Learning controller for the regulation and stabilization of flexible structures

This paper deals with the regulation and stabilization of lightly damped flexible structures under plant uncertainty. An intelligent controller consisting of a neural network based front-end together with a modular nonlinear tuning regulator is proposed. The neural network `learns' the essential plant information in order for the nonlinear tuning regulator to maintain closed loop stability and asymptotic regulation. The nonlinear tuning regulator, on the other hand, provides the sustained oscillation necessary for the convergence of the learning process. This combined controller is robust and requires minimal plant information to operate. The overall 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. Analysis and design are then carried out in the baseband to obtain the necessary bandwidth-conservative tuning regulator. The neural network front-end is a single layer recurrent-net which separates the plant output back into the N frequency components (modes). The separated modes are then fed to the N structurally identical tuning regulator modules. The tuning gains and the learning rate are derived by the on-line tuning method. No other plant information is required. A synthesis procedure is outlined in this paper to summarize the design steps in a systematic manner. Finally, a numerical example with closely spaced frequency components (within 25%) are provided. Simulation results indicate that the proposed controller maintains satisfactory stabilization/regulation for the nominal plant as well as for the perturbed plants (under both stable and unstable perturbations).