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Design and Implementation of Interior-Point Method Based Linear Model Predictive Controller

  • Vihangkumar V. Naik
  • D. N. Sonawane
  • Deepak D. Ingole
  • Divyesh L. Ginoya
  • Neha S. Girme
Part of the Communications in Computer and Information Science book series (CCIS, volume 296)

Abstract

Linear model predictive control (MPC) assumes a linear system model, linear inequality constraints and a convex quadratic cost function. Thus, it can be formulated as a quadratic programming (QP) problem. Due to associated computational complexity of QP solving algorithms, its applicability is restricted to relatively slow dynamic systems. This paper presents an interior-point method (IPM) based QP solver for the solution of optimal control problem in MPC. We propose LU factorization to solve the system of linear equations efficiently at each iteration of IPM, which renders faster execution of MPC. The approach is demonstrated practically by applying MPC to QET DC Servomotor for position control application.

Keywords

Model Predictive Control Interior-Point Method LU factorization DC Servomotor 

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References

  1. 1.
    Wills, A.G., Heath, W.P.: Interior-Point Methods For Linear Model Predictive Control. In: Control 2004. University of Bath, UK (2004)Google Scholar
  2. 2.
    Wills, A., Mills, A., Ninness, B.: FPGA Implementation of an Interior-Point Solution for Linear Model Predictive Control. In: Preprints of the 18th IFAC World Congress, Milano, Italy, pp. 14527–14532 (2011)Google Scholar
  3. 3.
    Rao, C.V., Wright, S.J., Rawlings, J.B.: Application of interior point methods to model predictive control. Journal of Optimization Theory and Applications, 723–757 (1998)Google Scholar
  4. 4.
    Ling, K.V., Yue, S.P., Maciejowski, J.M.: A FPGA Implementation of Model Predictive Control. In: Proceedings of the 2006 American Control Conference, Minneapolis, Minnesota, USA, pp. 1930–1935 (2011)Google Scholar
  5. 5.
    Sudarsanam, A., Hauser, T., Dasu, A., Young, S.: A Power Efficient Linear Equation Solver on a Multi-FPGA Accelerator. International Journal of Computers and Applications 32(1), 1–19 (2010)CrossRefGoogle Scholar
  6. 6.
    Chai, W., Jiao, D.: An LU Decomposition Based Direct Integral Equation Solver of Linear Complexity and Higher-Order Accuracy for Large-Scale Interconnect Extraction. IEEE Transactions on Advanced Packaging 33(4), 794–803 (2010)CrossRefGoogle Scholar
  7. 7.
    Mehrotra, S.: On Implementation of a primal-dual interior-point method. SIAM Journal on Optimization 2(4), 575–601 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Maciejowski, J.M.: Predictive Control with Constraints. Pearson Education LimitedGoogle Scholar
  9. 9.
    Wright, S.J.: Applying new optimization algorithms to model predictive control. In: Chemical Process Control-V, CACHE, AIChE Symposium Series, vol. 93(316), pp. 147–155 (1997)Google Scholar
  10. 10.
    Wills, A.G.: EE04025 - Notes on Linear Model Predictive Control. Technical Report (2004)Google Scholar
  11. 11.
    Kruth, T.R.: Interior-Point Algorithms for Quadratic Programming. IMM-M.Sc-2008-19, Technical University of Denmark (2008)Google Scholar
  12. 12.
    Nejdawi, I.M.: An Efficient interior Point Method for Sequential Quadratic Programming Based Optimal Power Flow. IEEE Trasactions on Power Systems 15(4), 1179–1183 (2000)CrossRefGoogle Scholar
  13. 13.
    Wills, A.G., Heath, W.P.: EE03016 Inerior-Point Methods for Linear Model Predictive Control. Technical Report, University of Newcastle, Australia (2003)Google Scholar
  14. 14.
    Stinga, F., Roman, M., Soimu, A., Bobasu, E.: Optimal and MPC Control of the Quanser Flexible Link Experiment. In: 4th WSEAS/IASME International Conference on Dynamical Systems and Control (Control 2008), Greece, pp. 175–180 (2008)Google Scholar
  15. 15.
    Introduction to QuaRc 2.0 & DCMCT Instructor manual and Hardware Guide. Quanser Inc., Markham, ON, Canada (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Vihangkumar V. Naik
    • 1
  • D. N. Sonawane
    • 1
  • Deepak D. Ingole
    • 1
  • Divyesh L. Ginoya
    • 1
  • Neha S. Girme
    • 1
  1. 1.Department of Instrumentation & Control EngineeringCollege of EngineeringPuneIndia

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