Control of Switched Affine Systems with Bounded Sampling Time Rate on the Switching Function: Application to Buck DC-DC Converter

Abstract


 The paper addresses the problem of designing a stabilizing control for switched affine and its experimental verification based on Linear Matrix Inequalities (LMIs). The main contribution is on the determination of a switching function that exploits the potential of LMI control approaches and which assures global stability and minimizes a guaranteed quadratic cost. Slack variables are introduced to reduce the design conservatism and new sufficient LMI conditions for the synthesis of the controllers are presented. Thus, it is showed that the performance of the control system is superior with a smaller guaranteed cost upper bound of that afforded by recent results. In addition, a theorem with sufficient conditions for the control of switched affine systems that allows a way to garantee a bounded sample time rate on the switching function is proposed. The implementation of the switching function taking into account a bounded sampling time is analysed and discussed with particular interest. Finally, the theoretical results are applied to Buck DC-DC converter. Several simulations show the usefulness of the methodology and experimental results obtained from a prototype validate this approach.

Design of a Switching Strategy for Output Voltage Tracking Control in a DC-DC Buck Power Converter

“…Condition (18) asks for the existence of an x belonging to the convex set defined by the half-planes characterized by H and S i U c for the scalars K 1 and K 2 and the function y d such that ∑ 2 j=1 K j d j y d dt j for each instant t ≥ 0. However, it is much easier to verify the following sufficient condition:…”

“…These values are selected in such a way as to obtain moderate current and voltage ripples [26] and, additionally, to satisfy condition (18). The proposed trajectories for voltage monitoring at the output of the Buck converter are two: one a Bézier type (29) and the other a sinusoidal type with exponential amplitude (30).…”

“…Another switching strategy consists of an adaptive sliding mode control that combines a robust proportional-derivative control law for the regulation of the DC/DC Buck converter-DC motor system presented in [17]. Additionally, Júnior et al, in [18], introduced a control based on Lyapunov stability using a quadratic function and linear matrix inequalities to improve the convergence speed to a constant reference voltage in the Buck DC-DC power converter. Recently, Hashemi et al,in [19], proposed a controller leveraging the power of composite switched Lyapunov functions to ensure stability for linear-switched systems, such as the Buck converter, with constant external input.…”

“…Motivated by the benefits of a commutated control strategy [12][13][14][15][16][17][18][19], the design of a suitable switching function by means of the application of convex sets for the output trajectory tracking of a Buck power electronic converter is presented here. Unlike in [12][13][14][15][16][17][18][19], this control resolves voltage tracking at the converter load.…”

“…Motivated by the benefits of a commutated control strategy [12][13][14][15][16][17][18][19], the design of a suitable switching function by means of the application of convex sets for the output trajectory tracking of a Buck power electronic converter is presented here. Unlike in [12][13][14][15][16][17][18][19], this control resolves voltage tracking at the converter load. The use of convex sets in the commutated control strategy presented here allows for resolving the tracking for different desired voltage trajectories for the Buck converter in milliseconds, even in the presence of abrupt disturbances in the load and source.…”