5 August 2003 Robust reduced order model-based control of a smart vibrating cantilever beam
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Abstract
Modern design briefs increasingly stipulate the need to reduce the weight of high technology structures due to the large costs involved in transport. As a result, these light structures are prone to unwanted vibrations. The uncertain surrounding environment necessitates the assumption of no fixed base to operate sensing/actuation devices with reference to. These conditions have made piezoceramic devices ideal candidates to operate as distributed actuators to apply vibration control to smart structures. The limited actuation of these devices, however, makes it essential to consider the problems associated with actuator saturation on the resulting controllers. This paper compares Pole-placement and Generalised Minimum Variance controllers for application to a vibrating cantilever beam. Certain desired closed-loop pole-positions are found to lead to limit cycling behaviour with the Pole-placement controller in both experiment and simulation. Subsequent application of saturation compensation is shown to return stability to the closed-loop system. Due to the control signal penalising property of the Generalised Minimum Variance controller this method is shown not to require compensation. Utilising the Nelder-Mead simplex algorithm, efficient controllers have been obtained for both controller types. Experimental results have shown that the controllers are able to suppress both the free and forced disturbances of the experimental system in the presence of control signal saturation and plant model mismatch. The results show that a developed reduced order model results in a controller performance that is comparable to that using a larger order Auto Regressive with eXogenous inputs model.
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Robin G. Scott, Robin G. Scott, Martin C. Levesley, Martin C. Levesley, Michael D. Brown, Michael D. Brown, } "Robust reduced order model-based control of a smart vibrating cantilever beam", Proc. SPIE 5056, Smart Structures and Materials 2003: Smart Structures and Integrated Systems, (5 August 2003); doi: 10.1117/12.499480; https://doi.org/10.1117/12.499480
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