Control of Dc-Dc Converters by Direct Pole Placement and Adaptive Feedforward Gain Adjustment Anthony Kelly Analog Devices Limerick, Ireland anthony-l.kelly@analog.com Karl Rinne Department of Electronic & Computer Engineering University of Limerick Limerick, Ireland karl.rinne@ul.ie Abstract— A direct pole-placement control strategy is introduced, and applied in the design of a buck type, dc-dc converter. The solution involves a feedforward component in the control strategy, to eliminate steady-state errors. The value of the feedforward gain which completely eliminates steady-state error, is dependant upon the gain of the plant, which may not be known exactly. In this design the feedforward gain is determined adaptively, so as to drive the steady state error to zero. Keywords– pole-placement, digital control, dc-dc converter, LMS, sigma-delta. I. INTRODUCTION Digital control of dc-dc converters is an active research topic in power control. Many controllers have been demonstrated [1-8]. Whilst the controllers differ in several aspects, the control strategies center around PD, PI, PID control; and compensation strategies generally incorporate classical methods such as gain and phase margin, root-locus. The designs incorporate both discrete-time emulation of an analog controller, and direct-digital design. In this paper, we apply an alternative controller design strategy to a buck converter; that is, design by direct pole placement. Direct-pole placement allows us to specify the location of the closed-loop poles, and therefore the closed-loop dynamics, as a design requirement. The direct-pole placement method used, is the polynomial approach, which involves the solution of Diophantine equations in order to calculate the required controller parameters. It will be seen that the solution involves a feedforward component to eliminate steady-state errors. The value of the feedforward gain which completely eliminates steady-state error, is dependant upon the gain of the plant, which may not be known exactly. In this design the feedforward gain is determined adaptively, so as to drive the steady state error to zero. This paper will demonstrate that direct pole-placement is a feasible strategy for dc-dc converter design, allowing the selection of a simple complex conjugate pair of closed-loop poles, and to introduce a novel method to achieve a zero steady-state error. II. DIOPHANTINE EQUATIONS Consider the control system of Figure 1. The plant may be described, in discrete time, by polynomial functions in z; B(z) and A(z), (1) and (2), where A(z) is monic: n n n n a z a z a z z A + + + + = - - 1 1 1 .. ) ( (1) n n n n b z b z b z b z B + + + + = - - 1 1 1 0 .. ) ( (2) Similarly, the controller may be described as: 1 2 2 1 1 0 .. ) ( - - - - + + + + = n n n n z z z z α α α α α (3) 1 2 2 1 1 0 .. ) ( - - - - + + + + = n n n n z z z z β β β β β (4) Examining the controller of Figure 1, its closed loop transfer function may be written as: U(z) V(z) ) ( ) ( z A z B ) ( ) ( z z α β Figure 1. Model of the control system