Background and Preliminaries

  • Konstantinos G. PapadopoulosEmail author


In this chapter, fundamental definitions and terminology are given to the reader regarding the closed-loop control system. The analysis of the control loop takes place in the frequency domain and, therefore all necessary transfer functions of the control loop are presented in Sect. 2.2. The important aspect of internal stability of a control loop is presented in Sect. 2.3, whereas in Sect. 2.4 the property of robustness in a control loop is analyzed. In Sect. 2.5, a clear definition of the type of the control loop is given, since in Part II, the proposed theory is dedicated to the design of type-I, type-II, and type-III, ... type-p control loops. Last but not least, in Sect. 2.6, the definitions of sensitivity and complementary sensitivity functions are presented so that the tradeoff feature in terms of controller performance that these two functions introduce is made clear to the reader. Finally, in Sect. 2.7, the principle of the Magnitude Optimum criterion is presented and certain optimization conditions are proved that comprise the basic tool for all control laws’ proof throughout this book. These optimization conditions serve to maintain the magnitude of the closed-loop frequency response equal to the unity in the widest possible frequency range as the Magnitude Optimum criterion implies. In the same section, the Magnitude Optimum criterion is proved to be considered as a practical aspect of the \(H_\infty \) design control principle.


Reference Signal Control Loop Disturbance Rejection Internal Stability Forward Path 
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  1. 1.
    Ang KH, Chong G, Li Y (2005) PID control system analysis, design, and technology. IEEE Trans Control Syst Technol 13(4):559–576CrossRefGoogle Scholar
  2. 2.
    Gunter S (2003) Respect the unstable. IEEE Control Syst Mag 23(4):12–25CrossRefGoogle Scholar
  3. 3.
    Horowitz I (1963) Synthesis of feedback systems. Academic Press, LondonzbMATHGoogle Scholar
  4. 4.
    Margaris NI (2003) Lectures in applied automatic control (in Greek), 1st edn. Tziolas, GreeceGoogle Scholar
  5. 5.
    Middleton RH (1991) Trade-offs in linear control system design. Automatica 27(2):281–292CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Morari M, Zafiriou E (1989) Robust process control, 1st edn. Prentice-Hall, New JerseyGoogle Scholar
  7. 7.
    Petridis V (2001) Automatic control systems, part B (in Greek), 2nd edn. Ziti, GreeceGoogle Scholar
  8. 8.
    Voda AA, Landau ID (1995) A method for the auto-calibration of PID controllers. Automatica 31(1):41–53CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Voronov AA (1985) Basic principles of automatic control theory—special linear and nonlinear systems. MIR Publishers, MoscowzbMATHGoogle Scholar
  10. 10.
    Zames G, Francis BA (1983) Feedback, minimax sensitivity, and optimal robustness. IEEE Trans Autom Control 28(5):585–600CrossRefzbMATHMathSciNetGoogle Scholar

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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.ATDDABB IndustriesTurgiSwitzerland

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