A method is presented to identify the steady-state gain matrix of a multivariable (SSGM) unstable system under closed-loop control. Effects of disturbances and measurement noise on the identification of SSGM were also studied. Davison's method (Davison, 1976) was modified to design single-stage multivariable PI controllers using only the steady-state gain matrix of the system. Since the overshoots in the responses are larger, a two-stage P-PI control system is proposed. Based on the SSGM, a simple proportional controller matrix was designed by the modified Davison's method (1976) to stabilize the system. Based on the gain matrix of the stabilized system, diagonal PI controllers were designed. The performance of the two-stage control system was evaluated and compared with that of single-stage multivariable controllers. Simulation results on two examples show the effectiveness of the proposed methods for both servo and regulatory problems. © 2015, Taylor & Francis Group, LLC.

V. Dhanya Ram

C. Rajapandiyan

Manickam Chidambaram

CLOSED-LOOP METHOD

Delay systems

GAIN MATRICES

MODIFIED DAVISON'S METHOD

Multi variables

Single stage

Unstable system

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

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

Steady-State Gain Identification and Control of Multivariable Unstable Systems

Chemical Engineering Communications

The chapter deals with the design of the decentralised PID controllers for the unstable system. The method focuses on incorporating the higher-order harmonics in evaluating the ultimate gain of the process. It is observed that the higher-order harmonic have significant affect on the system performance and the incorporation of the same improves the performance tremendously. © 2018, Springer Nature Singapore Pte Ltd.

Advances in Industrial Control

Decentralized PID controllers for unstable systems

In this chapter, an improved relay auto-tuning method, considering the higher-order harmonics, is proposed for different classes of the second-order unstable systems. © 2018, Springer Nature Singapore Pte Ltd.

Auto-tuning of unstable SOPTD systems

The biggest log modulus tuning (BLT) method is extended to unstable systems. The method is modified to design (i) decentralized Proportional-Integral (PI) controllers and (ii) centralized PI controllers for two-input two-output (TITO) systems. A method is given to specify the value for Lmax cm The internal model controller using Tanttu and Lieslehto method is applied for centralized controller design. The detuning parameter (F) is selected for both the schemes (centralized controller and decentralized controller) to get the value of BLT as +12 dB. Simulation studies are carried out for two TITO systems to evaluate the performance of both the proposed schemes. The centralized controllers produce superior performances and decreased interactions over the decentralized PI controllers. The present method gives robust performances. © 2017, © 2017 Indian Institute of Chemical Engineers.

Indian Chemical Engineer

BLT Method for PI Controllers of Unstable Systems

The study presents the concept of taking the into account the higher order harmonic terms during evaluation of the ultimate gain by relay auto-tuning method. The decentralised PID control for a second order diagonally unstable system is designed. The proposed method is compared using the time integral performance and maximum singular value for the perturbated input and load. The robustness studies are conducted to interpret the process behaviour in presence of multiplicative uncertainties. The closed loop performances with less settling time and oscillatory nature is obtained. The comparison with the conventional relay auto-tuning method highlights the effect of incorporating higher order harmonic. The study is implemented on a Two Input Two output sytem with second order unstable diagonal transfer functions. © 2017 IEEE.

Proceedings - TIMA 2017: 9th International Conference on Trends in Industrial Measurement and Automation

Auto tuning of decentralised PID controllers for TITO system

In this paper, the relay auto-tuning method is improved by modifying the Zeigler-Nichols method to obtain the improved value of the controller gains of a TITO unstable system. The effect of the higher order harmonic terms are also taken into consideration while designing the controllers. The proposed method is simulated on two 2×2 unstable transfer function matrices. The implementation of the method does not need the knowledge of the transfer function matrix. The performance of the proposed method is compared with the conventional method of relay tuning. The present method gives improved response and reduced interactions. The present method is also robust. © 2016 IEEE.

IEEE International Conference on Emerging Technologies and Factory Automation, ETFA

Improved relay auto-tuning method for unstable TITO systems

In this article, two methods of designing a centralized control system for multi-input, multi-output (MIMO) processes are presented. Centralized proportional-integral (PI) controllers are designed based on a direct synthesis method. The inverse of the process transfer function matrix in the direct synthesis method is approximated based on the relative gain array concept. The method is further improved by using a relative normalized gain array, and an equivalent transfer function for each element in the process transfer function matrix is derived for the closed-loop control system. The transpose of the effective transfer function is used to approximate the inverse of the process transfer function matrix. The simulation studies demonstrate the effectiveness of this method. The proposed centralized controllers reduce the interactions better than recently reported decentralized controllers do. A centralized controller designed based on a relative normalized gain array (RNGA) gives a better performance than a centralized controller designed based on a relative gain array (RGA). © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

ISA Transactions

Centralized PI controllers for interacting multivariable processes by synthesis method

Explicit design formula are derived for feedback controllers by model reference method, synthesis method and internal model control method for an unstable first-order plus time delay system. The performance of the proposed controllers is evaluated for perturbations in time delay, time constant and process gain. The performance is also compared with that of a conventional PI controller. Copyright © 1996 Elsevier Science Ltd. All rights reserved.

Computers and Chemical Engineering

Design of controllers for unstable first-order plus time delay systems

Explicit design formulae are derived for proportional (P), and proportional and integral (PI), controllers for unstable first-order plus time delay processes. A stability condition for the design of a PI controller is derived. The values of Kmax and τI from the proposed approximate analytical solutions are compared with the exact numerical solutions. The response of the controlled system with the proposed design settings is compared with that of the settings given by De Paor and O'Malley (1989). © 1994 Taylor &amp; Francis Ltd.

Journal	Data powered by TypesetChemical Engineering Communications
Publisher	Data powered by TypesetTaylor and Francis Ltd.
ISSN	00986445
Open Access	No