Reduced-Order Suboptimal Control Design for a Class of Nonlinear Distributed Parameter Systems Using POD and Θ-D Techniques

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.