Process Identification Using Open-loop and Closed-loop Step Responses

This paper is concerned with process identification by curve fitting step responses. Both open-loop and closed-loop identification are studied using simulated data for typical examples as well as experimental data from a laboratory plate heat exchanger. Timedomain curve fitting utilizing efficient local optimization techniques is employed to find the parameters of the process model. Process models are assumed to be first order plus dead time (FOPDT) and/or second order plus dead time with zero (SOPDTZ). Results show that closed-loop identification recovered model parameters that better represented the actual process compared to open-loop identification. Lastly, it was seen that, for experimental data, accurate recovery of model parameters was impeded by the presence of colored noise and/or unmeasured disturbances. Such impediments were absent in the simulated data enabling accurate estimation of model parameters. INTRODUCTION Proportional-Integral (PI) and Proportional–Integral–Derivative (PID) controllers are widely used in chemical and process industries because of their proven track record, simplicity, robustness and ability to remove offset. Tuning the controller to achieve good closed-loop performance is imperative. However, the processes in industry are complex and potentially non-linear, making controller tuning difficult. Hence, it is desirable to model the dynamics of these processes near the current operating point by simpler models such as the first order plus dead time (FOPDT) or second order plus dead time with zero (SOPDTZ) model for the purpose of controller design. In the past, many studies have been undertaken on process identification (e.g., Viswanathan and Rangaiah, 2001; Huang et al., 2001; Zhu et al., 2003). These identification methods can be divided into two broad categories such as on-line methods and off-line methods. The former methods refer to those that find the model while data are being collected, using what are known as recursive algorithms. Off-line methods use batch-wise data to perform identification. The focus of the present study is off-line identification, for which step testing is popular in the industry since the simplest form of open-loop or closed-loop testing is the step test. A step change is introduced in either the manipulated variable for the open-loop testing or the set point for the closed-loop testing, and the process response is noted. The main objective of this study is to compare models obtained and controllers designed from open-loop and closed-loop process identification using simulated data as well as experimental data. Effect of unmeasured disturbances during the test is also examined. 1 Department of Chemical and Biomolecular Engineering, National University of Singapore, Singapore 119260. Email: [email protected] Journal of The Institution of Engineers, Singapore Vol. 45 Issue 6 2005 PROCESS IDENTIFICATION Many industrial processes are non-linear and/or of high order. Simple and easy-to-use controller design equations for such processes are not available. Hence, it is desirable to model these processes by low order models such as FOPDT or SOPDTZ models and then design a PI or PID controller based on their low order representations. To identify an FOPDT or SOPDTZ model of a process, time domain curve fitting of step response is studied here. This method requires the process response, assumption of a suitable model and initial estimates of model parameters. The initial selection of the model could be based on the shape of the open-loop step response. Open-loop identification is widely used in the industry. To obtain an open-loop step response (Ya), the process should be perturbed by introducing a step change in the manipulated variable (MV), as shown in Figure 1. Gp(s) is the actual process with unknown parameters. Time-domain curve fitting is used to determine the best values of parameters in the assumed model, which can predict an output matching the actual response (see Zhu et al., 2003 for details). Numerical methods are used to minimize the sum of squares (SSQ) between the actual response, Ya and the calculated response, Yc (Luyben and Luyben, 1997). Figure 1: Block diagram and input/output graph of open-loop test. A step change is introduced in the manipulated variable (MV) to obtain output (Ya) Similar to open-loop process identification, closed-loop step response data are obtained by giving a step change in set point (R) as shown as in Figure 2. Note that the closed-loop process involves a feedback loop and a controller in addition to the process. This makes the response (Ya) different from the open-loop response as it is now a function of the process as well as the controller. A sample of the closed-loop response is also shown in Figure 2. Because of the controller and the feedback loop, the method of obtaining process model parameters is not as straightforward as that in open-loop identification. Analytical expressions are often not available to calculate the response, Yc(t) and numerical methods must be employed to obtain it. Calculated response, Yc(t) is a function of controller parameters as well as model parameters. Since the controller parameters are usually known, the closed-loop response can be considered a function of model parameters only. Similar to open-loop identification, the objective in closed-loop Journal of The Institution of Engineers, Singapore Vol. 45 Issue 6 2005 identification is to determine the best values of model parameters that minimize the SSQ between the actual and calculated responses. Figure 2: Block diagram and input/output graph of closed-loop test performed by introducing a step change to set point (R) to obtain output (Ya) IDENTIFICATION USING SIMULATED DATA A total of four examples are selected from Huang et al. (2001) for the simulation study. The first two examples have a positive or negative zero but their denominators are the same. This is to compare whether the curve fitting can identify correctly the positive or negative zero in a SOPDTZ model.