Transients and Stability: Electrical Systems Study with PID Tuning Methods Controller

Abstract

The transient response of electrical circuits often exhibits undesirable oscillations that hinder precise voltage regulation. This paper presents a comprehensive simulation-based study of a series RLC circuit and a buck converter controlled by proportional-integral-derivative (PID) controllers. Four tuning strategies are compared: manual tuning, Ziegler-Nichols, particle swarm optimization (PSO), and genetic algorithm (GA). Performance is assessed using time-domain metrics (overshoot, settling time, IAE, ITAE) and frequency-domain tools (Bode, Nyquist, sensitivity functions). Robustness is evaluated through parameter variations (R, L, C, ω₀, ζ), dynamic setpoint tracking, external disturbances, and Monte Carlo analysis (±20% component tolerances). The open-loop RLC circuit exhibits 80% overshoot and a settling time of 0.382 s. Manual PID tuning reduces overshoot to 13.7%, settling time to 0.024 s, and eliminates steady-state error. Ziegler-Nichols yields zero overshoot but an extremely slow response (rise time 0.617 s). PSO and GA produce the fastest rise times (5.6 ms) but increase overshoot to ≈21% and reduce phase margins to ≈8°, indicating fragility to model uncertainties. The manual PID demonstrates robust performance under all tested variations and maintains acceptable metrics under Monte Carlo simulation (mean overshoot 13.1%). For the buck converter, an optimized PID reduces the IAE by a factor of 2.5 compared to manual tuning, with identical control energy. This study confirms that the choice of PID tuning involves a clear trade-off between speed, overshoot, robustness, and control effort. Manual tuning offers the best balance for the RLC circuit, while optimization is highly beneficial for fast power electronics applications.