Optimal PID controller with evolutionary optimization algorithms for rehabilitation robots

• Published in: Discover applied sciences Vol. 7; no. 7; pp. 756 - 21
• Main Authors: Joyo, Kamran, Khan, Talha Ahmed, Kadir, Kushsairy Abdul, Bin Husen, Mohd Nizam, Nasir, Haidawati Mohamad, Azhar, Munaza
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 09.07.2025; Springer Nature B.V; Springer
• Subjects: Algorithms; Ant colony optimization; Applied and Technical Physics; Chemistry/Food Science; Comparative studies; Control algorithms; Control systems; Controllers; Cost function; Degree of freedom; Degrees of freedom; Dynamic models; Earth Sciences; Elbow; Engineering; Environment; Errors; Evolutionary algorithms; Firefly; Genetic algorithms; Gravity; Heuristic methods; Integral absolute error; Integral squared error; Manipulator; Materials Science; Mathematical models; Optimization; Parameters; Particle swarm optimization; Physical therapy; Process controls; Proportional integral derivative; Rehabilitation; Rehabilitation robots; Robotics; Robots; Settling; Settling behavior; Smoothness; Swarm intelligence; Systems stability; Tuning; Wrist; Integral squared error; Integral absolute error; Degree of freedom; Firefly; Upper extremity; Proportional integral derivative; Particle swarm optimization; Manipulator
• ISSN: 3004-9261; 2523-3963; 3004-9261; 2523-3971
• DOI: 10.1007/s42452-025-07424-0

Precision and smoothness in controlling mechanism is a mandatory requirement for those robotic applications, which are associated with upper limb rehabilitation and comprise of five degree of freedom. This study comprises of analysis of a vast range of techniques of optimization, for determining ideal parameters of a Proportional Integral Derivative (PID) controller, which is managing a dynamic model of the upper limb rehabilitation system. The control technique which has been proposed was carried out on a five-degree of freedom (DOF) hardware, and priory to any trials under clinics, more than five healthy subjects underwent trials following strict protocols. There exist evidences of rejection to the external disturbances by the control technique, alongside keeping the system stable during the course of harsh and extremely uneven circumstances. This research study validates the mathematical models for finding optimizing parameters of the PID, including a comparative study comprising of four diverse cost functions. The objective functions include Integral Absolute Error (IAE) and Integral Squared Error (ISE). A variety of PID tuning methods were assessed based on core performance indicators such as Integral Square Error (ISE), Integral Absolute Error (IAE), overshoot, rise time, and settling time. The PID controller tuned using Particle Swarm Optimization (PSO) struck a good balance, with relatively low IAE, moderate overshoot (4.51%), and a decent settling time of 8.28 s. The Firefly algorithm also delivered promising results, achieving the shortest rise time (0.689 s) and a quick settling time (1.08 s), while keeping the overshoot (4.45%) nearly on par with PSO. In comparison, Ant Colony Optimization (ACO) produced a significantly higher overshoot of 29.6% and longer settling behavior. The Artificial Bee Colony (ABC) method stood out with the lowest settling time (0.84 s) and minimal overshoot (4.29%). The classical Ziegler-Nichols approach, however, showed poor performance, with a high overshoot of 55.3% and slower system response. Overall, these outcomes suggest that nature-inspired techniques, especially Firefly and ABC, can offer more efficient and stable control than conventional tuning methods.