Abstract: The objective of this paper is to present a detailed study to design, model and simulate buck regulator with an analog lag lead compensator cascaded by sign inverter, then transpose into its equivalent digital form. The ease of implementation and the advantages given by the adaptability to the changes in the closed loop enable the digital controllers to become widely used during the last few decades. This is attributed to the tremendous growth in integrated circuits (ICs) technology and skyrocketed development in semiconductor devices which in turn fulfill the highly demanded microprocessors to more current at low voltages. Specifically, they received special attention in different applications such as renewable energy sources, Switched Mode Power Supplies (SMPS), drive systems, and High-Voltage DC (HVDC) transmission, etc. We have performed two algorithms, the first to design analog compensator aiming at achievement of specified requirements while the second to obtain the six transfer functions concerning the various (state/input/output) variables of the buck converter based on the small signal and averaged state space models. This facilitates obtaining an appropriate equivalent digital compensator using Bilinear Z-Transform (BZT), Matched Pole-Zero (MPZ) and Zero Order Hold (ZOH) methods. Also, simulative results have been depicted via MATLAB/Simulink model utilizing SimElectronics Toolbox. Moreover, these models represented by the state and output equations, enable the other modeling approaches to be computationally implemented. A special emphasis of our work is placed on the circuit and transfer function models. In addition, the dynamic response of our intended compensator under input voltage change and load current variations is illustrated. Simulation results ensure that the output voltage and inductor current can return to steady state even when they are affected by such variations, with a small overshoot and settling time for the investigated waveforms. As a result of the above, a precise and robust closed loop controller that can satisfy high degree of stability and performance conditions of the DC-DC synchronous buck regulator has been accomplished. Finally, the performed algorithms have paved the way towards practical implementation by microcontroller /DSP controller/ FPGA controller. In case of a change in converter parameters, the new values of the z-coefficients for the digital compensator are evaluated and programmed by software and no need for the designer to solder or redesign the printed board which is in opposite to the analog compensators.
Keywords: State-Space Averaging Model; Lag Lead Compensator; SMPS Regulator; Transfer Function Model; Input voltage and Load Variations; Bilinear Z-Transform (BZT); MPZ and ZOH Methods
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