In this paper, a method for process frequency response identification is proposed, which can identify multiple points on process frequency response from a single relay feedback test. The process input and output transients resulting from a relay feedback cannot be directly converted to the frequency domain to obtain a process frequency response using FFT. A decay exponential is then proposed to modify the process input and output, so that the process frequency response can be identified with the help of FFT. Real-time testing of the method on various processes gives quite accurate process frequency responses, especially in the frequency range [0, ωc], which is important for control design and process modelling. The method inherits and extends the advantages of the original relay auto-tuning technique. It can be easily applied to PID auto-tuning and to transfer function modelling.
"Wang et al. use a switching technique between a relay and a relay with an integrator to obtain sufficient information about the process, . Another modification of a relay experiment is using a biased relay to identify system's parameters, , . This method is very accurate when used to determine the open loop gain of the process. "
[Show abstract][Hide abstract] ABSTRACT: The work presented in this paper deals with the process of transfer function identification by using self-oscillation method (autotuning identification method). The algorithm is given in a general matrix form and some modifications are introduced. The modifications of the algorithm include augmentation of the initial algorithm for Type k systems, systems with delays and discrete-time systems. The paper also includes simulation examples which describe the introduced modifications. Apart from being rather simple, this method is applicable to real systems. Its greatest advantage is quick identification of a transfer function (depends on the system).
Control & Automation, 2007. MED '07. Mediterranean Conference on; 07/2007
"Another modification of the standard relay for multi point identification of frequency response is to superimpose a parasitic relay to the standard relay . In  an exponential decay data window was introduced to permit use of both the transient and periodic parts of the relay feedback generated data. To overcome limits of the describing function method, an alternative methodology to the relay experiment for extracting nonparametric information about a system frequency "
[Show abstract][Hide abstract] ABSTRACT: In this paper the authors propose a novel method in order to identify the Hammerstein model where the nonlinear process is approximated by a static nonlinear element followed by a linear dynamic second or third-order model. The method is able to determine the parameters of the linear plant and two point of the nonlinear element in a unique step by using a filtered equation and the least-squares method. One of the most significant simulation example applied to the identification of a dc-engine is reported; it demonstrates the effectiveness of the proposed method and its acceptable robustness to disturbance and to measurements noise.
Power Engineering, Energy and Electrical Drives, 2007. POWERENG 2007. International Conference on; 05/2007
"However, the two estimated points may provide insufficient information for controller design for some processes. To overcome this difficulty, Wang et al.  have suggested a multiple point identification method from a single standard relay test. Tan et al.  and Marchetti et al.  have proposed relay based identification for stable and unstable processes, respectively , using the describing function approach. "
[Show abstract][Hide abstract] ABSTRACT: A set of general expressions is derived from a single symmetrical relay feedback test for estimation of model parameters of lower-order processes. Using the expressions the exact parameters of open loop stable and unstable first order plus time delay (FOPDT) and second order plus time delay (SOPDT) transfer function models may be obtained from simple measurements made on the limit cycle. Further, the expressions can be used to estimate lower-order models of a higher order process with great accuracy when the steady state gain of the process is known a priori. Examples are given to illustrate the novelty of the proposed relay feedback based identification method.
American Control Conference, 2003. Proceedings of the 2003; 07/2003
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