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Ind. Eng. Chem. Res. 1996,34, 2406-2417

Closed-LoopAutomatic Tuning of Single-Input-Single-Output Systems
Shyh-Hong Hwangt
Department of Chemical Engineering, National Cheng-Kung University, Tainan, Taiwan 70101, Republic of China

Two closed-loop autotuning methods are developed to provide superior alternatives to tune a
proportional-integral-derivative (PID) controller forsingle-input-single-output systems. The first method is a closed-loop extension of the htrom-Hagglund autotuner. A relay is connected in the feedback loop to the PID control system to produce a stable limit cycle. On the basis of the resulting oscillations, the process is identified as a first- or second-order plus time-delay model. The second method is a time domain approach, which identifies theprocess as a secondorder plus time-delay model via an underdamped transient. The identification scheme permits the use of any control mode (P, PI, or PID) and any test input signal (step, pulse, or impulse) applied in setpoint. Simple-to-use correlation formulas based on the identified model are derived to provide optimum PID settings which yield the desired decay ratio, robustness, and minimumintegral of the absolute error. With an initial stabilizing controller, the two methods allow the control parameters to be adjusted iteratively to the correct values. The proposed methods are demonstrated to be valid for a wide range of process dynamics and insensitive to measurement noise and disturbances.

1 Introduction .
Automatic tuning of single-input-single-output (SISO) systems isaccomplished by measuring certain open-loop or closed-loop characteristics and determining optimum control parameters subsequently. Many autotuning methods (Yuwana and Seborg, 1982; k t r o m and Hagglund, 1984; Krishnaswamy et al., 1987) for proportional-integral-derivative (PID) controllers originated from the work of Ziegler and Nichols (1942). In the 2-N method, tuning is based on the critical gain andperiod which are determined by increasing the proportional gain until the stability limit is reached. In practice, this method may cause the risk of instability and is difficult to automate. To tune a PID controller automatically, the above methods utilize various techniques to estimate the critical gain and period without destabilizing the system during tuning. Yuwana and Seborg (1982) proposedthe estimation of the critical gain and period based on a first-order plus time-delay model identified from a step setpoint response of the proportional control system. The method was improved later in various ways (Jutan and Rodriguez, 1984; Lee, 1989; Chen, 1989; Lee et al., 1990; Hwang, 1993; Hwang and Shiu, 1994). The main practical advantage of the method is that it requires only a singletransient response experiment under stable operation. Consequently, the identification procedure is easy to implement and disruption to normal process operation can be kept small. However, the method still suffers from several shortcomings. First, since the Z-N tuning rules are followed, the method will inherit the limitations of empiricism. For example, the method does not always produce satisfactoryresponses especially for open-loop underdamped or nonminimum phase processes. Second, as the identification procedure presumes a simple first-order plus time-delay model, the results may not be accurate for complicated processes. Third, the identification test stipulates a step
+ E-mail address: hwang@chehp.che.ncku.edu.tw. Fax: (06) 234-4496.

input signal; other convenient alternatives, suchas a pulse signal, cannot be employed. Finally, some practical issues, such as the effects of measurement noise and disturbances present during tuning, have not been explored thoroughly. k t r o m and Hagglund (1984) proposed the use of a relay in place of the proportional controller in the feedback loop for autotuning. This will introduce a periodic square wave to the process input. The...