Enhanced Computational Efficiency and Accuracy of Discrete-Time PID-DPWM Equation

The technique of using the duty cycle output of a proportional integral derivative controller as the input for a count-based digital pulse width modulation module to process digital PWM signals is widely applied across various industrial fields, including automotive, power control, and motor control. This paper refers to this approach as the classic PID-DPWM equation. Classic PID-DPWM equations have been studied with the perspective that the raw-data measured input, and the integer-value duty value are integers. This study presents the improved PID-DPWM equations that start with the initial data scaling equation and perform integer-based computations and one floating-point operation. Consequently, the proposed equations become equivalent to the classic PID-PWM equations, enhancing computational efficiency and accuracy. The enhancement in computational efficiency was verified mathematically, and the improvement in accuracy was validated using performance index tests. A validation test of a closed-loop system in MATLAB/Simulink demonstrated that the improved standard PID-DPWM equation outperformed the classic standard PID-DPWM equation, achieving improvements in performance indices (ISE = 0.0001%, IAE = 0.27%, IE = 0.035%, ITSE = 0.012%, and ITAE = 2.85%). Furthermore, the improved difference PID-DPWM equation demonstrates further improvements over the classic difference PID-DPWM equation, achieving improvements in performance indices (ISE = 0.98%, IAE = 4.79%, IE = 15.87%, ITSE = 4.25%, and ITAE = 26.89%). Overall, the improved standard PID-DPWM equation exhibited enhanced performance in ISE, IAE, and ITAE, whereas the improved difference PID-DPWM equation exhibited superior performance in IE and ITSE.