Using a single-symmetric relay feedback test, a method is proposed to identify all three parameters of a stable second-order plus time delay (SOPTD) model with equal time constants [k p exp(-Ds)/(τs + 1) 2]. The conventional analysis of the relay auto-tune method gives 27% error in the calculation of k u, for a large D/τ. In the present work, a method is proposed to improve the accuracy in the k u calculation by incorporating higher order harmonics. Three simulation examples are given for SOPTD and higher order time delay transfer function models. The estimated model parameters of the SOPTD model are compared with those of the Li et al. (1991) method and those of the Thyagarajan and Yu (2003) method. The open-loop performance of the identified model is compared with that of the actual system. The proposed method gives performance close to that of the actual system. Simulation results are also given for a nonlinear bioreactor system. The closed-loop performance of the model identified by the proposed method is close to that of the actual system. © 2012 Copyright Taylor and Francis Group, LLC.

Manickam Chidambaram

Actual system

AUTO-TUNE

Autotuning

Bioreactor system

Closed-loop performance

DAMPED SYSTEMS

ESTIMATED MODEL

Higher order harmonics

Open loops

PID controllers

RELAY FEEDBACK TEST

Second orders

Simulation example

SYMMETRIC RELAY

Three parameters

Time constants

Transfer function model

Bioreactors

Identification (control systems)

Three term control systems

Time delay

Transfer functions

Computer simulation

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IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

An improved relay auto tuning of pid controllers for critically damped soptd systems

Chemical Engineering Communications

A method is proposed to identify the model parameters of a stable, critically damped second-order plus time delay system. The method uses a step response of the closed-loop system using a PID controller. The two dominant poles of the closed-loop model were obtained using the step response. The process gain was calculated using the steady-state deviation values of the output and the input variable of the process. Using the identified dominant poles in the derived closed-loop characteristic equations, the relevant two nonlinear algebraic equations were derived to calculate the process delay and time constant. Three simulation examples were considered to show the effectiveness of the proposed method. The open-loop and as well as the closed-loop responses of the process were compared with those of the identified model and of the controller design based on the models. A significant improvement was obtained in the performance of the critically damped SOPTD model over that of the FOPTD model. The identified model parameters by the present method were compared with those of the relay auto-tuning method. A simulation study on a nonlinear bio reactor is also reported. © Taylor & Francis Group, LLC.

On-line controller tuning for critically damped SOPTD systems

In the present work, the equating coefficient method (ECM) of designing proportional integral derivative (PID) controllers is applied to critically damped stable second-order plus time delay (SOPTD) systems. Four simulation examples representing the higher-order models and based on the identified critically damped SOPTD model are considered to show the effectiveness of the proposed method. A good improvement in the closed-loop system performance is achieved for the ECM when compared to that the internal model control (IMC) method. A significant improvement is obtained in the performance of the control systems based on the critically damped SOPTD model over that of the first-order plus time delay (FOPTD) model. The ECM of designing PID controllers is also given for stable general SOPTD systems (under damped or over damped). © 2014, © 2014 Indian Institute of Chemical Engineers.

Indian Chemical Engineer

Tuning of Proportional Integral Derivative Controllers for Critically Damped Second-Order Plus Time Delay Systems

The objective of this paper is to design a robust PI controller for a second order system plus delay (SOSPD) which has an inherent nonlinearity by the virtue of its structural dynamics. An example of Dual Spherical Tank Liquid Level System (DSTLLS), which is non linear, has been chosen to analyse the performance of the robust PI controller designed. The DSTLLS has been linearized and modelled using black box modelling technique by performing the real-time experimentation and the performance of the applied controller has been analysed in simulation by MATLAB Simulink. This paper also discusses about the simulation efficiency using the performance indices like Integrated Squared Error (ISE) and Integrated Absolute Error (IAE). © 2015 IEEE.

2015 International Conference on Control, Instrumentation, Communication and Computational Technologies (ICCICCT)

Linearized PI controller for real-time delay dominant second order nonlinear systems

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 unstable bioreactor. © 2016, Copyright © Taylor & Francis Group, LLC.

Improved Relay Auto-Tuning of PID Controllers for Unstable SOPTD Systems

The method of identifying first order plus time delay transfer function model proposed for unstable systems by Ananth and Chidambaram [Closed loop identification to transfer function model for unstable systems, J. Franklin Inst. 336 (1999) 1055-1061] is modified to avoid the stability problems [Cheres, Parameter estimation of an unstable system with a PID controller in a closed loop configuration, J. Franklin Inst., 2005, accepted for publication] of the method. Two modifications are proposed. In the first modification of the method, the under-determined algebraic equations problem is converted into an optimization problem for calculation of the three parameters of the first order plus time delay (FOPTD) model. A simple method is given for the initial guess values of the model parameters. In the second approach, from the definition of Laplace transform of the output response, a third equation is formulated. The resulted three equations, in terms of the three parameters of the transfer function model, are then numerically solved. Simulation results are given for the second order plus time delay transfer function considered by Cheres 2005 [Parameter estimation of an unstable system with a PID controller in a closed loop configuration, J. Franklin Inst., 2005, accepted for publication]. The responses of the identified models with the same PID controllers are compared with that of the actual system. PID controllers are designed based on the identified models. The closed loop responses of the controllers on the original system are evaluated and compared. The present methods give better control performances. © 2005 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Journal of the Franklin Institute

Improved closed loop identification of transfer function model for unstable systems

Using a single symmetric relay feedback test, a method is proposed to identify all the three parameters of a first order plus time delay (FOPTD) unstable model. It is found by simulation that, the relay autotune method gives -23% error in the calculation of ku, when D/τ = 0.6. In the present work, a method is proposed, by incorporating the higher order harmonics to explain the error in the ku calculation. A method is proposed to estimate all the parameters of an unstable FOPTD system. Two simulation results are given on unstable first and second order plus time delay transfer function models. The estimated model parameters of the unstable FOPTD model are compared with the methods of Majhi, S. &amp; Atherton, D.P. [(2000). Online tuning of controllers for an unstable FOPTD process. IEE Proceedings Control Theory Applications, 147(4), 421-427] and the Thyagarajan, T., &amp; Yu, C.C. [(2003). Improved autotuning using the shape factor from relay feedback, Industrial engineering Chemistry Research, 42, 4425-4440] PID controllers are designed for the identified model and for the actual system. The proposed method gives performance close to that of the actual system. For a second order plus time delay system, the latter two methods fail to identify the FOPTD model. Simulation results are also given for a nonlinear bioreactor system. The PID controller designed on the model identified by the proposed method gives a performance close to that of the controller designed on the locally linearized model. © 2005 Elsevier Ltd. All rights reserved.

Computers and Chemical Engineering

An improved relay auto tuning of PID controllers for unstable FOPTD systems

Using a single symmetric relay feedback test, a method is proposed to identify all the three parameters of a first order plus time delay (FOPTD) model. On identifying a higher order dynamics system by a FOPTD model, the conventional method identifies a negative time constant [Li, W., Eskinat, E., & Luyben, W. L. (1991). An improved auto tune identification method. Industrial and Engineering Chemistry Research, 30, 1530-1541] due to the error in neglecting higher order dynamics in the system output. In the present work, all the parameters of a FOPTD model are estimated with adequate accuracy. Three simulation examples are given. The estimated model parameters of a FOPTD model are compared with that obtained by Li et al. [Li, W., Eskinat, E., & Luyben, W. L. (1991). An improved auto tune identification method. Industrial and Engineering Chemistry Research, 30, 1530-1541] and also that with exact model parameters of the system. The performance of the controller designed on the identified model is compared with that identified by Li et al. [Li, W., Eskinat, E., & Luyben, W. L. (1991). An improved auto tune identification method. Industrial and Engineering Chemistry Research, 30, 1530-1541] and with that of the actual process. The proposed method gives performance close to that of the actual system. Simulation results for stable and unstable systems are given. © 2005 Elsevier Ltd. All rights reserved.

Identification using single symmetrical relay feedback test

Industrial & Engineering Chemistry Research

Area Methods for Relay Feedback Tests

AN IMPROVED RELAY AUTO TUNING OF PID CONTROLLERS FOR CRITICALLY DAMPED SOPTD SYSTEMS

Journal	Chemical Engineering Communications
ISSN	00986445
Open Access	No