Model Reduction-Based Control of the Buck Converter Using Linear Matrix Inequality and Neural Networks

A new method to control the Buck converter using new small signal model of the pulse width modulation (PWM) switch is introduced. The new method uses recurrent supervised neural network to estimate certain parameters of the transformed system matrix [ A~ ]. Then, linear matrix inequality (LMI) optimization is used to obtain the permutation matrix [P] so that system transformation {[ B~ ], [ C~ ], [ E~ ]} is achieved. The transformed model is then reduced using the singular perturbation method, and state feedback control is applied to enhance system performance. The eigenvalues of the resulting transformed reduced model are an exact subset of the original (non-transformed fullorder system), and this is important since the eigenvalues in the non-transformed reduced order model will be different from the eigenvalues of the original full-order system. The experimental simulation results show that the new control method simplifies the model in the Buck converter and thus uses a simpler controller that produces the desired system response for performance enhancement. Index Terms Buck Converter, Feedback Control, Linear Matrix Inequality (LMI), Neural Network, Order Model Reduction, Supervised Learning.