Robust Relay-Feedback Based Autotuning for DC-DC Converters L. Corradini Department of Information Engineering University of Padova – Italy luca.corradini@dei.unipd.it P. Mattavelli DTG University of Padova – Italy paolo.mattavelli@unipd.it D. Maksimovic Colorado Power Electronics Center University of Colorado at Boulder maksimov@colorado.edu Abstract – This paper addresses the design and practical implementation of a digital controller for switched-mode DC- DC converters with self-tuning capabilities. The proposed tuning technique is based on digital relay feedback and exhibits some features specifically developed to improve accuracy and robustness in practical applications. The most relevant property is the elimination of the measurement of the output voltage oscillation amplitude, which is critical from the accuracy point of view, if the oscillation amplitude is only a few Least Significant Bits (LSBs) of the A/D converter. The proposed tuning technique is presented and the complexity of the resulting algorithm is further analyzed, its performances compared to other recently proposed tuning techniques. The described approach is simple, quite accurate, and robust. Experimental results on a 10 A, 1.5 V point-of-load converter are provided to show the effectiveness of the discussed approach. I. INTRODUCTION The design flow of an analog controller for a DC-DC power converter usually requires a rather precise knowledge of its control-to-output transfer function, in order to achieve proper stability margins and dynamic closed-loop performances. Other sources of process parametric variations such as component tolerances and aging, temperature dependences, number and type of output decoupling capacitors, are generally handled through a worst-case design. This well-established design approach has two major drawbacks, since often the resulting analog controller cannot achieve the best performances for a specific power converter, and it cannot track any process parametric variations that may occur over time. On the other hand, the intrinsic programmability of a digital controller gives rise to the opportunity of implementing self-tuning compensators, capable of self-adjusting their own parameters to the specific power stage. A tuning algorithm identifies the key properties of the process under control and subsequently calculates the compensator coefficients. The opportunity of giving such autotuning techniques a robust, simple and cost-effective implementation can be considered a breakthrough for digital control in power electronics [1-5]. A general block diagram of a self-tuning PID compensator is shown in Fig. 1; the general form of a discrete-time PID controller is: 1 1 2 1 1 1 ) 1 )( 1 ( ) ( − − − − − − = z z z z z K z PID (1) A tuning algorithm identifies one or more system parameters and adjusts the programmable PID controller transfer function until predefined constraints are met, usually expressed in terms of stability margins and closed-loop bandwidth. Several interesting works in this area have been reported in literature, presenting many different approaches for system identification and practical online tuning [6-12]. In this paper the relay-feedback based tuning technique [13- 16] is extended and a practical implementation is proposed that allows for high tuning accuracy and repeatability. Unlike previously reported approaches based on induced limit cycling oscillations [6,7], the proposed solution does not rely on the knowledge of any power stage parameter nor does it require any measurement of the output voltage oscillation amplitude. Section II briefly introduces the digital relay feedback approach, while in section III a detailed description of the proposed improved tuning technique is presented. Simulation results are presented in Section IV, while experimental results are reported in Section V. II. RELAY-FEEDBACK AUTOTUNING The relay-feedback based tuning technique identifies the key properties of the process by inducing amplitude- controlled limit cycle oscillations and measuring the corresponding oscillating frequencies. Figure 2 shows the system during the tuning process; the tuning operates in closed-loop configuration with a relay block inserted in the feedback loop. The relay block is very simple and can be considered a 1-bit quantizer: its output is equal to +R whenever its input is positive, or negative and equal to –R whenever its input is negative. Because of the nonlinearity introduced by the relay, a limit cycle oscillation at frequency f osc and amplitude A osc (measured at the power stage output) will arise in the system, with A osc and f osc satisfying the fundamental equation: 1 ) ( 4 − = osc osc f T A R π (2) where T is the linear part of the system’s loop gain, i.e. T(z)=G c (z)G vd (z), where G vd (z) is the control-to-output + - V ref 1 1 2 1 1 1 ) 1 )( 1 ( ) ( − − − − − − = z z z z z K z PID Tuning Algorithm K, z 1 and z 2 tuning Programmable PID Compensator i o (t) ESR C L V in Buck Converter i o (t) ESR C L V in Buck Converter DPWM A/D A/D Fig. 1 – Digitally controlled buck converter with self-tuning PID compensator 2196 1-4244-0655-2/07/$20.00©2007 IEEE