Constrained Genetic-Algorithm-Based PID Gain Optimization for Servo Control of a Diverter Valve in a 200 kg Gravimetric Liquid Flow Calibration Module

Genetic algorithms provide a flexible strategy for tuning control parameters in engineering systems where nonlinear dynamics, variable loads, and physical constraints make fixed-gain controllers difficult to adjust systematically. This work formulates and experimentally validates a constrained genetic-algorithm-based optimization strategy for PID gain tuning in the servo-electric actuation of a diverter valve in a 200 kg gravimetric module, operating in the interval from 2 L/min to 40 L/min. The optimization problem is defined by treating the PID gains as decision variables, bounded by feasible intervals obtained from classical PID tuning, and evaluated through a weighted fitness function that includes accumulated tracking error, normalized switching-time deviation, overshoot, normalized steady-state position error, and a penalty term for unsuccessful or infeasible simulated responses. The gravimetric module is used as a real engineering case study in which the hydrodynamic load varies with the flow rate and the angular position of the valve. At 40 L/min, the original pneumatic system presented a collection-interval standard deviation of 0.6149 s, while with the servo-electric system and the optimized PID, this value decreased to 0.0832 s, equivalent to a reduction of 86.5%. Likewise, the relative diverter-associated contribution decreased from 5.10% to 0.688%. The results show that constrained evolutionary PID gain optimization improves the repeatability of the effective collection interval and reduces the equivalent mass variability associated with the diverter under changing hydraulic conditions, although this contribution does not represent, by itself, the complete uncertainty budget of the gravimetric module.