Since chemical processes are very complex and some parameters are often unknown or time varying, the derivation of rigorous dynamic model is very difficult and requires extensive engineering manpower. On the other hand, a good dynamic process model is always necessary for the design of the control system. Therefore, system identification becomes an important issue. Recent advances in stochastic or deterministic identification lead to a general conclusion: identify the model for the purpose of control system design (control relevant identification). However, interconnection characteristics of chemical processes impose another constraint: the identification procedure should give as little process upset as possible. In other words, closed-loop identification is preferred for chemical processes.Recently, the relay feedback tests have received a great deal of attention in system identification. Astrom and Hagglund (1984) suggest the use of an ideal (on-off) relay to generate sustained oscillation in closed-loop identification. Subsequently, the important process information, ultimate gain ( K , ) and ultimate frequency (w,), can be found in a straightforward manner. The relay feedback system of an autotuner gains widespread acceptance in pro2ess industries for its reliability and simplicity (Hagglund and Astrom, 1991; and many commercial products for autotuning have appeared in the market since the mid-1980s. Extensions of relay feedback system to monitoring and gain scheduling have also been made (Chiang and Yu, 1993;Lin and Yu, 1993;Luyben and Eskinat, 1994). Moreover, multivariable autotuners were also proposed (Shen and Yu, 1994;Friman and Waller, 1994).The success of the relay feedback autotuner lies on the fact that it identifies one important point on the Nyquist curve: the point at the crossover frequency (ultimate frequency). Luyben (1987) is among the first to employ the relay feedback test for system identification. The autotune variation (ATV) method back calculates system parameters from ultimate gain and ultimate frequency obtained from a relay feedback experiment. Since only process information K , and w, are available, additional process information, such as steady-state gain, should be known apriori in order to fit a typical transfer function (such as a first-, second-or thirdCorrespondence concerning this work should be addressed to C. C. Yu.
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April 1996order plus dead time system). In order to alleviate this stringent requirement, Li et al. (1991) and Leva (1994) propose the use of two relay feedback tests to find two points on the Nyquist curve and the least-square method is employed to estimate the parameters of the transfer function. Therefore, the time required for plant test increases as the number of experiments doubled. Then, a question remains: do we really need two relay feedback experiments to identify two points on a Nyquist curve?The biased relay offers some light along this direction. Oldenburger and Boyer (1962) try to eliminate sustained oscillation in some nonlinear elements by ...