Comparative Evaluation of PID Voltage Mode, PI Current Mode, Fuzzy and PWM Based Sliding Mode Control for DC-DC converters Omar Ellabban, and Joeri Van Mierlo Vrije Universiteit Brussel, IR-ETEC, Pleinlaan 2, B-1050 Elsene, Belgium Omar.Ellabban@vub.ac.be Abstract- This paper presents a comparison between the application of four control techniques in DC-DC converters. PID voltage mode (PID-VM), PI current mode (PI-CM), fuzzy, and PWM based sliding mode (SM) controllers are applied to buck converter. The design procedures of controllers are reviewed. The dynamic performance of these controllers under star-up, steady state, input voltage variation, load current disturbances and EMI spectrum are presented and compared. I. INTRODUCTION DC-DC converters are nonlinear systems due to their inherent switching operation, they represent a big challenge for control design. Many linear and nonlinear control techniques had been applied to control DC-DC converters. Linear PID voltage mode (PID-VM) and PI current mode (PI-CM) controllers are usually designed for DC-DC converters using standard frequency response techniques based on the small signal model of the converter [1-3]. A Bode plot is used in the design to obtain the desired loop gain, crossover frequency and phase margin. The stability of the system is guaranteed by an adequate phase margin. However, linear PID and PI controllers can only be designed for one nominal operating point. A buck converter’s small signal model changes when the operating point varies. Therefore, it is difficult for the PID-VM and PI- CM controllers to respond well to changes in operating point. Nonlinear controllers which are more robust and have faster dynamic response are applied to power converters to solve this problem. Many nonlinear control schemes have been proposed for DC-DC converters. Between these schemes, sliding mode (SM) and fuzzy control have advantages such as simple and model free implementation [5-14]. This paper comprises the application of PID-VM, PI-CM, Fuzzy and PWM based SM control methods for buck converter. Simulation results using Matlab for the four control techniques are evaluated and compared. II. BUCK CONVERTER MODELING The buck converter is one of the simple but most useful power converters; a chopper circuit that converts a dc inputs to a dc output at a lower voltage. The buck converter shown in Fig.1, which is operating with the switching period of  and duty cycle ܦis considered [4]. During continuous conduction mode of operation, the state Fig. 1 Buck converter: (a) circuit; (b) switch on; (c) switch off space equations when the switch is ON (Fig. 1-b) are given by, ௗ௜ ಽ ௗ௧ ൌ ଵ ௅ ሺ ௜ െ  ଴ ሻ ௗ௏ బ ௗ௧ ൌ ଵ ஼ ሺ ௅ െ ௏ బ ோ ሻ , 0൏ ݐ൏ ܦ (1-a) and when the switch is OFF (Fig. 1-c) are presented by, ௗ௜ ಽ ௗ௧ ൌ ଵ ௅ ሺെ ଴ ሻ ௗ௏ బ ௗ௧ ൌ ଵ ஼ ሺ ௅ െ ௏ బ ோ ሻ , ܦ൏ ݐ൏ (1-b) Using the state space averaging method, these sets of equations can be written as, ݔሶ ଵ ൌ െ ଵ ௅ ݔ ଶ ൅ ஽ ௅  ௜ ݔሶ ଶ ൌ ଵ ஼ ݔ ଵ െ ଵ ோ஼ ݔ ଶ (2) where ݔ ଵ is the inductor current and ݔ ଶ is the capacitor voltage. The small signal modeling for the buck converter is done assuming perturbations in the supply voltage and the duty cycle. Equation (3) gives the output to control transfer function ܩ ௩ௗ ሺݏሻ of a voltage mode buck converter, it has two poles and can be modeled as a second-order equation, ܩ ௩ௗ ሺݏሻൌ ௩ ෤ బ ௗ ෨ ቚ ௩ ෤ ೔ ୀ଴ ൌ ௏ బ ஽ ଵ ଵା௦ ಽ ೃ ା௦ మ ௅஼ (3) A current mode buck converter also has two poles. However, the second pole is located near the switching frequency away from the dominant pole. Therfore, the model can be approximated into a first-order equation with a single pole. Control to output transfer function G ୴ୡ ሺsሻ of a current mode buck converter can be expressed as, ܩ ௩௖ ሺݏሻൌ ௩ ෤ బ ప̃ ೎ ቚ ௩ ෤ ೔ ୀ଴ ൌ ோ ଵା௦ோ஼ (4) where  ௖ is the control signal.