Karimi A., D. Garcia and R. Longchamp. PID Controller Tuning Using Bode’s Integrals. IEEE Transactions on Control Systems Technology, (November 2003), Vol. 11, No. 6, 812-821
Karimi A., D. Garcia and R. Longchamp. Iterative Controller Tuning using Bode’s Integrals. 41st IEEE Conference on Decision and Control, Las Vegas, Nevada USA / December 2002, 4227-4232
Karimi A., D. Garcia and R. Longchamp. PID Controller Design Using Bode’s Integrals. IEEE ACC, Anchorage, Alaska, USA (May 2002), 5007-5012 KARIMI Alireza, GARCIA Daniel, LONGCHAMP Roland
In this project, an iterative controller tuning based on a frequency criterion is proposed. The frequency criterion can be defined as the weighted sum of squared errors between the desired and measured gain margin, phase margin and crossover frequency. The method benefits from specific feedback relay tests to determine the gain margin, the phase margin and the crossover frequency of the closed-loop system. The Bode’s integrals are used to approximate the derivatives of amplitude and phase of the plant model with respect to the frequency without any model of the plant. This additional information is employed to estimate the gradient and the Hessian of the frequency criterion in the iterative controller tuning method. Simulation examples and experimental results illustrate the effectiveness and the simplicity of the proposed method to design and tune the controllers.
New nonlinear experiments will be designed to measure directly the modulus margin (the inverse of the infinity norm of the closed-loop sensitivity function). This new information can be used in an iterative robust controller tuning approach.