Estimation of Five Parameters of an Unstable SOPTD Model with a Zero Using a Single Relay Feedback Test
TL;DR: In this paper, a method is proposed to identify the five parameters of an unstable second-order plus time delay model with a zero (SOPTDZ): G p =k p(1±τ 1s) exp(−τ d s)/[(τ 2s±1)(τ 3s − 1)].
Abstract: A method is suggested to identify the five parameters of an unstable second-order plus time delay model with a zero (SOPTDZ): G p=k p(1±τ 1s) exp(−τ d s)/[(τ 2s±1)(τ 3s − 1)]. Three simulation examples are given (delay system with one unstable pole, one stable pole and a negative zero; delay system with one unstable pole, one stable pole and a positive zero; delay system with two unstable poles and one negative zero). The five parameters of the SOPTDZ model are estimated adequately. The performance of the controller designed using the identified model is compared with that of the controller designed using the actual transfer function model. The method gives a good closed loop performance. The methods are given for an asymmetric relay test. A simulation example of a third-order nonlinear continuous stirred tank reactor system is also given.
Citations
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TL;DR: In this article, an improved analysis of the relay auto-tuning method is proposed to calculate the maximum value of the controller gain by considering the higher-order harmonics, which gives enhanced closed-loop performances in all the cases.
Abstract: In the present work an improved analysis of the relay auto-tuning method is proposed to calculate the maximum value of the controller gain by considering the higher-order harmonics. The reported Fourier series analysis for a first-order plus time delay (FOPTD) unstable system (Vivek and Chidambaram, 2005) is modified to an unstable second-order plus time delay system (SOPTD). Improved results in the ultimate gain values of the controller are obtained. The effectiveness of the method is demonstrated by simulation on three SOPTD transfer function models. The different models considered are: (i) a system with two unstable poles and a negative zero; (ii) a system with one stable and one unstable pole; and (iii) a system with two unstable poles and a positive zero. A simple method is also proposed to calculate the minimum value of the controller gain. The proposed method gives enhanced closed-loop performances in all the cases. The method is also applied by simulation on the nonlinear model equations of an uns...
9 citations
Cites methods from "Estimation of Five Parameters of an..."
...The method proposed by Vivek and Chidambaram (2012) is extended here to unstable SOPTD systems to determine the ultimate gain...
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...Vivek and Chidambaram (2012) extended the method for unstable FOPTD systems....
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...Also, we should recall that, for an unstable system, the value of D=s should be less than 1 to stabilize the system using a proportional controller (Vivek and Chidambaram, 2012)....
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29 Jan 2015
TL;DR: Simulation result has proven the feasibility of the technique by showing the robustness in the presence of static load disturbances and measurement noise, and new optimum proportional–integral–derivative gains are obtained from a novel technique of evolutionary algorithm.
Abstract: Nonminimum phase processes with poles and/or zeros in the right half plane are always difficult to estimate and design a regulator assuring the better performance. In this article, exact analytical expressions of the time-domain output for a class of nonminimum phase processes are derived under a relay control system. Process parameters are assumed to be unknown before the test. A single symmetrical relay test is performed to estimate up to five unknown parameters of process model effectively. Based on the estimated process model, new optimum proportional–integral–derivative gains are obtained from a novel technique of evolutionary algorithm. A new control performance index has been defined to achieve a balanced tradeoff between transient performance and actuator preservation. Simulation result has proven the feasibility of the technique by showing the robustness in the presence of static load disturbances and measurement noise.
2 citations
Cites background or methods from "Estimation of Five Parameters of an..."
...Finally, substituting equations (26) and (31) in equation (21) and rearranging the equation, the expression for the steady-state gain becomes...
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...The procedures for determination of the parameters (other than the delays) obtained from equations (20), (26), (31) and (32) for the nonminimum phase process model are given in Table 1....
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...Putting the expression for T1 T2 of equation (26) in equation (30), one obtains a second linear equation of the form...
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TL;DR: A technique to identify integrating processes based on time domain analysis of the relay response curve by means of a single symmetrical relay experiment without solving any nonlinear equations is presented.
Abstract: This paper presents a technique to identify integrating processes based on time domain analysis of the relay response curve. Explicit analytical expressions are provided for first- and second-order integrating process models in terms of a few critical point data. Models with up to three parameters are estimated by means of a single symmetrical relay experiment without solving any nonlinear equations. The procedure requires less time for the autotuning test as it uses only half-output limit cycle data. Simulation examples illustrate the simplicity of the presented method.
1 citations
Cites methods from "Estimation of Five Parameters of an..."
...Recently, Vivek and Chidambaram (17) have suggested a method to identify the five parameters of an unstable SOPDT with a zero based on an asymmetric relay test....
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References
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TL;DR: In this paper, the three principal control effects found in present controllers are examined and practical names and units of measurement are proposed for each effect and corresponding units for a classification of industrial processes in terms of two principal characteristics affecting their controllability.
Abstract: In this paper, the three principal control effects found in present controllers are examined and practical names and units of measurement are proposed for each effect. Corresponding units are proposed for a classification of industrial processes in terms of the two principal characteristics affecting their controllability. Formulas are given which enable the controller settings to be determined from the experimental or calculated values of the lag and unit reaction rate of the process to be controlled
5,412 citations
01 Jan 1942
TL;DR: In this paper, the three principal control effects found in present controllers are examined and practical names and units of measurement are proposed for each effect.
3,869 citations
"Estimation of Five Parameters of an..." refers methods in this paper
...The relay feedback method is time consuming when compared with the continuous cycling method of Ziegler and Nichols [2]....
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TL;DR: A simple method for estimating the critical gain and the critical frequency is described, which may be used for automatic tuning of simple regulators as well as initialization of more complicated adaptive regulators.
1,763 citations
Book•
15 Apr 1999
TL;DR: Proportional-Integral-Derivative Control with Autotuning for Plantwide Control Systems and Guidelines for Autotune Procedure.
Abstract: Introduction.- Relay Feedback Approach.- Systems with Unstable Zeros or Poles.- Multiloop SISO Control.-. Multivariable Composition.- Load Disturbances.- Process Nonlinearity.- Controller Monitoring.-. Application to Plantwise Control.- Guidelines of Autotune Procedure.- Appendix .
306 citations
TL;DR: Mise en place d'une procedure de commande simple which utilise la methode "autotune" d'Astrom for obtenir les gains and les frequences critiques for chaque element diagonal de la matrice des fonctions de transfert as discussed by the authors.
Abstract: Mise en place d'une procedure de commande simple qui utilise la methode «autotune» d'Astrom pour obtenir les gains et les frequences critiques pour chaque element diagonal de la matrice des fonctions de transfert. Il ne faut que N tests pour un systeme a N×N variable. La procedure, testee sur un exemple, est efficace
209 citations