Practical Nonlinear Control Systems

  • Ying Bai
  • Zvi S. Roth
Part of the Advances in Industrial Control book series (AIC)


This chapter, on practical nonlinear control design, includes a variety of open-loop and closed-loop control design techniques that not only do not avoid the nonlinearities of the model but sometimes utilize the nonlinearities as part of a successful control strategy. The chapter includes many MATLAB Simulink examples. One of the chapter purposes is to serve as a MATLAB Simulink tutorial. Nonlinearities in the process model are often the “heart and soul” of the process model. We tried to demonstrate it with many real-life examples—aircraft motion models, missile guidance, physiological models, and more. In all these examples, the nonlinearities play a central role. Dynamic simulations, if done carefully and systematically, can compensate for the lack of full control design experience and training. A simulator in the loop that performs multiple runs of a slow enough process can provide meaningful control insight that can be put into action in real time. Sliding mode control and Lyapunov Design are powerful control design techniques in their own right. These control design methods particularly shine in the presence of modeling uncertainties and poorly modeled disturbance signals. One may even apply these methods to linear process in order to obtain superior performance at certain circumstances. Due to time and space constraints, several subjects regrettably ended up being omitted from this chapter (awaiting possibly future editions of this book). These subjects include Model Linearization by means of MATLAB and Simulink and PID Control Auto-Tuning.


  1. 1.
    Dabney, J. B., & Harman, T. L. (2004). Mastering SIMULINK. Prentice-Hall.Google Scholar
  2. 2.
    Phillips, C. L., & Harbor, R. D. (2000). Feedback control systems (4th edn.). Prentice-Hall.Google Scholar
  3. 3.
    Schoen, E. Selected Control Systems 1 Lecture Notes, 1973-1978, Technion, Israel Institute of Technology (in Hebrew).Google Scholar
  4. 4.
    Murray, J. D. (2002). Mathematical biology: I. an introduction (3rd edn.). Springer.Google Scholar
  5. 5.
    Britton, N. F. (2003). Essential mathematical biology. London: Springer.CrossRefGoogle Scholar
  6. 6.
  7. 7.
    Khoo, M. C. K. (1999). Physiological control systems: Analysis, simulation and estimation. IEEE Press Series on Biomedical Engineering.Google Scholar
  8. 8.
    Truxal, J. G. (1955). Automatic feedback control system synthesis. McGraw-Hill.Google Scholar
  9. 9.
    Slotine, J. J., & Shankar Sastry, S. (1983). Tracking control of non-linear systems using sliding surfaces, with application to robot manipulators. International Journal of Control, 38(2), 465–492.MathSciNetCrossRefGoogle Scholar
  10. 10.
    Slotine, J.-J. E., & Li, W. (1991). Applied nonlinear control. Prentice-Hall.Google Scholar
  11. 11.
    Khalil, H. K. (2015). Nonlinear control. Pearson Education.Google Scholar
  12. 12.
    Margaliot, M., & Langholz, G. (1999). Fuzzy Lyapunov-based approach to the design of fuzzy controllers. Fuzzy Sets and Systems, 106, 45–59.MathSciNetCrossRefGoogle Scholar
  13. 13.
    Astrom, K. J., & Hagglund, T. (1984). Automatic tuning of simple regulator with specification on phase and amplitude margin. Automatica, 20(5), 645–651.MathSciNetCrossRefGoogle Scholar
  14. 14.
    Voda, A., & Landau, I. D. (1995). A method for the auto-calibration of PID controllers. Automatica, 31(2).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ying Bai
    • 1
  • Zvi S. Roth
    • 2
  1. 1.Department of Computer Science and EngineeringJohnson C. Smith UniversityCharlotteUSA
  2. 2.Department of Electrical and Computer ScienceFlorida Atlantic UniversityBoca RatonUSA

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