CLOSED-LOOP PROCESS IDENTIFICATION USING TIME DOMAIN CURVE-FITTING

Abstract

Process identification to obtain a control-relevant dynamic model of a process is an integral part of controller design and tuning. Closed-loop process identification is preferable to open-loop identification since the process remains under feedback control during the test. Existing approaches for closed-loop identification employ different analyses. In this study, closed-loop process identification using time domain curve- fitting via global optimization methods, is proposed and evaluated. The perceived difficulties in this methodology are the need for global optimization due to possible existence of multiple minima, extensive computations, numerical derivative evaluation for efficient optimization methods, and accuracy and reliability of the results. Closed-loop process identification by time domain curve-fitting involves the introduction of a step change in the set point of a Pl/PID controller or a relay test to obtain the actual response. The process is approximated by a SOPDT or FOPDT model, whose parameters are determined by the minimization of sum of squares (SSQ) of error between the process (actual) and model (calculated) closed-loop responses. Minimization of the SSQ is carried out using global optimization methods such as Multi-pass random search algorithm of Luus (1998) and genetic algorithms. The solutions obtained are then refined using conventional search algorithms, namely, modified simplex and BFGS methods. The methodology was applied to stable, unstable and integrating SISO processes as well as to MIMO processes. Different controller settings, types of closed-loop response (underdamped or overdamped), duration of the closed-loop test and presence of measurement noise, were considered to study the accuracy and robustness of the proposed methodology. Results obtained show that time domain curve-fitting provides an accurate and reliable model for SISO and MIMO processes, and is also robust towards measurement noise. Parameter estimates are independent of controller settings employed and nature of the closed-loop response. For stable SISO processes, only a few minima exist in process identification from step response whereas several minima are likely in process identification from relay response. Results obtained further show that two minima are likely in the case of unstable processes, of which one is easy to recognize, whereas only one minimum is likely in the case of integrating processes. Thus, a local optimization method can often be used with care for closed-loop process identification of SISO processes by time domain curve-fitting. For MIMO identification, SSQ minimization has multiple minima because of which a global optimization method like genetic algorithms is necessary. CPU time on a Pentium II computer for process identification by time domain curve-fitting via global optimization methods is about 10 mins for SISO processes, and it is about two to three hours for MIMO processes. Duration of the closed-loop test for process identification of various processes using time domain curve-fitting, can be reduced considerably without affecting results but with obvious practical advantages. This also easily compensates the computational time on a personal computer. Potential exists for improving the accuracy of model approximation by using higher order models. In summary, this study demonstrates the applicability and efficacy of time domain curve-fitting via a suitable optimization method, for closed-loop identification of SISO and MIMO processes.