Regularization Embedded Nonlinear Control Designs for Input-Constrained and Ill-Conditioned Thermal System

Abstract

New regularization embedded nonlinear control designs are proposed for the temperature control of an input-constrained and ill-conditioned thermal process. A classic nonlinear controller applied to such a process is shown to provide good temperature tracking but generates physically unreasonable actuator solutions, i.e. input-constraint-violation. The reason of input-constraint-violating control solutions—ill-conditionedness—is shown by applying singular value decomposition (SVD) on the linear algebraic equivalence of the nonlinear controllers (LAENC). Based on the analogy of LAENC and regularization method for the linear algebraic equations, Tikhonov, truncated singular value decomposition (TSVD) and modified TSVD (MTSVD) methods are embedded in the design of feedback linearizing controllers (FBL) and sliding mode controllers (SMC). These regularization embedded nonlinear controllers (RENLC) provide good temperature tracking and generate physically reasonable and actuator-constraint-satisfying solutions for the ill-conditioned system, in spite of the modeling errors inherent in applying regularization. The optimal Tikhonov parameter is found using an L-curve. Quantitative comparisons of the residuals and standard deviations of the control inputs are used as criteria to select the optimal truncated singular value decomposition (TSVD) parameter.