Lee, Y.-S. and Elliott, S.J.
Active position control of a flexible smart beam using internal model control
Journal of Sound and Vibration, 242, (5), . (doi:10.1006/jsvi.2000.3379).
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The problem of controlling the position at the tip of a flexible cantilever beam to follow a command signal is considered, by using a pair of piezoelectric actuators at the clamped end. The beam is lightly damped and so the natural transient response is rather long, and also since the sensor and actuator are not collocated, the plant response is non-minimum phase. Two control strategies were investigated. The first involved conventional PID control in which the feedback gains were adjusted to give the fastest closed-loop response to a step input. The second control strategy was based on an internal model control (IMC) architecture. The control filter in the IMC controller was a digital FIR device designed to minimize the expectation of the mean square tracking error. In practice, such smart beams could be exposed to temperature fluctuations and changes in geometry. The effect of these variations on the stability was studied and it is shown that the need for robustness to such variations leads to a limitation in the performance of an IMC controller. The improvement in the stability robustness by incorporating control effort weighting into the cost function being minimized was investigated, as was the incorporation of modelling delay in the design of the IMC control filter. The IMC controller designed for the beam was found to have much reduced settling times to a step input compared with those of the PID controller while maintaining good robustness to changes in temperature. However, the extremely low damping of the experimental beam made it difficult to implement an accurate plant model in practice.
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