A Simple Analytical Method for Estimation of the Five-Parameter Model: Second-Order with Zero Plus Time Delay

Process models play an important role in the process industry. They are used for simulation purposes, quality control, fault detection, and control design. Many researchers have been engaged in model identification. However, it is difficult to find an analytical identification method that provides a good model and requires a relatively simple experiment. This is the advantage of the method of moments. In this paper, an analytical method based on the measurement of the process moments (characteristic areas) is proposed, to identify the five-parameter model (second-order process with zero plus time delay) from either the closed-loop or open-loop time responses of the process (in the time-domain), or the general-order transfer function with time delay (in the frequency-domain). The only parameter required by the user is the type of process (minimum phase or non-minimum phase process), which in practice can be easily determined from the time response of the process. The method can also be used to reduce the higher-order process model. The proposed identification method was tested on several illustrative examples, and compared to other identification methods. The comparison with existing methods showed the superiority of the proposed method. Moreover, the tests confirmed that the algorithm of the proposed method works properly for a wide family of process models, even in the presence of moderate process noise.