Discrete-time first-order plus dead-time model-reference trade-off PID control design

Ryo Kurokawa, Takao Sato, Ramon Vilanova, Yasuo Konishi

Research output: Contribution to journalArticleResearch

7 Citations (Scopus)


© 2019 by the authors. The present study proposes a novel proportional-integral-derivative (PID) control design method in discrete time. In the proposed method, a PID controller is designed for first-order plus dead-time (FOPDT) systems so that the prescribed robust stability is accomplished. Furthermore, based on the control performance, the relationship between the servo performance and the regulator performance is a trade-off relationship, and hence, these items are not simultaneously optimized. Therefore, the proposed method provides an optimal design method of the PID parameters for optimizing the reference tracking and disturbance rejection performances, respectively. Even though such a trade-off design method is being actively researched for continuous time, few studies have examined such a method for discrete time. In conventional discrete time methods, the robust stability is not directly prescribed or available systems are restricted to systems for which the dead-time in the continuous time model is an integer multiple of the sampling interval. On the other hand, in the proposed method, even when a discrete time zero is included in the controlled plant, the optimal PID parameters are obtained. In the present study, as well as the other plant parameters, a zero in the FOPDT system is newly normalized, and then, a universal design method is obtained for the FOPDT system with the zero. Finally, the effectiveness of the proposed method is demonstrated through numerical examples.
Original languageEnglish
Article number3220
JournalApplied Sciences (Switzerland)
Publication statusPublished - 1 Aug 2019


  • Discrete time system
  • FOPDT system
  • Model-based design
  • PID control
  • Robust stability
  • Sensitivity function


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