Relay feedback test identification and autotuning
Proportional-integral-derivative (PID) control is the main type of control used in the process industry. PID controllers are usually implemented as configurable software modules within distributed control systems (DCS). The DCS configuration software is constantly evolving and giving developers many new features. One of most useful features is the controller autotuning feature. This trend can be seen in the development of new releases of such popular DCS software as Honeywell Experion PKS and Emerson DeltaV. Despite the existence of a large number of tuning algorithms, there is still a need for simple and precise loop tuning algorithms that can be embedded as additional au-totuning add-ons in the PID controllers of DCS. The requirements of the controller autotuners are simplicity, precision, and robustness.
One of the most convenient tests on the process is the relay feedback test proposed in . This method has received a lot of attention from both industry and the worldwide research community. It has become a starting point for a number of directions of research as well. In comparison to the original approach by Ziegler and Nichols , which was aimed at obtaining the values of the ultimate gain and ultimate frequency (i.e., the minimal gain that brings the system to the state of self-excited oscillations and the frequency of those oscillations), it was proposed in  that the relay feedback test be used for process parameters identification. This idea was further developed and extended to various models and types of processes. The survey of available tuning methods and techniques based on the relay feedback test is presented in . However, despite the obvious success of the relay feedback test in au-totuning and identification, it can lead to significant errors. The errors come from the model of the oscillations based on the application of the approximate describing function method. There have been a few attempts to overcome this source of inaccuracy which have solved the problem to some degree. In , for example, it is proposed that the amplitude of the oscillations be used in addition to the imaginary part of the Tsypkin locus . This results in a precise model for two simple transfer functions. In  and , it is shown how the parameters of first-order and second-order process transfer functions with time delay can be found exactly using the A-locus  from measurements of the asymmetric limit cycle. In , exact parameters of first-order and second-order plus dead-time models are obtained from measurements of the asymmetric limit cycle. In , a relay feedback and wavelet-based method for estimation of unknown processes is proposed. In , it is proposed that the saturation function should be used instead of the relay nonlinearity, which transforms the square wave into a nearly sinusoidal one and, consequently, brings the test to the limitations of the describing function method.
KeywordsProportional Gain Bias Function Distribute Control System Tuning Algorithm Integral Absolute Error
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