Abstract
This paper deals with the application of a randomised optimisation method to obtain the optimum weights of a nonlinear PID gains. This method is based on a particle swarm optimisation (PSO) and is described as more speedy and more accurate optimisation methods. First, a general form of the H∞ control law is given by solving the Hamilton-Jacobi-Isaacs partial differential equation. An analytic solution to this equation is described for the Euler-Lagrange Systems. Second, based on this solution and on the nonlinear PID control law resulting, it is shown how to use the optimisation method to adjust optimally the controller's weight ensuring a minimum L2-gain and thus disturbance attenuation. Third, the optimisation algorithm is used in the trajectory tracking and disturbance attenuation problem of a forth degree SCARA robot manipulator. The simulation results show the effectiveness of the nonlinear PID control law optimised by the PSO algorithm.
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