An Optimal Control Scheme for a Class of Duty-Cycle Modulation Buck Choppers: Analog Design and Virtual Simulation

Abstract

This paper presents a design methodology and a virtual simulation framework, of the optimal feedback control scheme for DCM (duty-cycle modulation)  Buck choppers. The transfer function of an open loop DCM chopper, is built from the numerical analysis of a virtual step response, with Ref = 2 volts as step control input. Then, the optimal PID controller for DCM Buck Choppers is formulated and synthetized as a LQR (Linear Quadratic Regulator) equivalent control, and the associated Riccati equations is easily solvable using Matlab/LQR tool. As a relevant implication, the parameters of the corresponding optimal PID, are straightforwardly obtained from the LQR gains according to a LQR/PID equivalence principle, which is proven for a relevant class of second order dynamic systems.  In addition, in order to show the feasibility of the designed optimal PID control scheme, a whole prototyping DCM Buck chopper with given operating  conditions  ( main DC supplied (12 V),  load resistance (3.3 Ω), basic DCM frequency (30 kHz)), is virtually implemented and well tested using  Multisim. The virtual simulation results obtained from numerous operating conditions (e.g., open loop, closed loop, load variations), are presented and discussed. Furthermore, relevant results and findings are reported, e.g., transient characteristics (i.e. controllability, stability, overshoot (4%), and time response (1,5 ms)) and static performance levels (e.g. static error (0 %), high robustness under 50 % load variations). These results are a great challenge for the first virtual DCM Buck chopper, operating under a well tested optimal PID-based control policy.