Identification and control of process using the Modified asymmetrical Relay Feedback method

Multiple frequency response points identification through single asymmetric relay feedback experiment

“…Such works usually require either to extend the duration of the experiments or to modify the loop structure to a different extent. For example, several works modify the relay setup to obtain oscillation frequencies lower than the ultimate frequency, to that end, different strategies can be implemented, for instance including time delays in the loop [16,17,30], inserting an integrator [7,33,39], modifying the hysteresis of the relay [18] or modifying the vertical asymmetry [11].…”

Parameter Estimation Method for the Unstable Time Delay Process

“…Frequency responses of the real process and the received models, with three different proportional gains Kp, are provided in Figure 4. The validation of the received models has been carried out by applying (21) Table 2. It can be observed, based on the results in Table 2, that the considered unstable FOPTD process has been adequately identified, and that the model received by using the proportional controller gain Kp=6 with parameters K=1, T=1.0719 and θ=0.1074 has the lowest MAE and RMSE index, i.e.…”

“…The identification of the unstable model by using the relay feedback method is one of the methods that appears in literature. Using a single symmetric relay test all three parameters of unstable FOPTD model [20] have been identified, an asymmetrical relay feedback test is introduced along with sinusoidal signal for finding model parameters of various processes, among which is the unstable FOPTD model [21], method for identification of low order unstable process by using of relay with additional delay is given in [22], two identification algorithms using a single biased/unbiased relay feedback waveforms for the identification of unstable FOPTD model have been proposed in [23]. Identification method of parameters of an unstable FOPDT model when a limit cycle exists by using a single relay controllers is given in [24], two different techniques of process identification of unstable FOPTD model are analyzed in [25] by using the PID controller, while the improvements of the existing techniques of identification are [25] and [26], which solves the problems of stability and attains better time delay estimations, are given in [27].…”

“…RMSE index(21) are used to measure the Mean Absolute Error and Root Mean Squared Error between ythe real process output and ymthe output produced by the model. MAE and RMSE of 0, indicates a perfect model.…”

Asymmetric delayed relay feedback identification based on the n -shifting approach

“…If more information is required to fit a more complex model, additional experiments are necessary to force the system to oscillate at other frequencies to find additional points in the Nyquist map. Techniques to generate oscillations at lower frequencies than the original ω osc are based on including additional time delays (Leva et al, 2006;Li et al, 1991;Scali et al, 1999;Tan et al, 1996), inserting an integrator (Friman & Waller, 1997;Sung & Lee, 2006;Wang & Shao, 1999), or modifying the hysteresis (Liu & Gao, 2012) or the asymmetry of the relay (Kishore et al, 2018). The original idea of this family of methods was proposed in a seminal paper by Åström & Hägglund, 1984.…”