of the experimental setup at the University of Waterloo and discuss the derivation of the state space model of the beam using the method of modal expansions. The model is an eighth order nonminimum phase system with poles on the imaginary axis. The stable factorization approach is used to obtain the optimal step response of the system in the sense that the mean square tracking error is minimized over all the stabilizing controllers. Since the plant is strictly proper, the optimal step response is not realizable and only suboptimal controllers, whose responses approach the optimal step response, can be constructed. First, the one parameter compensator is studied. The results are discussed and the effect of weighting the error is analyzed. A two parameter compensator is also simulated and the result is compared to the one parameter compensator. The paper concludes with suggestions for future research.