Simple nonlinear controller to reduce line and load disturbances in HBCC converter L. Garcı ´a de Vicun ˜ a, J.M. Guerrero, J. Matas, M. Castilla and J. Miret A simple nonlinear control scheme that reduces line and load disturbances in the half-bridge complementary-control (HBCC) converter is proposed. The control scheme is devised by imposing a desired linear dynamic behaviour on the output voltage, by means of input-output feedback linearisation techniques. Introduction: Nowadays, new integrated circuits (ICs) require power supplies that can deliver low voltages with tight regulation and fast transient response [1, 2]. The use of the half-bridge complementary- control (HBCC) converter with synchronous rectifiers is a suitable solution to supply low voltage and high current to new ICs. The main advantages of this topology can be summarised as follows [3]. (i) The input voltage of the converter is high; therefore, conduction losses can be reduced, since the input current is low. (ii) The waveforms for self- driven synchronous rectifiers are optimum, and the performance of the synchronous rectification stage is very simple. (iii) The output filter is small, since the input voltage at this stage is always positive and its waveform is between two positive levels that are close to the output voltage. In a previous work, a control scheme based on a small-signal model of this converter was proposed [4]. However, the main disadvantage of this control is its high sensitivity to input voltage disturbances, thus making it necessary to use a pre-regulator. In this Letter, we present a nonlinear control for this structure capable of overcoming this drawback. The controller allows one to decouple the output filter dynamics from the input voltage and to impose a desired linear dynamic behaviour on the output voltage. Circuit description and nonlinear model: Fig. 1 shows the HBCC power stage. It consists of a half-bridge inverter loaded by an isolated synchronous rectifier and a lowpass filter. The converter can be described by the following bilinear model: C eq dv C2 dt ¼ C 1 dE dt þ i m þ ni L ð2u  1Þ ð1Þ L m di m dt ¼ Eu  v C2 ð2Þ L di L dt ¼ nEu  nv C2 ð2u  1Þ v o ð3Þ C dv o dt ¼ i L  v o R ð4Þ where C eq is C 1 þ C 2 , and u is the control variable, which takes the following values: u ¼ 1 (when S1 is ON and S2 is OFF), and u ¼ 0 (when S1 is OFF and S2 is ON). Fig. 1 Power stage of HBCC converter and block diagram scheme of proposed nonlinear controller Control design: Our aim in this Section is to introduce input-output feedback linearisation [5, 6] in order to deduce a nonlinear controller that decouples the output voltage dynamics from the input voltage. To deduce the controller description which stabilises the external dynamics, it is necessary to find a differential equation of the output voltage v o in which the control variable u explicitly appears. By using (3) and (4) and taking the average value over one switching period, the output voltage dynamics can be found: LC d 2 hv o i dt 2 þ L R dhv o i dt þhv o i¼hnEu  nv C2 ð2u  1Þi ð5Þ where the symbol hi denotes the average value. To linearise the output voltage dynamics, we propose to implement the controller by means of the following equality:  k p hv o iþ k i ð t 1 ðV o ref hv o iÞdt  k d dhv o i dt ¼hnEu  nv C2 ð2u  1Þi ð6Þ From (5) and (6), the closed-loop output voltage dynamics then yields: LC d 3 hv o i dt 3 þ L R þ k d   d 2 hv o i dt 2 þð1 þ k p Þ dhv o i dt þ k i hv o i¼ k i V o ref ð7Þ As it can be seen, the above equation, which is the external dynamics, is decoupled from the internal dynamics (i m and v C2 ). The stability of the internal dynamics can be easily proved by means of the zero dynamics approach [5]. Moreover, the zero dynamics is independent from the control parameters, and, consequently, no design constraints are derived from this analysis. Thus, by choosing k p , k i , and k d , we can obtain a proper dynamics of the output voltage. Controller implementation: Fig. 1 also shows the block diagram of the proposed nonlinear control. This controller implements (6), which includes the following nonlinear term: hv F i¼hnEu  nv C2 ð2u  1Þi ð8Þ The implementation of this term is very simple by sensing v F and using a lowpass filter. The control law is carried out by a comparator and a flip-flop. Experimental results and remarks: A prototype was built and tested to prove the validity of the proposed controller, using the following parameters: E ¼ 48 V, C 1 ¼ C 2 ¼ 1 mF, L m ¼ 200 mH, n ¼ 1=6, C ¼ 3000 mF, L ¼ 3 mH, R ¼ 0.25 O, V o ref ¼ 3.3 V, f S ¼ 100 kHz. The constants k p , k i , and k d were chosen to ensure stability and a good transient response, according to (7), being k p ¼ 1, k i ¼ 1000, and k d ¼ 2.5  10 4 . Fig. 2 shows a comparison between simulation (7) and the experimental results of the closed-loop output voltage during the start-up. The excellent agreement proves the validity of this control approach. Fig. 3a shows the output-voltage transient response for input voltage variations, from 48 to 64 and back to 48V. The maximum overshoot obtained is less than 2%. Note that good line regulation and high robustness against large-signal input-voltage changes are obtained. Fig. 3b shows the transient response of the output voltage for load step changes, from 13.5 to 0.5 and back to 13.5 A. As can be seen, voltage overshoot is only about 4%. This result demonstrates the low sensitivity of the output voltage against large load changes. Fig. 2 Output voltage behaviour during start-up a Simulation of (7) b Output voltage of HBCC with proposed control ELECTRONICS LETTERS 5th December 2002 Vol. 38 No. 25