PID controller tuning for the first-order-plus-dead-time process model via Hermite-Biehler theorem Anindo Roy, a, * Kamran Iqbal b,† a Department of Applied Science, University of Arkansas at Little Rock, Little Rock, AR 72204, USA b Department of Systems Engineering, University of Arkansas at Little Rock, Little Rock, AR 72204, USA Received 22 May 2003; accepted 8 December 2004 Abstract This paper discusses PID stabilization of a first-order-plus-dead-time FOPDT process model using the stability framework of the Hermite-Biehler theorem. The FOPDT model approximates many processes in the chemical and petroleum industries. Using a PID controller and first-order Pade ´ approximation for the transport delay, the Hermite- Biehler theorem allows one to analytically study the stability of the closed-loop system. We derive necessary and sufficient conditions for stability and develop an algorithm for selection of stabilizing feedback gains. The results are given in terms of stability bounds that are functions of plant parameters. Sensitivity and disturbance rejection charac- teristics of the proposed PID controller are studied. The results are compared with established tuning methods such as Ziegler-Nichols, Cohen-Coon, and internal model control. © 2005 ISA—The Instrumentation, Systems, and Automa- tion Society. Keywords: FOPDT process; PID control; Stability analysis; Hermite-Biehler theorem 1. Introduction The first-order-plus-dead-time FOPDT model not only provides a simple characterization of a process but is known to capture fairly well the dynamics of many applications in process control industry 1,2. The process has been extensively studied, and various controller schemes, tuning rules 3–5, and identification methods 6–11 have been applied to it. FOPDT represents a simple way to separate process dynamics into pure dead-time and first-order lag. This simplifying as- sumption is made possible because many indus- trial processes are monotonic and self-saturating in step-input response 12. For example, in Ref. 11 it is shown that the FOPDT model produced neg- ligible error when compared with the model of a system consisting of four time constants. Further, the FOPDT model can be adapted to represent first-order integrating processes with transport lag, by assuming an FOPDT process in series with an integrator. In the process industry, plants are com- monly modeled with these transfer functions so most control engineers are familiar with their pa- rameters. This paper discusses an innovative method for PID tuning of a FOPDT model in a typical process control environment. While we aim for results that are general enough to be useful in that environ- ment, certain assumptions are necessary in order to limit the complexity of the problem. A question that commonly arises is what information should be assumed for controller design. Detailed knowl- *Tel.: +1-501-569-8800; fax: +1-501-569-8698. E-mail address: axroy@ualr.edu † Corresponding author. Tel.: +1-501-371-7617; fax: +1- 501-569-8698. E-mail address: kxiqbal@ualr.edu ISA TRANSACTIONS ® ISA Transactions 44 2005 363–378 0019-0578/2005/$ - see front matter © 2005 ISA—The Instrumentation, Systems, and Automation Society.