PID Controller Design Based on Laguerre Orthonormal Functions

In this paper, an analytical method for designing Proportional-Integral-Derivative (PID) controllers based on Laguerre orthonormal functions is presented. The PID controller parameters are calculated after matching the first three coefficients of Laguerre series of the open loop gain with the ideal one. To reach this goal, the plant, the PID controller and the ideal open loop gain transfer functions are represented in terms of their corresponding Laguerre series. The pole of the Laguerre basis function could be appropriately selected to assure the closed loop stability. Moreover, the optimum value of this parameter is determined to reach the best fitting to the desired step response considering the control signal constraint. The simulation results and the experimental tests on a DC servomotor system are given to show the effectiveness of the proposed method.