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

✍ Scribed by Radhakant Padhi; Ming Xin; S. N. Balakrishnan

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 603 KB
• Volume: 29
• Category: Article
• ISSN: 0143-2087
• DOI: 10.1002/oca.822

✦ Synopsis

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‐based problem‐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 θ–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. Copyright © 2007 John Wiley & Sons, Ltd.