LMI-based Integral fuzzy control of DC-DC converters

In this paper, we propose a T-S fuzzy controller which combines the merits of: i) the capability for dealing with nonlinear systems; ii) the powerful LMI approach to obtain control gains; iii) the high performance of integral controllers; iv) the workable rigorous proof for exponential convergence of error signals; and v) the flexibility on tuning decay rate. The output regulation problems of a basic buck converter and a zero-voltage-transition (ZVT) buck converter are used as application examples to illustrate the control performance of the proposed methodology. First, we consider a general nonlinear system which can represent the large-signal models of the converters. After introducing an added integral state of output regulation error and taking coordinate translation on an equilibrium point, the resulting augmented system is represented into a Takagi-Sugeno (T-S) fuzzy model. Then, the concept of parallel distributed compensation is applied to design the control law whereby the control gains are obtained by solving linear matrix inequalities (LMIs). An interesting result is that the obtained control law is formed only by the linear state feedback signals weighted by grade functions. In addition, the robustness analysis is carried out when uncertainty and disturbance are taken into consideration. The performance of numerical simulations and practical experiments results is satisfactory.