Volume 13 Number 5
October 2016
Article Contents
Shamik Misra, Rajasekhara Reddy and Prabirkumar Saha. Model Predictive Control of Resonant Systems Using Kautz Model. International Journal of Automation and Computing, vol. 13, no. 5, pp. 501-515, 2016. doi: 10.1007/s11633-016-0954-x
Cite as: Shamik Misra, Rajasekhara Reddy and Prabirkumar Saha. Model Predictive Control of Resonant Systems Using Kautz Model. International Journal of Automation and Computing, vol. 13, no. 5, pp. 501-515, 2016.

# Model Predictive Control of Resonant Systems Using Kautz Model

Author Biography:
• ORCID iD: 0000-0002-1684-4174

E-mail: rajasekhara@iitg.ernet.in

• Corresponding author: ORCID iD: 0000-0002-1121-1829
• Accepted: 2015-02-15
• Published Online: 2016-04-27
• The scope of this paper broadly spans in two areas: system identification of resonant system and design of an efficient control scheme suitable for resonant systems. Use of filters based on orthogonal basis functions (OBF) have been advocated for modelling of resonant process. Kautz filter has been identified as best suited OBF for this purpose. A state space based system identification technique using Kautz filters, viz. Kautz model, has been demonstrated. Model based controllers are believed to be more efficient than classical controllers because explicit use of process model is essential with these modelling techniques. Extensive literature search concludes that very few reports are available which explore use of the model based control studies on resonant system. Two such model based controllers are considered in this work, viz. model predictive controller and internal model controller. A model predictive control algorithm has been developed using the Kautz model. The efficacy of the model and the controller has been verified by two case studies, viz. linear second order underdamped process and a mildly nonlinear magnetic ball suspension system. Comparative assessment of performances of these controllers in those case studies have been carried out.
•  [1] C. T. Huang, C. J. Chou. Estimation of the under damped second-order parameters from the system transient. Industrial and Engineering Chemistry Research, vol. 33, no. 1, pp. 174-176, 1994.  doi: 10.1021/ie00025a024 [2] K. J. Åström, T. Hägglund. PID Controllers: Theory, Design, and Tuning, New York, USA: The International Society of Automation, 1995. [3] W. K. Ho, C. C. Hang, J. H. Zhou. Self tuning PID control of a plant with under damped response with specifications on gain and phase margins. IEEE Transactions on Control System Technology, vol. 5, no. 4, pp. 446-452, 1997. [4] C. Brosilow, B. Joseph. Techniques of Model-based Control, New Jersey, USA: Prentice-Hall, 2002. [5] D. E. Riveara, M. Morari, S. Skogestad. Internal model control: PID controller design. Industrial and Engineering Chemistry Process Design and Development, vol. 25, no. 1, pp. 252-265, 1986.  doi: 10.1021/i200032a041 [6] B. W. Bequette. Process Control: Modeling, Design, and Simulation, New Jersey, USA: Prentice Hall PTR, 2003. [7] K. S. Holkar, L. M. Waghmare. An overview of model predictive control. International Journal of Control and Automation, vol. 3, no. 4, pp. 47-63, 2010. [8] I. Rivals, L. Personnaz. Black-box modeling with statespace neural networks. Neural Adaptive Control Technology I, pp. 237-264, 1996. [9] A. da Rosa, R. J. G. B. Campello, W. C. Amral. Exact search directions for optimization of linear and nonlinear models based on generalized orthonormal functions. IEEE Transactions on Automatic Control, vol. 54, no. 12, pp. 2757-2772, 2009.  doi: 10.1109/TAC.2009.2031721 [10] W. Mi, T. Qian, F. Wan. A fast adaptive model reduction method based on Takenaka-Malmquist systems. Systems & Control Letters, vol. 61, no. 1, pp. 223-230, 2012. [11] P. Saha, S. C. Patwardhan, V. S. R. Rao. Maximizing productivity of a continuous feremeter using nonlinear adaptive control. Bioprocess Engineering, vol. 20, no. 1, pp. 15-20, 1999.  doi: 10.1007/s004490050553 [12] B. Wahlberg, P. M. Mäkilä. On approximation of stable linear dynamical systems using Laguerre and Kautz functions. Automatica, vol. 32, no. 5, pp. 693-708, 1996.  doi: 10.1016/0005-1098(95)00198-0 [13] W. H. Kautz. Transient synthesis in the time domain. Transactions of the IRE Professional Group on Circuit Theory, vol. CT-1, no. 3, pp. 29-39, 1954. [14] B.Wahlberg. Identification of resonant systems using Kautz filters. In Proceedings of the 30th IEEE Conference on Decision and Control, IEEE, Brighton, UK, pp. 2005-2010, 1991. [15] P. S. Agachi, Z. K. Nagy, M. V. Cristea, A. I. Lucaci. Model Based Control, New York, USA: John Wiley & Sons Inc., 2007.
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## Model Predictive Control of Resonant Systems Using Kautz Model

• ###### Corresponding author:ORCID iD: 0000-0002-1121-1829

Abstract: The scope of this paper broadly spans in two areas: system identification of resonant system and design of an efficient control scheme suitable for resonant systems. Use of filters based on orthogonal basis functions (OBF) have been advocated for modelling of resonant process. Kautz filter has been identified as best suited OBF for this purpose. A state space based system identification technique using Kautz filters, viz. Kautz model, has been demonstrated. Model based controllers are believed to be more efficient than classical controllers because explicit use of process model is essential with these modelling techniques. Extensive literature search concludes that very few reports are available which explore use of the model based control studies on resonant system. Two such model based controllers are considered in this work, viz. model predictive controller and internal model controller. A model predictive control algorithm has been developed using the Kautz model. The efficacy of the model and the controller has been verified by two case studies, viz. linear second order underdamped process and a mildly nonlinear magnetic ball suspension system. Comparative assessment of performances of these controllers in those case studies have been carried out.

Shamik Misra, Rajasekhara Reddy and Prabirkumar Saha. Model Predictive Control of Resonant Systems Using Kautz Model. International Journal of Automation and Computing, vol. 13, no. 5, pp. 501-515, 2016. doi: 10.1007/s11633-016-0954-x
 Citation: Shamik Misra, Rajasekhara Reddy and Prabirkumar Saha. Model Predictive Control of Resonant Systems Using Kautz Model. International Journal of Automation and Computing, vol. 13, no. 5, pp. 501-515, 2016.
Reference (15)

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