Digital Design of Robust Fractional PID Controller for Uncertain Systems

B. Saidi; Messaoud Amairi; Slaheddine Najar; Mohamed Aoun

doi:10.15866/iremos.v9i5.10474

Digital Design of Robust Fractional PID Controller for Uncertain Systems

B. Saidi^(1*), Messaoud Amairi⁽²⁾, Slaheddine Najar⁽³⁾, Mohamed Aoun⁽⁴⁾

^(*) Corresponding author

Authors' affiliations

DOI: https://doi.org/10.15866/iremos.v9i5.10474

Abstract

This paper deals with digital fractional order PID controller design. A numerical constrained optimization and a bilinear transform to convert continuous-time system to discrete-time system and vice-versa are used in this design method. To obtain the fractional controller parameters a design approach uses bilinear transforminstead of analog design. Then to discrete the controller a simple substitution is used.By considering explicitly the parameters uncertainties, the proposed method offers more robustness for digital control system. A numerical example and an application to the liquid carbon monoxide level control are considered to show the efficiency of theproposed methodespecially in term of robustness and in calculation time by the use of higher sampling period.
Copyright © 2016 Praise Worthy Prize - All rights reserved.

Keywords

Constrained Numerical Optimization; Digital Design; Fractional Controller; Parameter Uncertainty; Robustness

Full Text:

PDF

References

Amairi M, Aoun M and Saidi B (2014) Design of robust fractional rder PI for FOPDT systems via set inversion. In: Control Applications (CCA), 2014 IEEE Conference on. IEEE, pp. 1166–1171.
http://dx.doi.org/10.1109/cca.2014.6981486

Barbosa RS, Machado JT and Ferreira IM (2004) Tuning of PID controllers based on bodes ideal transfer function.Nonlinear dynamics 38(1-4): 305–321.
http://dx.doi.org/10.1007/s11071-004-3763-7

Ben Hmed A, Amairi M, Najar S and Abdelkrim MN (2013) Design of fractional PI controller with guaranteed time and frequency-domain performances. In: 10th International Multi-Conference on Systems, Signals & Devices (SSD). IEEE, pp. 1–6.
http://dx.doi.org/10.1109/ssd.2013.6564103

Charef A (2006) Analogue realization of fractional-order integrator, differentiator and fractional PIλDµcontroller.IEE Proceedings-Control Theory and Applications 153(6): 714–720.
http://dx.doi.org/10.1049/ip-cta:20050019

Das S, Saha S, Das S and Gupta A (2011) On the selection of tuning methodology of FOPID controllers for the control of higher order processes. ISA transactions 50(3)
http://dx.doi.org/10.1016/j.isatra.2011.02.003

Feliu-Batlle V, Rivas R and Castillo F (2009) Fractional order controller robust to time delay variations for water distribution in an irrigation main canal pool. Computers and Electronics in agriculture 69: 185–197.
http://dx.doi.org/10.1016/j.compag.2009.08.005

Hamamci SE (2008) Stabilization using fractional-order PI and PID controllers. Nonlinear Dynamics 51(1-2): 329–343.
http://dx.doi.org/10.1007/s11071-007-9214-5

Hmed AB, Amairi M and Aoun M (2016) Robust stabilization and control using fractional order integrator.Transactions of the Institute of Measurement and Control : 0142331216645178.
http://dx.doi.org/10.1177/0142331216645178

Monje C, Vinagre B, Feliu V and Chen Y (2008) Tuning and auto-tuning of fractional order controllers for industry applications. Control Engineering Practice 16(7): 798–812.
http://dx.doi.org/10.1016/j.conengprac.2007.08.006

O’Dwyer A (2009) Handbook of PI and PID controller tuning rules, volume 57. World Scientific.
http://dx.doi.org/10.1142/p575

Petras I (2009) Fractional-order feedback control of a dc motor. Journal of Electical Engineering 21: 3182–3187.
http://dx.doi.org/10.1109/acc.2009.5160719

Podlubny I (1999) Fractional-order systems and PIλDν controller. IEEE Transaction on automatic Control 44:208–214.
http://dx.doi.org/10.1109/9.739144

Pop CI, Ionescu C, De Keyser R and Dulf EH (2012) Robustness evaluation of fractional order control for varying time delay processes. Signal, Image and Video Processing 6(3): 453–461.
http://dx.doi.org/10.1007/s11760-012-0322-4

Saidi B, Amairi M, Najar S and Aoun M (2014a) Fractional PI design for time delay systems based on min-max optimization. In: InternationalConference on Fractional Differenciation and its applications (ICFDA). IEEE
http://dx.doi.org/10.1109/icfda.2014.6967440

Saidi B, Amairi M, Najar S and Aoun M (2014b) Min-max optimization-based design of fractional PID controller.In: International Conference on Sciences and Techniques of Automatic control(STA). IEEE, pp. 1–6.
http://dx.doi.org/10.1109/sta.2014.7086745

Saidi B, Amairi M, Najar S and Aoun M (2015a) Bode shaping-based design methods of a fractional order PID controller for uncertain systems. Nonlinear Dynamics 80(4): 1817–1838.
http://dx.doi.org/10.1007/s11071-014-1698-1

Saidi B, Amairi M, Najar S and Aoun M (2015b) Multi-objective optimization based design of fractional PID controller. In: 12th International Multi-Conference on Systems, Signals & Devices (SSD). IEEE, pp. 1–6.
http://dx.doi.org/10.1109/ssd.2015.7348218

Saidi B, Najar S, Amairi M and ABDELKRIM MN (2012) Design and digital implementation of a fractional PIDcontroller. In: 4 eme Colloque de Recherche Appliquee et de Transfert de Technologie (CRATT2012).
http://dx.doi.org/10.1109/ssd.2013.6564102

Saidi B, Najar S, Amairi M and Abdelkrim MN (2013) Design of a robust fractional PID controller for a second order plus dead time system. In: 10th International Multi-Conference on Systems, Signals & Devices (SSD). IEEE, pp. 1–6.
http://dx.doi.org/10.1109/ssd.2013.6564102

Sangyam T, Laohapiengsak P, Chongcharoen W and Nilkhamhang I (2010) Path tracking of uav using self-tuning PID controller based on fuzzy logic. In: SICE Annual Conference 2010, Proceedings of. IEEE, pp. 1265–1269.
http://dx.doi.org/10.1109/iecon.2015.7392862

Valerio D and da Costa J (2010) A review of tuning methods for fractional PIDs. In: 4th IFAC Workshop on Fractional Differentiation and Its Applications, FDA, volume 10.
http://dx.doi.org/10.1007/978-1-4020-6042-7_32

Deif, T., Kassem, A., El Baioumi, G., Modeling and Attitude Stabilization of Indoor Quad Rotor, (2014) International Review of Aerospace Engineering (IREASE), 7 (2), pp. 43-47.
http://dx.doi.org/10.15866/irease.v7i2.783

Payam, A., Hassani, F., Fathipour, M., Design of Hybrid Closed Loop Control Systems for a MEMS Accelerometer Using Nonlinear Control Principles, (2014) International Review of Aerospace Engineering (IREASE), 7 (5), pp. 164-170.
http://dx.doi.org/10.15866/irease.v7i5.4972

Bouallegue, S., Khoud, K., Integral Backstepping Control Prototyping for a Quad Tilt Wing Unmanned Aerial Vehicle, (2016) International Review of Aerospace Engineering (IREASE), 9 (5), pp. 152-161.
http://dx.doi.org/10.15866/irease.v9i5.10476

Swain, S., Khuntia, P., Kharitonov Based Robust Stability for a Flight Controller, (2013) International Review of Aerospace Engineering (IREASE), 6 (6), pp. 290-297.

Jin, Y., Lee, S., Kim, S., Yoon, Y., A Control Scheme for Price-Responsive Generations and Loads in support of Frequency Control within a Decentralized Environment, (2014) International Review of Electrical Engineering (IREE), 9 (3), pp. 527-537.

Vikhram, G., Latha, S., Vikhram, G., Robust Shunt FACTS Controller Design for Power System Damping Improvement, (2013) International Review of Electrical Engineering (IREE), 8 (2), pp. 792-809.

Ibrahim, H., Mahmoud, A., DC Motor Control Using PID Controller Based on Improved Ant Colony Algorithm, (2014) International Review of Automatic Control (IREACO), 7 (1), pp. 1-6.
http://dx.doi.org/10.15866/ireaco.v7i1.1283

Taki El-Deen, A., Mahmoud, A., R. El-Sawi, A., Optimal PID Tuning for DC Motor Speed Controller Based on Genetic Algorithm, (2015) International Review of Automatic Control (IREACO), 8 (1), pp. 80-85.
http://dx.doi.org/10.15866/ireaco.v8i1.4839

Gaya, M., Bisu, A., Salim, S., Madugu, I., Yusuf, L., Kaurangini, M., Khairi, M., Optimal PID Design Approaches for an Inverted Pendulum System, (2016) International Review of Automatic Control (IREACO), 9 (3), pp. 167-174.
http://dx.doi.org/10.15866/ireaco.v9i3.9160

Ćalasan, M., Dlabač, T., Ostojić, M., PID Parameters Determination of Synchronous Machine AVR System, (2013) International Review of Automatic Control (IREACO), 6 (4), pp. 425-430.

Tovar-Rivera, A., Amaya-Hurtado, D., Carrillo, J., Automation of Pneumatic Actuators for Testing of Small-Specimens Using Mini Load-Frames, (2016) International Review of Mechanical Engineering (IREME), 10 (6), pp. 373-380.
http://dx.doi.org/10.15866/ireme.v10i6.8808

Refbacks

There are currently no refbacks.

Username
Password
Remember me