LPV Modeling Of Buck Converter And Robust Gain-Scheduling Control

Switching mode power supply is a typical nonlinear system. Currently the methodologyof controlling switching mode power supply can be classified into geometric-based oraverage-based methods in which the switched nonlinear characteristic of DC-DC converter isneglected. This method leads to an approximate model. Therefore，the technology based on itcannot further improve the effectiveness of control and stability of the converter to meet therequirements for high-performance.In this paper, which takes the Buck converter as an example, The ideal switched model,the state-pace average model and the small-signal model of the Buck converter are analyzedfirstly. On the basis of analyzing the conventional modeling of DC-DC converter, The linearparameter-varying(LPV) dynamic equation is presented with the load and the input voltage asthe scheduled parameters. Moreover the LPV dynamic equation is translated into convexpolytope through the combination of the extremums of the variable parameter. Therefore, it isno longer necessary to analyze or design all the points of the convex polytope when weanalyze the stability and design controller of the obtained convex polytope. The controllerdesign is simplified to the vertex controller design of the plant polytope, which greatlydecreases the calculating work and makes the controller possesses gain continuously and hasglobal speciality.The dynamic of the Buck converter will change when the input voltage or the loadchange. Therefore, the concept of Buck linear parameter varying(LPV) and polytope isintroduced in this paper to design a polytopic gain scheduled state feedback controller basedon the LPV model of the Buck converter is designed in the paper. Based on it, the closed-loopsystem poles assignment is taken to the specific area with gain scheduled state feedback vialinear matrix inequalities (LMIs) technique, the gain scheduled state feedback is designed toregulate the duty cycle of the switch conduction. Compared with robust state feedback control,it has better disturbance rejection performance.