Robust pid controller design for ball and beam system using classical loop-shaping technique

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2 Citations (Scopus)


In this paper, classical loop-shaping technique-based robust proportional, integral and derivative (PID) control for ball and beam system, a particular example of double integrator with time delays is investigated. Double integrator systems are simple but important class of second-order systems as they model single degree of freedom translation and rotational systems. H∞ and μ synthesis have been widely used to design controllers to achieve robust performance. However, these automated tools often do not provide much insight into the relationship between the open-loop frequency response and the performance in the presence of time delays in system. This paper first presents a method for translating the robust performance criterion into contours on the open-loop Bode plot of a compensated single input single output (SISO) system so that robust controllers can be directly synthesized with classical loop shaping and then it adopts an approximation method to extract PID parameters from robust controller itself to reduce a high-order controller. The simulation results of this paper show that a robust PID controller outperforms in the ball and beam system as well as effective for controlling double integrator system with time delays.

Original languageEnglish
Pages (from-to)10-17
Number of pages8
JournalControl and Intelligent Systems
Issue number1
Publication statusPublished - 2016

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications


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