Control of Nonlinear Chemical Processes Using Adaptive Proportional-Integral Algorithms Emad Ali* Chemical Engineering Department, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia It is believed that a fixed-parameter proportional-integral derivative (PID) may not do well for nonlinear, time-variant, or coupled processes. It needs to be re-tuned adequately to retain robust control performance over a wide range of operating conditions. Alternatively, nonlinear control algorithms can be employed. To avoid complexity introduced by such nonlinear controllers, modified PID algorithms that have the ability to adapt their tuning parameters on-line can be used instead to perform as well. An automatic on-line tuning strategy for PI controllers is proposed and compared with other existing adaptive PI algorithms such as fuzzy gain scheduling, model-based gain scheduling, a nonlinear version of PI, internal model control, and self-tuning adaptive control. The proposed tuning methodology adapts the PI settings by direct utilization of explicit expressions for the gradients of the closed-loop response with respect to the PI settings. The adapted parameters are determined such that the resulting closed-loop response lies inside predefined time-domain constraints. Application of the proposed technique as well as the other aforementioned systems to two nonlinear simulated continuously stirred tank reactor examples is demonstrated. These examples present challenging control problems because of their interesting dynamics such as time-varying gain and gain with changing sign character. Simulation results indicated that the proposed tuning algorithm can provide comparable, if not superior, performance to those obtained by the other tested algorithms. Introduction The conventional proportional-integral derivative (PID) algorithm is still widely used in the industry because it is simple, robust, and time-tested. However, its perfor- mance may degrade when applied to highly nonlinear processes, which are the fact rather than the exception in the chemical process industry. Many tuning proce- dures for PID algorithms were proposed in the literature to retain good performance. 1 However, despite their differences, these methods provide only initial (fixed) good values. Generally, standard PID algorithms with fixed parameters may perform poorly when the process gain varies substantially with operating conditions. In this case, different sets of controller parameters should be used for differently partitioned regions of the operat- ing condition space; otherwise, nonlinear control such as nonlinear model-predictive control should be used. 2 Gain-scheduled control and adaptive PI control are other alternatives for handling processes with known nonlinearities. 3 Recently, the future of these schemes became more promising. 4 Ali 1 proposed an automatic on- line tuning (ATN) approach for PI algorithms, which is capable on nonlinear compensation. The approach adapts the PI settings continuously on-line to force the resulted closed-loop response to satisfy predefined performance specifications. The approach can improve the control performance, even if no a priori knowledge of good values for the PI settings is available. The special features of the proposed automatic tuner can be sum- marized as follows: 1. It incorporates closed-loop prediction criteria. This allows advance correction of the controller settings. It includes feedback; thus, it can compensate for modeling errors. 2. The performance specification is expressed in the form of time domain constraints, which makes it more appealing for a practitioner. This also adds some flex- ibility because the user can adjust his/her specification on-line for trade-off. 3. The method can adjust the parameters of all control loops simultaneously and interactively where other methods tune each loop individually. A similar approach was used by Zhou et al. 5 to tune generic model control. However, in their approach an open-loop prediction of the output response is used. The objective of this paper is then to test the proposed ATN and compare its performance with those obtained by different existing adaptive PI schemes, among which are fuzzy gain scheduling 6 (FGS), model-based gain sched- uling 7 (MGS), a nonlinear version of PI algorithms 8 (NLPI), internal model control 9 (IMC), and a self-tuning controller (STC) with a PID structure. 10 The intent is to demonstrate how the proposed automatically tuned PI algorithm would provide improved performance over those obtained by a fixed-parameter PID and adaptive (gain-scheduled) control algorithms when applied to processes with time-varying dynamics. In addition, a similar performance improvement can also be achieved for processes with gain that changes the sign in which conventional PID controllers fail. Thus, such a controller can deliver robustness over a broader range of operating conditions. It should be mentioned that the proposed algorithm is a hybrid system of standard PI algorithm in the lower level and a model-based tuning algorithm in the higher level. The purpose of the tuning algorithm is to update the PI parameters each sampling time or at scheduled time intervals. No specific type of model is required for the tuning algorithm. Any form of models that can predict the output response and sensitivity to PI tuning parameters is sufficient. In this case, the proposed * To whom correspondence should be addressed. Fax: ++(9661)467-8770. Phone: ++(9661)467-6871. E-mail: amkamal@ksu.edu.sa. 1980 Ind. Eng. Chem. Res. 2000, 39, 1980-1992 10.1021/ie990517n CCC: $19.00 © 2000 American Chemical Society Published on Web 05/05/2000