A robustly stable output feedback saturated controller for the Boost DC-to-DC converter

Abstract

The problem of regulating the output voltage of the Boost DC-to-DC power converter has attracted the attention of many control researchers for several years now. Besides its practical relevance, the system is an interesting theoretical case study because it is a switched device whose averaged dynamics are described by a bilinear second order non-minimum phase system with saturated input, partial state measurement and a highly uncertain parameter -the load resistance-. In this paper we provide a solution to the problem of designing an output-feedback saturated controller which ensures regulation of the desired output voltage and is, at the same time, insensitive to uncertainty in the load resistance. Furthermore, bounds on this parameter can be used to tune the controller so as to (10-cally) ensure robust performance, e.g., that the transient has no (under)over-shoot. The controller, which is designed following the energy-balancing methodology recently proposed by Ortega, van der Schaft and Maschke, is a simple static nonlinear output feedback, hence it is computationally less demanding than the industry standard lead-lag filters. Problem formulationThe averaged model of the DC-to-DC Boost converter depicted in Fig. 1 is given by [3 ], [4](1.1)c 1 1 x 2 = --x 2 + -u x 1 rC L 4 0 ) = (21(0), 2 2 ( 0 ) ) E R ? o where x 1 is the inductance flux, 2 2 is the charge in the capacitor voltage, and U is the continuous control signal, which represents the slew rate of a PWM circuit controlling the switch position in the converter. The positive constants C, L , r, E are the capacitance, 'This work has been partially supported by CONACyT of 2Author to whom all correspondence should be addressed. Mexico inductance, load resistance, and voltage source, respectively, and 7Z:o denotes the open first quadrant. The u = o Figure 1: Boost converter circuit. following conditions of operation of the device are imposed by technological considerations: C . l The only signal available for measurement is 2 2 . C.2 The control signal U ranges in the set (0,l). C.3 The state vector 2 lives in R;,. C.4 All parameters, except the load resistance r , are known. The control objective is to regulate the output capacitor voltage & 2 2 to a desired constant value V, > E , verifying the conditions C.l-C.4.The main contribution of this paper is to show that the energy-balancing methodology recently proposed in [5] yields a solution to this problem. Furthermore, the resulting controller is a simple static nonlinear output feedback, hence it is computationally less demanding than (even) the industry standard lead-lag filters. Remarks1. If we fix U to a constant value, the equilibria of (l.l), (1.2) (denoted Z), verify the algebraic relation (1.3) L Z1= -T E C 2 2 2 2 Hence, if we fix 6 5 2 at the desired output voltage V,, we get the equilibrium point we want to stabilize x+ and the corresponding constant control U* as L E rE V* (1.4) 2* = ( 2 1 * , 2 2 * ) = (-V,", CV*), U* = -0-7803-5250-5/99/$10.00 0 1999 IEEE 2100

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