A PID tuning problem is the multivariate optimization task of choosing Kp, Ki, and Kd to produce a desirable control response. Because the parameters interact, reference tables guide tuning but do not guarantee independent effects. section 8.7
Evaluate candidate settings with response-quality metrics:
- ITAE penalizes errors that persist over time, emphasizing transient response and settling time. section 8.7
- ITSE penalizes persistent errors while emphasizing larger errors through squaring. section 8.7
- IAE measures total error magnitude without weighting its duration. section 8.7
- ISE emphasizes large errors through squaring. section 8.7
Optimizing a simulated controller with a genetic algorithm
Model a transfer function, compute its step response, define a performance objective, and search Kp, Ki, and Kd with a genetic algorithm. A pymoo implementation uses 50 individuals for 60 generations, then plots the best response and reports rise time, settling time, overshoot, and steady-state value.
