PID Tuning Using Differential Evolution With Success-Based Particle Adaptations

Proportional-Integral-Derivative (PID) is a simple and intuitive feedback-based control mechanism being useful to track set points and to reject disturbances. A key question in gradient-free optimization is to ascertain whether the class of optimization algorithms based on the difference of vectors generalize reasonably well to tackle a large class of PID control problems. For generalization and practical purposes, it would be desirable to render algorithms being able to tune PID controllers over a diverse and large set of control problems/tasks with minimal human intervention (self-adaptation features), and under tight computational budgets. In this paper, aiming to fill the above-mentioned gap, we propose and investigate the effectiveness of a new class of algorithm based on the difference of vectors and self-adaptation mechanisms for PID tuning. As such, we introduce a new class of Differential Evolution with success-based Particle Adaptations (DEPA), which unifies the principles of difference of vectors, particle schemes and trial/parameter adaptation through archive (memory) mechanisms. Our computational simulations using a large/relevant set of 25 control problem instances (tracking of linear, nonlinear, continuous, and discontinuous trajectories in motor position control, motor velocity control, magnetic levitation, inverted pendulum, crane stabilization), and the comparisons with a large set of closely related optimization algorithms, and their extended adaptive variants (23 optimization algorithms in total) has shown the outperforming benefits of the proposed approach in convergence performance under tight function evaluation budgets (1000 function evaluations). Also, the experiments on a real-world inverted pendulum device show the potential for transferability of the learned gains to unseen situations during training. Furthermore, we evaluated the algorithmic extension and the generalization towards diverse fitness landscapes in the CEC 2017 benchmark suite, showing the attractive/outperforming performance overall problem instances. In particular, the proposed framework performed better in 558 control instances when using ISE as a performance metric, and in 358 control instances when using IAE, ITAE and ITSE as performance metrics. Also, the algorithmic extension for general optimization landscapes performed better than the related algorithms in 182, 215 and 235 problem instances of CEC 2017 benchmark suite for 10, 30 and 50 dimensions, respectively. Our obtained results have the potential to further advance towards developing efficient and self-adaptive optimization algorithms based on the difference of vectors, which may find use in a wider set of optimization and control problems.