Heuristic kalman algorithm optimization: Application in H∞ - PID controller tuning of Lagrangian system

This paper deals with the application of a randomized optimization method to obtain the optimum PID gains. This method is based on a heuristic Kalman algorithm (HKA) and is described as more speedy and more accurate optimization methods. First, we introduce the general form of the H_∞ control law obtained by solving a partial differential equation labeled Hamilton-Jacobi-Isaacs equation. An analytic solution to this equation is described for the Euler-Lagrange Systems. Second, based on this solution and on the PID control law resulting, it is shown how to use the optimization method to adjust optimally the controller´s gains ensuring a minimum L₂ - gain and thus disturbance attenuation. Third, we apply this optimization algorithm in the trajectory tracking and disturbance attenuation problem of a three degree of freedom robot manipulator. The simulation results show the effectiveness of the H_∞-PID control law optimized by the HKA method.