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Designing of the PID and PIλ Dμ Controller for DC Motor

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Part of the Lecture Notes on Multidisciplinary Industrial Engineering book series (LNMUINEN)


In this paper, a novel approach has been proposed for consistent controller design. Engineers and scientists are often challenged with the design, analysis, and synthesis of actual problems. The development of a ‘mathematical model’ can be a feasible substitute for the actual problem. Here the construction of a mathematical model is from a process or plant. If the plant and the controller are described by a set of fractional differential equations then the fractional derivative and integral provide a wide range of applications for such dynamical systems. Here the stability of a DC motor is checked at a different level and it is found that, the existence of a large stability region in the complex plane with fractional-order system. Additional reliability and flexibility are obtained for system implementation in the control engineering with the large stability region. Instead of an analytically or experimentally approaches if a fractional-order controller design approach is used for a given process then the measured parameter gives the better result.


  • DC motor
  • Fractional-order system
  • Fractional-order calculus
  • Stability
  • Function under class
  • Ziegler–Nichols method

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  • DOI: 10.1007/978-981-15-4619-8_46
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Fig. 46.1
Fig. 46.2
Fig. 46.3
Fig. 46.4
Fig. 46.5
Fig. 46.6
Fig. 46.7
Fig. 46.8
Fig. 46.9
Fig. 46.10
Fig. 46.11
Fig. 46.12
Fig. 46.13



Proportional integral derivative


Linear time invariant

\(G{\text{cl}}_{\text{ZN}}\) :

Close-loop response of Ziegler–Nichols method

\(G_{\text{Plant}}\) :

Plant transfer function

\(G_{{R1{\text{cl}}}} (s)\) :

Close-loop transfer function of plant


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Correspondence to Parvendra Kumar .

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Kumar, P., Eligo, D.M. (2020). Designing of the PID and PIλ Dμ Controller for DC Motor. In: Sharma, V., Dixit, U., Sørby, K., Bhardwaj, A., Trehan, R. (eds) Manufacturing Engineering . Lecture Notes on Multidisciplinary Industrial Engineering. Springer, Singapore.

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