Delay Margin Achievable by PID Controllers

Abstract

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.