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The focus of this contribution is twofold. The first part aims at the rigorous and complete analysis of pole loci of a simple delayed model, the characteristic function of which is represented by a quasi-polynomial with a non-delay and a delay parameter. The derived spectrum constitutes an infinite set, making it a suitable and simple-enough repres...
Citations
... Boussaada et al. 19 discussed the recent results on maximal multiplicity induced dominancy for spectral values in reduced order time delay systems, and they extend these results to a general class of second order retarded differential equations. Pekař et al. 20 analyzed the pole loci and characteristic function of simple delayed model, and applied the infinite-dimensional model to a complex heating-cooling process with heat exchangers. For systems with delays, Pekař and Matušů 21 offered a suboptimal shifting based pole-zero placement method which is essentially also a dominant pole placement method. ...
... If k p = 2 is chosen, then k i = 0.2942 and k d = −5.8861 can be obtained by Eq. (20) and Eq. (21). ...
In this paper, we mainly considered the problem of nonovershooting control of high order systems with or without time delay by simple controllers. As basic principles for nonovershooting control systems, three propositions are offered and proved. Under direction of these principles, a nonovershooting dominant pole control structure having three dominant poles, i.e., one real pole and a pair of complex conjugate poles on its left, is proposed. While its zeroes and nondominant poles are on the left side of these three dominant poles with sufficient distance. The controllers adopted are composed by first order filter and PD-PID controller. Dominance of the three dominant poles can be checked and ensured through the computational method we offered. Two illustrating examples are given to show the effectiveness of our method.
... Furthermore, many controllers require an exact process model to optimize control 16 . Managing dead-time processes in industrial environments is challenging due to the inherent time delay that characterizes these systems 42,43 . It is essential to note that conventional PI controllers will perform poorly in the closed-loop control system, which can significantly affect the system's overall performance 26 . ...
Wireless technology is becoming increasingly critical in industrial environments in recent years, and the popular wireless standards are WirelessHART, ZigBee, WLAN and ISA100.11a, commonly used in closed-loop systems. However, wireless networks in closed-loop control experience packet loss or drops, system delay and data threats, leading to process instability and catastrophic system failure. To prevent such issues, it is necessary to implement dead-time compensation control. Traditional techniques like model predictive and predictive PI controllers are frequently employed. However, these methods’ performance is sluggish in wireless networks, with processes having long dead times and set-point variations, potentially affecting network and process performance. Therefore, this paper proposes a fractional calculus-based predictive PI compensator for wired and wireless networks in the process control industries. The proposed technique has been simulated and evaluated on industrial process models, including pressure, flow, and temperature, where measurement and control are carried out wirelessly. The wireless network’s performance has been evaluated based on packet loss, reduced throughput, and increased system latency. The proposed compensator outperformed traditional methods, demonstrating superior set-point tracking, disturbance rejection, and delay compensation characteristics in the performance evaluations of the first, second, and third-order systems. Overall, the findings indicate that the proposed compensator enhances wireless networks’ performance in the process control industry and improves system stability and reliability by reducing almost half of the overshoot and settling an average of 8.3927% faster than the conventional techniques in most of the systems.
... The considered time-delay identification problem [25] is defined by a model transfer function G m : C → C (6), ...
... Then the obtained results are considerably erroneous when computing integrals around the setpoint. We have observed the described effect when performing standard relay-based identification experiments in a laboratory [44]. To judge this effect rigorously, it is possible to formulate the following simple lemma. ...
... A saturation relay with both symmetric and asymmetric settings is the second DF-based method [21], [44]. Let the former setting be labeled as METHOD-IIa, and the latter one (METHOD-IIb) should prove the advantage of an asymmetric system input level in the light of Assumption 3. The (asymmetric) saturation relay static characteristic is displayed in Fig. 7 and the corresponding DF is given by (29). ...
This paper proposes an innovative framework of a parameter estimation procedure based on the well-established relay-feedback experiment paradigm. The novelty consists in consideration of asymmetric dynamics and non-equal static gains of the identified system. A different system behavior after changing the input variable polarity near the operating point is rarely considered or even omitted within relay-based parameter identification tests, in contrast to the common use of asymmetry in the nonlinear relay element. The thing is that many existing relay-based identification techniques in the frequency domain use integrations, assuming that the system output operating point coincides with the setpoint value (i.e., the offset between them is zero). However, this is not true for asymmetric dynamic systems, which yields considerably erroneous parameter estimation as the integration result is highly sensitive to the baseline value. The resulting iterative numerical optimization-based algorithm is built-up using a chain of natural assumptions and step-by-step thought experiments. The proposed framework is applied to the well-established exponential decaying method in this paper. Some computation aspects of the algorithm are discussed. A comparative numerical study illustrates the efficacy of the proposed strategy, where several frequency-fitting-based and descriptive-function-based competitive approaches are considered.
... Model parameters were identified in a two-step procedure, where parameters affecting the static gain were determined first, followed by the estimation of the rest. A relay-based identification strategy incorporating the so-called dominant spectrum subset of the model was proposed for the same appliance and model structure in Ref. [27]. A similar modelling idea was applied to a looped experimental heat transfer setup followed by a Krylov-based model order reduction procedure [28]. ...
... The second step estimated static parameters for each single process submodel separately and the results of each substep were used to determine the parameters of the following submodel. Another approach to identifying the model parameters based on the relay-feedback experiment was published in Ref. [27]. While the computational and experimental burden was less than in the previous method, worse results were obtained. ...
... Such a model might perform worse robustness despite its better nominal accuracy. Second, the best model obtained by the relay-feedback test [27] is assumed. The research question is whether such a model can yield sufficient control responses. ...
The aim of this research is to revise and substantially extend experimental modelling and control of a looped heating-cooling laboratory process with long input-output and internal delays under uncertainties. This research follows and extends the authors' recent results. As several significant improvements regarding robust modelling and control have been reached, the obtained results are provided with a link and comparison to the previous findings. First, an infinite-dimensional model based on mathematical-physical heat and mass transfer principles is developed. All important heat-fluid transport and control-signal delays are considered when assembling the model structure and relations of quantities. Model parameter values optimization based on the measurement data follows. When determining static model parameter values, all variations in steady-state measured data are taken into account simultaneously, which enhances previously obtained models. Values of dynamic model parameters and delays are further obtained by least mean square optimization. This innovative model is compared to two recently developed process models and to the best-fit model that ignores the measured variations. Controller structures are designed using algebraic tools for all four models. The designed controllers are robust in the sense of robust stability and performance. Both concepts are rigorously assessed, and the obtained conditions serve for controller parameter tuning. Two different control systems are assumed: the standard closed-loop feedback loop and the two-feedback-controllers control system. Numerous experimental measurements for nominal conditions and selected perturbations are performed. Obtained results are further analyzed via several criteria on manipulated input and controlled temperature. The designed controllers are compared to the Smith predictor structure that is well-established for time-delay systems control. An essential drawback of the predictor regarding disturbance rejection is highlighted.
... However, if the model has more than two unknown parameters, the identification procedure cannot run under a single test. The reader is referred to [18] for further details; in particular, rigorous root loci analysis and significantly richer comparative study of using various relay types and optimization techniques can be found therein. However, the results presented in this contribution provide the best pioneering findings concisely via the core of a well-applicable identification technique in practice. ...
... Parameter sets of Model 1[18]. τ is fixed for sets I and II, while it is an optimized parameter in sets III and IV when solving(10).The corresponding initial values sets of denominator parameters of the transfer function (4) (step 4) are displayed inTable 2. In step 5, the artificial delays are selected as tively. ...
... Initial denominator parameter sets of (4)[18].Table 3. Final parameter sets of Model 2[18]. ...
This study aims at an extension and substantial improvement of the recently published relay-feedback parameter identification of an infinite-dimensional system thermal process model. The original procedure has applied the standard on/off relay to get a simplified model. Then, the dominant pole assignment has given rise to the process model characteristic quasi-polynomial via the Levenberg-Marquardt algorithm. Finally, the same optimization tool has been used to determine transfer function numerator parameters. On the contrary, a saturated relay is used to receive an improved initial simplified-model estimation in this contribution. As the process model in question has eight unknown parameters, a doubled relay test with artificial delay is made, which enables the estimation of all the parameters simultaneously. Moreover, the Nelder-Mead algorithm is used as the optimization tool. A numerical example validates an enhanced estimation in time and frequency domains.KeywordsArtificial delayInfinite-dimensional modelNelder-Mead algorithmRelay-based identification
... In the paper [2] we have described an application of sociocognitive metaheuristics to optimize the time-delay problem (from the class of identification and control problems) [3]. The whole problem was described in detail and the results of application of classic metaheuristics was discussed. ...
Following the introduction of the socio-cognitive caste-based algorithms into the classic evolutionary metaheuris-tics, in this paper we focus on similar task regarding agent-based universal optimization methods. We tackle EMAS and DE algorithms and enrich them also with TOPSIS-inspired mechanism. Besides giving the details of the methods and the background, we present preliminary results after applying those techniques to solving the problem of optimization of time-delay system model.
... In [8], a parameter identification approach based on the use of the on/off relay and the relay with saturation in the closed loop was presented. As a virtual testbed, a laboratory circuit cooling-heating process model with internal delays was utilized. ...
... A. Relay-in-loop with decaying identification principle Since the pioneering work published byÅstrom and Hägglund [10], the use of relays in the closed-feedback loop for process model parameters' identification has received great attention. The framework principle scheme is displayed in Fig. 1 [8]. Many techniques and methods have been developed within the principle so far [11], [12]. ...
... The advantage of this framework is that the process output remains close to the setpoint (if the process is stabilizable by the feedback loop), which is a feature desirable in practice. Fig. 1: Feedback relay-based identification experiment test basic scheme [8] Besides techniques using the so-called describing function with only a limited knowledge of the frequency response (e.g., as in [8]), there exist methods attempting to fit multiple frequency points without the apriori knowledge about the relay dynamic. The approach utilizing the exponential decay followed by the discrete-time Fourier transform [13] is representative of this family. ...
