A Fractional Order Proportional and Derivative (FOPD) Motion Controller: Tuning Rule and Experiments

In recent years, it is remarkable to see the increasing number of studies related to the theory and application of fractional order controller (FOC), specially PI ¿ D ¿ controller, in many areas of science and engineering. Research activities are focused on developing new analysis and design methods for fractional order controllers as an extension of classical control theory. In this paper, a new tuning method for fractional order proportional and derivative (PD ¿) or FO-PD controller is proposed for a class of typical second-order plants. The tuned FO-PD controller can ensure that the given gain crossover frequency and phase margin are fulfilled, and furthermore, the phase derivative w. r. t. the frequency is zero, i.e., the phase Bode plot is flat at the given gain crossover frequency. Consequently, the closed-loop system is robust to gain variations. The FOC design method proposed in the paper is practical and simple to apply. Simulation and experimental results show that the closed-loop system can achieve favorable dynamic performance and robustness.

[1]  Xavier Moreau,et al.  The CRONE Suspension , 1996 .

[2]  Y. Chen,et al.  A fractional order PID tuning algorithm for a class of fractional order plants , 2005, IEEE International Conference Mechatronics and Automation, 2005.

[3]  I. Podlubny.  Fractional-Order Systems and -Controllers , 1999 .

[4]  YangQuan Chen,et al.  Fractional order PID control of a DC-motor with elastic shaft: a case study , 2006, 2006 American Control Conference.

[5]  Igor Podlubny,et al.  Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers , 1999 .

[6]  I. Podlubny.  Fractional-order systems and PIλDμ-controllers , 1999, IEEE Trans. Autom. Control..

[7]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[8]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[9]  Alain Oustaloup,et al.  The CRONE toolbox for Matlab , 2000, CACSD. Conference Proceedings. IEEE International Symposium on Computer-Aided Control System Design (Cat. No.00TH8537).

[10]  J. G. Ziegler,et al.  Optimum Settings for Automatic Controllers , 1942, Journal of Fluids Engineering.

[11]  Naresh K. Sinha,et al.  Modern Control Systems , 1981, IEEE Transactions on Systems, Man, and Cybernetics.

[12]  Alain Oustaloup,et al.  From fractal robustness to the CRONE control , 1999 .

[13]  YangQuan Chen,et al.  Fractional Horsepower Dynamometer - A General Purpose Hardware-In-The-Loop Real-Time Simulation Platform for Nonlinear Control Research and Education , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.