Improved Performance in the Control of DC-DC Three-Phase Power Electronic Converter Using Fractional-Order SMC and Synergetic Controllers and RL-TD3 Agent

In this article, starting from a benchmark represented by a Direct Current-to-Direct Current (DC-DC) three-phase power electronic converter used as an interface and interconnection between the grid and a DC microgrid, we compare the performances of a series of control structures—starting with the classical proportional integrator (PI) type and continuing with more advanced ones, such as sliding mode control (SMC), integer-order synergetic, and fractional-order (FO) controllers—in terms of maintaining the constant DC voltage of the DC microgrid. We present the topology and the mathematical modeling using differential equations and transfer functions of the DC-DC three-phase power electronic converter that provides the interface between the grid and a DC microgrid. The main task of the presented control systems is to maintain the DC voltage supplied to the microgrid at an imposed constant value, regardless of the total value of the current absorbed by the consumers connected to the DC microgrid. We present the elements of fractional calculus that were used to synthesize a first set of FO PI, FO tilt-integral-derivative (TID), and FO lead-lag controllers with Matlab R2021b and the Fractional-order Modeling and Control (FOMCON) toolbox, and these controllers significantly improved the control system performance of the DC-DC three-phase power electronic converter compared to classical PI controllers. The next set of proposed and synthesized controllers were based on SMC, together with its more general and flexible synergetic control variant, and both integer-order and FO controllers were developed. The proposed control structures are cascade control structures combining the SMC properties of robustness and control over nonlinear systems for the outer voltage control loop with the use of properly tuned synergetic controllers to obtain faster response time for the inner current control loop. To achieve superior performance, this type of cascade control also used a properly trained reinforcement learning-twin delayed deep deterministic policy gradient (RL-TD3) agent, which provides correction signals overlapping with the command signals of the current and voltage controllers. We present the Matlab/Simulink R2021b implementations of the synthesized controllers and the RL-TD3 agent, along with the results of numerical simulations performed for the comparison of the performance of the control structures.