Advanced Control Strategies for Crouzet DC and Mitsubishi SC-QR AC Motors: A Review of Mathematical Models and Simulations

Abstract

This paper reviews the mathematical modeling and simulation of two distinct motor types: the Crouzet DC motor (model 82800502) and the Mitsubishi Electric SC-QR 1/2 HP 1-phase AC motor. The study focuses on deriving their electromechanical models using differential equations, Laplace transforms, and transfer functions to analyze their dynamic behaviors. For the Crouzet DC motor, key parameters such as armature resistance (3.9 Ω), inductance (9.35 mH), torque constant (0.0627 Nm/A), and mechanical time constant (15 ms) are utilized to develop first and second-order transfer functions. The Mitsubishi AC motor, a capacitor-start induction motor, is modeled considering stator resistance (4 Ω), inductance (162 mH), and rotor inertia (0.003 kg.m²), with emphasis on dq-axis transformations for dynamic analysis.

The transient and steady-state responses of both motors are simulated using MATLAB/Scilab, highlighting the DC motor's faster response (10 ms rise time) due to linear dynamics, compared to the AC motor's slower start-up (0.5 s) influenced by its starting capacitor. Stability analysis reveals that the DC motor's dominance of mechanical dynamics ensures robustness, while the AC motor requires careful tuning to mitigate transient disturbances during capacitor switching. Block diagram reduction techniques are applied to simplify control system designs, demonstrating the DC motor's suitability for precision applications (e.g., robotics [2], [5], [6]) and the AC motor's efficiency (>70%) in steady-state operations.

The study underscores the importance of accurate modeling for controller design, proposing PID and adaptive strategies for performance optimization. Challenges such as parameter estimation uncertainties and nonlinear effects (e.g., flux saturation in AC motors) are discussed, along with recommendations for experimental validation and advanced digital control implementations (e.g., DSP-based V/f control). This review provides a foundation for future work on real-time simulations and hardware-in-the-loop testing to bridge theoretical models and practical applications.