PROCESS DESIGN AND CONTROL A Modified Smith Predictor for a Process with an Integrator and Long Dead Time C. C. Hang, Qing-Guo Wang,* and Xue-Ping Yang Department of Electrical & Computer Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore In this paper, a new modified Smith predictor using a rapid load estimator scheme is proposed. The advantage of the design is that the load estimator does not involve the solution of a closed- loop equation that contains dead time, and this can achieve a better load disturbance response. This scheme can be easily extended to the case of double integrators. Robust stability of the proposed method is analyzed, and a simple and effective robust controller design rule is derived. It is demonstrated by simulations that the new controller provides a similar or better setpoint response and a faster load disturbance rejection than the dead-time compensator in other papers. 1. Introduction The original Smith predictor 4 is applicable only to open-loop stable systems. For an unstable system, an inner loop controller may first be used to stabilize the process before the Smith predictor is applied. The design of the main controller will then become more difficult because it has to be designed to control a modified process with a more complex transfer function. For a process with an integrator and long dead time, two modifications have been reported in the literature to overcome this problem. Wantanabe 5 first proposed a modification using a mismatched process model. This requires the dead time to be accurately estimated in order to remove the offset caused by a step load disturbance. In refs 1 and 6 further modifications were made to improve load rejection without compromising the setpoint response. A disadvantage of this modified Smith predictor is that it is internally unstable and more care is needed in its implementation. An alterna- tive approach in refs 2 and 7 that avoids the internally unstable signal is to use an estimate of the load disturbance. The disadvantage of this modification is that the load estimator involves the solution of a closed- loop equation that contains dead time, and this would limit its performance when the dead time is relatively long. In this paper, a new modified Smith predictor using a rapid load estimator scheme is proposed. Compared with the original Smith predictor, this configuration is not only applicable to open-loop stable systems. In the case of the process with an integrator and significant time delay, it avoids the internally unstable signals and does not incur the solution of a closed-loop equation that contains dead time. A comparison of this performance with the dead-time compensator (DTC) in refs 1-3 will be made. The paper is organized as follows: An overview of the proposed modified Smith predictor is presented in section 2. In section 3, the robust stability of the proposed method is analyzed and the robust controller design rule is derived. Simulation results are given in section 4. Finally, some concluding remarks are pre- sented in section 5. 2. Proposed Modified Smith Predictor The proposed modified Smith predictor makes use of the rapid load detector scheme 8 and is shown in Figure 1 for the process of Ge -sL ) (k p /s)e -sL , where G(s)e -sL is the given process to be controlled, G ˆ e -sL ˆ is a model of the process, and P 1 and P 2 are the two controllers. In this structure, P 1 is optimized for setpoint response, while P 2 is optimized for load disturbance. The output of P 2 is effectively an estimate of the load disturbance. Because no dead time is involved in this generation and a much higher controller gain in P 2 is allowed, this load estimator has a rapid response and can be used ef- fectively in a feedforward control loop as shown in Figure 1. Both P 1 and P 2 can be simple proportional controllers, i.e., P 1 ) k c1 and P 2 ) k c2 , without producing steady-state errors. The assumption is that the model is a perfect representation of the unknown plant, i.e., G ˆ (s) ) G(s) and L ˆ) L. The setpoint and load distur- bance responses are given by and Because 1 - e -sL has s 1 as its lowest power of s, the * To whom all correspondence should be addressed. E- mail: elewqg@nus.edu.sg. Tel: (+65) 874 2282. Fax: (+65) 779 1103. H yr (s) ) k p k c1 s + k p k c1 e -sL (1) H yd (s) ) k p [s + k p k c1 (1 - e -sL )][s + k p k c2 (1 - e -sL )] s(s + k p k c1 )(s + k p k c2 ) e -sL (2) 484 Ind. Eng. Chem. Res. 2003, 42, 484-489 10.1021/ie010881y CCC: $25.00 © 2003 American Chemical Society Published on Web 01/04/2003