Control Theory for Automation – Advanced Techniques

Part of the Springer Handbooks book series (SHB)


Analysis and design of control systems is a complex field. In order to develop appropriate concepts and methods to cover this field, mathematical models of the processes to be controlled are needed to apply. In this chapter mainly continuous-time linear systems with multiple input and multiple output (MIMO systems) are considered. Specifically, stability, performance, and robustness issues, as well as optimal control strategies are discussed in detail for MIMO linear systems. As far as system representations are concerned, transfer function matrices, matrix fraction descriptions, and state-space models are applied in the discussions. Several interpretations of all stabilizing controllers are shown for stable and unstable processes. Performance evaluation is supported by applying H 2 and H norms. As an important class for practical applications, predictive controllers are also discussed. In this case, according to the underlying implementation technique, discrete-time process models are considered. Transformation methods using state variable feedback are discussed, making the operation of nonlinear dynamic systems linear in the complete range of their operation. Finally, the sliding control concept is outlined.


Robust Stability Linear Quadratic Regulator Recede Horizon Control Transfer Function Matrix Generalize Predictive Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



dynamic matrix control


eigenvalue–eigenvector decomposition


generalized predictive control




instrument meteorological condition


internal model controller


left matrix fraction description


linear quadratic


linear quadratic regulator


multifunction display


multi-input multi-output


model-based predictive control


nominal performance


nondeterministic polynomial-time


nominal stability


receding horizon control


right matrix fraction description




robust stability


single-input single-output


  1. 10.1.
    T. Kailath: Linear Systems (Prentice Hall, Upper Saddle River 1980)zbMATHGoogle Scholar
  2. 10.2.
    G.C. Goodwin, S.F. Graebe, M.E. Salgado: Control System Design (Prentice Hall, Upper Saddle River 2000)Google Scholar
  3. 10.3.
    W.S. Levine (Ed.): The Control Handbook (CRC, Boca Raton 1996)zbMATHGoogle Scholar
  4. 10.4.
    B.G. Lipták (Ed.): Instrument Engineersʼ Handbook, Process Control and Optimization, 4th edn. (CRC, Boca Raton 2006)Google Scholar
  5. 10.5.
    P.K. Sinha: Multivariable Control (Marcel Dekker, New York 1984)zbMATHGoogle Scholar
  6. 10.6.
    S. Skogestad, I. Postlethwaite: Multivariable Feedback Control (Wiley, New York 2005)Google Scholar
  7. 10.7.
    A.F. DʼSouza: Design of Control Systems (Prentice Hall, Upper Saddle River 1988)Google Scholar
  8. 10.8.
    R. Bars, P. Colaneri, L. Dugard, F. Allgöwer, A. Kleimenow, C. Scherer: Trends in theory of control system design, 17th IFAC World Congr., Seoul, ed. by M.J. Chung, P. Misra (IFAC Coordinating Committee on Design Methods, San Francisco 2008) pp. 93–104Google Scholar
  9. 10.9.
    K.J. Åström, B. Wittenmark: Computer-Controlled Systems: Theory and Design (Prentice Hall, Upper Saddle River 1997)Google Scholar
  10. 10.10.
    G.C. Goodwin, R.H. Middleton: Digital Control and Estimation: a Unified Approach (Prentice Hall, Upper Saddle River 1990)zbMATHGoogle Scholar
  11. 10.11.
    R. Isermann: Digital Control Systems, Vol. I. Fundamentals, Deterministic Control (Springer, Berlin Heidelberg 1989)zbMATHGoogle Scholar
  12. 10.12.
    R. Isermann: Digital Control Systems, Vol. II. Stochastic Control, Multivariable Control, Adaptive Control, Applications (Springer, Berlin Heidelberg 1991)Google Scholar
  13. 10.13.
    J.M. Maciejowski: Multivariable Feedback Design (Addison-Wesley, Indianapolis 1989)zbMATHGoogle Scholar
  14. 10.14.
    J.D. Aplevich: The Essentials of Linear State-Space Systems (Wiley, New York 2000)Google Scholar
  15. 10.15.
    R.A. Decarlo: Linear Systems. A State Variable Approach with Numerical Implementation (Prentice Hall, Upper Saddle River 1989)Google Scholar
  16. 10.16.
    D.C. Youla, H.A. Jabs, J.J. Bongiorno: Modern Wiener–Hopf design of optimal controller, IEEE Trans. Autom. Control 21, 319–338 (1976)CrossRefzbMATHGoogle Scholar
  17. 10.17.
    M. Morari, E. Zafiriou: Robust Process Control (Prentice Hall, Upper Saddle River 1989)Google Scholar
  18. 10.18.
    E.C. Garcia, M. Morari: Internal model control: 1. A unifying review and some new results, Ind. Eng. Chem. Process Des. Dev. 21, 308–323 (1982)CrossRefGoogle Scholar
  19. 10.19.
    O.J.M. Smith: Close control of loops with dead time, Chem. Eng. Prog. 53, 217–219 (1957)Google Scholar
  20. 10.20.
    V. Kučera: Diophantine equations in control – a survey, Automatica 29, 1361–1375 (1993)CrossRefzbMATHGoogle Scholar
  21. 10.21.
    J.B. Burl: Linear Optimal Control: H 2 and H !!!*AMP*!!!#8734; Methods (Addison-Wesley, Indianapolis 1999)Google Scholar
  22. 10.22.
    J.C. Doyle, B.A. Francis, A.R. Tannenbaum: Feedback Control Theory (Macmillan, London 1992)Google Scholar
  23. 10.23.
    K. Zhou, J.C. Doyle, K. Glover: Robust and Optimal Control (Prentice Hall, Upper Saddle River 1996)zbMATHGoogle Scholar
  24. 10.24.
    M. Vidyasagar, H. Kimura: Robust controllers for uncertain linear multivariable systems, Automatica 22, 85–94 (1986)CrossRefzbMATHGoogle Scholar
  25. 10.25.
    B.D.O. Anderson, J.B. Moore: Optimal Control (Prentice Hall, Upper Saddle River 1990)zbMATHGoogle Scholar
  26. 10.26.
    A.E. Bryson, Y. Ho: Applied Optimal Control (Hemisphere/Wiley, New York 1975)Google Scholar
  27. 10.27.
    A.E. Bryson: Dynamic Optimization (Addison-Wesley, Indianapolis 1999)Google Scholar
  28. 10.28.
    H. Kwakernaak, R. Sivan: Linear Optimal Control Systems (Wiley-Interscience, New York 1972)zbMATHGoogle Scholar
  29. 10.29.
    F.L. Lewis, V.L. Syrmos: Optimal Control (Wiley, New York 1995)Google Scholar
  30. 10.30.
    S.I. Lyashko: Generalized Optimal Control of Linear Systems with Distributed Parameters (Kluwer, Dordrecht 2002)zbMATHGoogle Scholar
  31. 10.31.
    D.S. Naidu: Optimal Control Systems (CRC, Boca Raton 2003)Google Scholar
  32. 10.32.
    D.P. Bertsekas: Dynamic Programming and Optimal Control, Vol. I,II (Athena Scientific, Nashua 2001)Google Scholar
  33. 10.33.
    E.F. Camacho, C. Bordons: Model Predictive Control (Springer, Berlin Heidelberg 2004)zbMATHGoogle Scholar
  34. 10.34.
    D.W. Clarke (Ed.): Advances in Model-Based Predictive Control (Oxford Univ. Press, Oxford 1994)zbMATHGoogle Scholar
  35. 10.35.
    J.M. Maciejowski: Predictive Control with Constraints (Prentice Hall, Upper Saddle River 2002)Google Scholar
  36. 10.36.
    J.A. Rossiter: Model-Based Predictive Control – a Practical Approach (CRC, Boca Raton 2003)Google Scholar
  37. 10.37.
    R. Soeterboek: Predictive Control – a Unified Approach (Prentice Hall, Upper Saddle River 1992)zbMATHGoogle Scholar
  38. 10.38.
    D.W. Clarke, C. Mohtadi, P.S. Tuffs: Generalised predictive control – Part 1. The basic algorithm, Automatica 23, 137 (1987)CrossRefzbMATHGoogle Scholar
  39. 10.39.
    D.W. Clarke, C. Mohtadi, P.S. Tuffs: Generalised predictive control – Part 2. Extensions and interpretations, Automatica 23, 149 (1987)CrossRefzbMATHGoogle Scholar
  40. 10.40.
    C.R. Cutler, B.L. Ramaker: Dynamic matrix control – a computer control algorithm, Proc. JACC (San Francisco 1980)Google Scholar
  41. 10.41.
    C.E. Garcia, D.M. Prett, M. Morari: Model predictive control: theory and practice – a survey, Automatica 25, 335–348 (1989)CrossRefzbMATHGoogle Scholar
  42. 10.42.
    D.Q. Mayne, J.B. Rawlings, C.V. Rao, P.O.M. Scokaert: Constrained model predictive control: stability and optimality, Automatica 36, 789–814 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  43. 10.43.
    F. Borrelli: Constrained Optimal Control of Linear and Hybrid Systems (Springer, Berlin Heidelberg 2003)zbMATHGoogle Scholar
  44. 10.44.
    T.A. Badgewell, S.J. Qin: Nonlinear Predictive Control Chapter: Review of Nonlinear Model Predictive Control Application, IEE Control Eng. Ser., Vol. 61, ed. by M.B. Cannon (Kouvaritabis, London 2001)Google Scholar
  45. 10.45.
    A. Isidori: Nonlinear Control Systems (Springer, Berlin Heidelberg 1995)zbMATHGoogle Scholar
  46. 10.46.
    J.J.E. Slotine, W. Li: Applied Nonlinear Control (Prentice Hall, Upper Saddle River 1991)zbMATHGoogle Scholar
  47. 10.47.
    V.I. Utkin: Sliding Modes in Control and Optimization (Springer, Berlin Heidelberg 1992)zbMATHGoogle Scholar
  48. 10.48.
    Control system toolbox for use with MATLAB. Userʼs guide (The Math Works Inc. 1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of Automation and Applied InformaticsBudapest University of Technology and EconomicsBudapestHungary
  2. 2.Department of Automation and Applied InformaticsBudapest University of Technology and EconomicsBudapestHungary
  3. 3.Department of Automation and Applied InformaticsBudapest University of Technology and EconomicsBudapestHungary

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