Discrete-Time PID Speed Control for DC Motor via Z-Transform: Performance Analysis Across Simulation and Embedded Implementation Environments

Abstract

This paper presents the design and comparative performance analysis of a discrete-time Proportional-Integral-Derivative (PID) controller for DC motor speed regulation using the Z-transform method and Zero-Order Hold (ZOH) discretization. The principal contribution is a systematic analysis of controller behavioral differences between an ideal simulation environment (MATLAB/Simulink) and a microcontroller-based simulation platform (Tinkercad Arduino), revealing the quantitative impact of discretization effects on closed-loop dynamic response. System stability is rigorously verified through pole-zero analysis in the Z-plane. Performance evaluation encompasses time-domain metrics rise time, settling time, percent overshoot, and steady-state error supplemented by integral performance indices (ISE, IAE, and ITAE). The Tinkercad implementation yields an underdamped response (tr = 0.827 s, ts = 13.74 s, Mp = 64.78%, ess = 0), while the Simulink simulation produces a critically damped response without overshoot. These discrepancies are quantitatively attributed to finite-precision arithmetic, computational delay, and PWM output resolution constraints inherent to the microcontroller platform. The findings underscore the critical necessity of implementation-aware evaluation in the development of reliable embedded control systems.