Title: H∞ nonlinear PID controller tuning based on simple constrained particle swarm optimisation
Authors: Rochdi Bachir Bouiadjra; Mohamed Fayçal Khelfi
Mathematics and Computer Science Department, University of Mascara, Mascara 29000, Algeria; Faculty of Exact and Applied Sciences, Laboratory of Research in Industrial Computing and Networks, University of Oran 31000, Algeria
Faculty of Exact and Applied Sciences, Laboratory of Research in Industrial Computing and Networks, University of Oran 31000, Algeria
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.
Keywords: nonlinear control; H-infinity control; stabilisation; trajectory tracking; disturbance attenuation; robot control; PID control; Hamilton-Jacobi-Isaacs equation; particle swarm optimisation; PSO; constrained optimisation; controller tuning; SCARA robots; simulation.
Int. J. of Industrial and Systems Engineering, 2015 Vol.21, No.4, pp.515 - 533
Available online: 28 Oct 2015