H ∞ nonlinear PID controller tuning based on simple constrained particle swarm optimisation

Rochdi Bachir Bouiadjra and Mohamed Fayçal Khelfi

International Journal of Industrial and Systems Engineering, 2015, vol. 21, issue 4, 515-533

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. (search for similar items in EconPapers)
Date: 2015
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