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Nonlinear Tuning Regulator for the Control of Lightly Damped Structures

This paper deals with the control of lightly damped flexible structures under plant uncertainty. The control objectives are 1) closed loop stability and 2) asymptotic regulation of the amplitude of each resonant mode of the flexible structure. Furthermore, it desired to conserve control bandwidth so as to minimize implementation costs. Since the dynamics of a flexible structure can be decomposed into N resonant subsystems whose energy is mainly distributed in the passband, frequency translation technique based on the Hilbert transform is first applied to the nominal plant to obtain a low frequency equivalent model that also includes various filter dynamics. Analysis and design are then carried out in the baseband to obtain the necessary bandwidth-conservative controller. The resultant control system is modular, consisting of N structurally identical modules. The controller parameters are derived by the on-line tuning method [3] together with an estimate of the resonant frequencies of the flexible structure. No other plant information is required. The proposed controller does not suffer from spillover effects that sometimes occur in conventional designs. A synthesis procedure is outlined in this paper to summarize the design steps in a systematic manner. Finally, a numerical example based on the control of a stainless steel flexible beam is also provided to illustrate the design steps.