The Impact of Fitness Functions for Optimal Tuning of PID Controller Applied to DC Motor

This chapter presents a comparative analysis of different fitness functions for optimizing PID controller parameters using a genetic algorithm (GA) in the context of controlling the speed of a DC motor. The study focuses on three fitness functions: integral absolute error (IAE), mean squared error (MSE), and integral of time-weighted absolute error (ITAE). The GA is employed to iteratively adjust the PID gains (K-p, K-i, K-d) to optimize the control system's performance. Python libraries for control and GA are used for simulations, enabling analysis of system behavior under different fitness functions. The DC motor system is modeled using transfer functions and differential equations. The PID controller design is explained, highlighting its three components: proportional, integral, and derivative. A block diagram of the proposed controller with unit feedback is provided. The chapter discusses simulation and analysis results for each fitness function. The IAE fitness function shows the impact of mutation and crossover probabilities on system performance. The MSE fitness function has less influence on simulation results. The ITAE fitness function demonstrates that constant mutation yields better results than crossover. In conclusion, the chapter emphasizes the significance of selecting an appropriate fitness function for optimizing PID controller parameters. Simulation results provide insights into system performance under different fitness functions, aiding in the selection of optimal PID gains for controlling the DC motor's speed.