(302t) Integrals of Relay Feedback Responses for Extracting Process Information | AIChE

(302t) Integrals of Relay Feedback Responses for Extracting Process Information


Sung, S. W. - Presenter, Kyungpook National University

Since Astrom and Hagglund (1984) introduced an autotuning method which uses the relay feedback, plentiful variations have been now available for tuning of PID controllers (Astrom and Hagglund, 1995; Yu, 2006; Hang et al., 2002). For better approximations of ultimate data, a saturation relay (Yu, 2006), relay with a P control preload (Tan et al., 2005) and a two level relay (Sung et al., 1995) have been introduced. To obtain a Nyquist point other than the critical point, a relay with hysteresis or a dynamic element such as time delay has been used (Astrom and Hagglund, 1994). Recently, two channel relay has been proposed to obtain a Nyquist point data with a given phase angle (Friman and Waller, 1997). Several Nyquist points for the dynamics of process can be extracted by storing transient responses including the converged relay responses and applying the FFT (fast Fourier transformations) technique (Wang et al., 1997). It provides detailed information about process dynamics. However, computations for this are somewhat complex. Laplace transformation of a periodic function (Ma and Zhu, 2005) has been used to obtain frequency responses. Biased relay has been proposed to obtain the steady state gain information (Shen et al, 1996a). Methods to overcome unknown load disturbances and restore symmetric relay oscillations have been available (Hang et al., 1993; Shen et al, 1996b; Sung and Lee, 2006) Parametric model has also been identified from the relay feedback tests. A first order plus time delay (FOPTD) model can be obtained from the ultimate data plus the process steady state gain. The process steady state gain usually needs an additional experiment like a step change. An biased asymmetric relay can be used to get effects of the step change and to obtain the process steady state gain (Shen et al., 1996). Huang et al. (2005) used integrals of relay transients to obtain the process steady state gain. The shape factor (Luyben, 2001) was used to extract three-parameter model. Exact expression for FOPTD process was obtained by Kaya and Atherton (2001) and Panda and Yu (2003) and used to extract parameters of FOPTD model. Process model may be extracted from the converged relay feedback response alone. However, it is not robust and can provide poor model parameters such as negative process gain when model structure is different (Panda and Yu, 2005). Second order plus time delay (SOPTD) model can also be extracted from the converged relay response and its analytic equation. As in the FOPTD model case, the method is not robust. Relay experiment with a subsequent P control experiment or another relay feedback test can be used to obtain a SOPTD model robustly. Here methods to extract more accurate ultimate data and parametric models from a single conventional relay feedback test are proposed. Instead of modifying the relay feedback system usually used to enhance identification performances in previous works, we use various integrals of the original relay feedback responses. As in the step response method (Astrom and Hagglund, 1995), areas will have merits over point data and they are investigated here. Since the conventional relay feedback is used, the proposed method shares its practical and theoretical merits. Integrals of responses are used for the first harmonic term to be dominant. Quantities based on the Parseval theorem or integrations of products of converged relay responses are used. It is not required for the whole trajectories to be stored. Because computations are simple, the proposed method can be applied easily to cheap commercial PID controllers.