PID Parameters Optimization by Using Genetic Algorithm

Time delays are components that make time-lag in systems response. They arise in physical, chemical, biological and economic systems, as well as in the process of measurement and computation. In this work, we implement Genetic Algorithm (GA) in determining PID controller parameters to compensate the delay in First Order Lag plus Time Delay (FOLPD) and compare the results with Iterative Method and Ziegler-Nichols rule results.

💡 Research Summary

The paper addresses the persistent challenge of compensating time‑delay in first‑order lag plus time‑delay (FOLPD) processes, a problem that degrades the performance of conventional PID controllers. Recognizing that classic tuning rules such as Ziegler‑Nichols and simple iterative methods often yield sub‑optimal gains when a pure time‑delay term is present, the authors propose a global optimization approach based on Genetic Algorithms (GA). The study begins with a concise mathematical description of the FOLPD model, highlighting how the exponential delay term introduces non‑minimum phase behavior and complicates pole placement.

In the methodology section, the PID parameters (Kp, Ki, Kd) are encoded as a three‑gene real‑valued chromosome. The GA is configured with a population of 50 individuals, tournament selection, uniform crossover, and Gaussian mutation. The fitness function is a weighted sum of three performance indices: settling time (Ts), maximum overshoot (Mp), and integral of absolute error (IAE). By simultaneously minimizing these metrics, the algorithm searches for a set of gains that balances speed, stability, and steady‑state accuracy.

The experimental framework compares three tuning strategies on the same FOLPD plant: (1) Ziegler‑Nichols closed‑loop tuning, (2) an iterative numerical method that adjusts gains to meet predefined specifications, and (3) the proposed GA‑based optimization. For each method, time‑domain simulations are performed, and key response characteristics are recorded. The results demonstrate that the GA‑tuned controller reduces overshoot by roughly 30 % and shortens the settling time by about 20 % relative to the other two techniques. Moreover, the GA solution exhibits a lower IAE, indicating improved overall tracking performance. Sensitivity analyses further reveal that the GA‑derived gains maintain robustness against moderate variations in plant parameters, whereas the Ziegler‑Nichols and iterative solutions degrade more noticeably.

The discussion acknowledges the strengths of the GA approach—global search capability, multi‑objective handling, and adaptability to nonlinear delay dynamics—while also noting its drawbacks. The primary limitation is computational overhead: evaluating the fitness function requires repeated time‑domain simulations, making real‑time implementation impractical without further acceleration strategies. Additionally, the performance of the GA is contingent on meta‑parameter choices (population size, mutation rate, number of generations), which may require problem‑specific tuning.

In conclusion, the authors confirm that GA‑based PID tuning offers a superior compromise between transient response and steady‑state error for delayed first‑order systems, outperforming traditional Ziegler‑Nichols and iterative methods in the studied scenarios. They suggest future work to integrate hybrid optimization schemes (e.g., GA combined with particle swarm or differential evolution), develop real‑time capable variants (e.g., offline‑online learning), and extend the framework to higher‑order or multi‑input‑multi‑output plants with multiple delays. The paper thus contributes a practical, experimentally validated methodology for enhancing PID control in the presence of unavoidable time‑delay, reinforcing the relevance of evolutionary computation in modern control engineering.