Optimizing control motion of a human arm with PSO-PID controller

Functional electrical stimulation is the most commonly used system for restoring function after spinal cord injury. In this study, a model consists of a joint, two links with one degree of freedom, and two muscles as flexor and extensor of the joint, which simulated in MATLAB using Sim-Mechanics and Simulink Toolboxes, is used. The muscle model is based on Zajac musculotendon actuator and composed of a nonlinear recruitment curve, a nonlinear activation-frequency relationship, calcium dynamics, fatigue/recovery model, and an additional constant time delay, force -length and force-velocity factors. A classic controller for regulating the elbow joint angle; a Proportional- Integral- Derivative (PID) controller, is used. First, the PID coefficients are tuned using trial and error method, and then a particle swarm optimization (PSO) algorithm was used to optimize them. The important features of this algorithm include flexibility, simplicity, short solution time, and the ability to avoid local optimums. This PSO-PID controller uses the PSO algorithm to get the required pulse width for stimulating the biceps to reach the elbow joint to the desired angle. The fitness function is defined as sum square of error. The results of PSO -PID controller show the faster response for reaching the range of the set point than the PID controller tuned by trial and error. However, the PSO -PID is much better in terms of the rise time and the settling time, although the PID tuned by trial and error has no overshoot. The time to reach the zero steady state error is half in PSO -PID in comparison to PID tuned by trial and error.

Keywords:

Functional electrical stimulation (FES) , PID controller , Particle swarm optimization algorithm , Transverse plane