Reduced-order suboptimal control design for a class of nonlinear distributed parameter systems using POD and \theta –D techniques

Padhi, Radhakant and Xin, Ming and Balakrishnan, SN (2008) Reduced-order suboptimal control design for a class of nonlinear distributed parameter systems using POD and \theta –D techniques. In: Optimal Control Applications and Methods, 29 (3). pp. 191-224.

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Abstract

A new computational tool is presented in this paper for suboptimal control design of a class of nonlinear distributed parameter systems (DPSs). In this systematic methodology, first proper orthogonal decomposition-basedproblem-oriented basis functions are designed, which are then used in a Galerkin projection to come up with a low-order lumped parameter approximation.This technique has evolved as a powerful model reduction technique for DPSs. Next, a suboptimal controller is designed using the emerging \theta –D technique for lumped parameter systems. This time domain control solution is then mapped back to the distributed domain using the same basis functions, which essentially leads to a closed form solution for the controller in a state-feedback form. We present this technique for the class of nonlinear DPSs that are affine in control. Numerical results for a benchmark problem as well as for a more challenging representative real-life nonlinear temperature control problem indicate that the proposed method holds promise as a good optimal control design technique for the class of DPSs under consideration.

Item Type:	Journal Article
Publication:	Optimal Control Applications and Methods
Publisher:	John Wiley and Sons, Inc.
Additional Information:	Copyright of this article belongs to John Wiley and Sons, Inc.
Keywords:	Suboptimal control design;distributed parameter system;finite difference;proper orthogonal decomposition;heat transfer;temperature control.
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	01 Aug 2008
Last Modified:	19 Sep 2010 04:48
URI:	http://eprints.iisc.ac.in/id/eprint/15345

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