Delay Margin Achievable by PID Controllers

  • Jing ZhuEmail author
  • Tian Qi
  • Dan Ma
  • Jie Chen
Part of the Advances in Delays and Dynamics book series (ADVSDD, volume 8)


A time-honored method seemingly of infinite staying power, PID control is favored for its ease of implementation and undoubtedly, has been the most popular means of controlling industrial processes with its unparallel simplicity and unsurpassed effectiveness. This chapter studies the delay margin achievable by LTI controllers of further restricted structure and complexity, i.e., those of PID type. We develop explicit expressions of the exact delay margin and its upper bounds achievable by a PID controller for low-order delay systems, notably the first- and second-order unstable systems. While furnishing the fundamental limits of delay within which a PID controller may robustly stabilize a delay process, our results should also provide useful guidelines in tuning PID parameters and in the analytical design of PID controllers.

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.College of Automation EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.Center for Control and OptimizationSouth China University of TechnologyGuangzhouChina
  3. 3.College of Information Science and EngineeringNortheastern UniversityShenyangChina
  4. 4.Department of Electronic EngineeringCity University of Hong KongHong KongHong Kong

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