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Journal ArticleDOI

Steady-State Gain Identification and Control of Multivariable Unstable Systems

01 Feb 2015-Chemical Engineering Communications (Taylor & Francis Group)-Vol. 202, Iss: 2, pp 151-162
TL;DR: In this article, a method is presented to identify the steady-state gain matrix of a multivariable (SSGM) unstable system under closed-loop control and the effects of disturbances and measurement noise on the identification of SSGM were also studied.
Abstract: 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.
Citations
More filters
Journal ArticleDOI
TL;DR: The authors present a hierarchical gradient-based iterative (HGI) algorithm by using the hierarchical identification principle to solve the difficulty that the identification model contains the unmeasurable variables and noise terms in the information matrix.
Abstract: This study applies the filtering technique to system identification to study the data filtering-based parameter estimation methods for multivariable systems, which are corrupted by correlated noise – an autoregressive moving average process. To solve the difficulty that the identification model contains the unmeasurable variables and noise terms in the information matrix, the authors present a hierarchical gradient-based iterative (HGI) algorithm by using the hierarchical identification principle. To improve the convergence rate, they apply the filtering technique to derive a filtering-based HGI algorithm and a filtering-based hierarchical least squares-based iterative (HLSI) algorithm. The simulation examples indicate that the filtering-based HLSI algorithm has the highest computational efficiency among these three algorithms.

90 citations

Journal ArticleDOI
TL;DR: The result of the present method is shown to be equivalent to the empirical method proposed by Davison EJ, which is based on the static decoupler design followed by SISO PI/PID controllers design and combining the resulted decoupling and the diagonal PI(D) controllers as the centralized controllers.
Abstract: A method is given to design multivariable PI/PID controllers for stable and unstable multivariable systems. The method needs only the steady state gain matrix (SSGM). The method is based on the static decoupler design followed by SISO PI/PID controllers design and combining the resulted decoupler and the diagonal PI(D) controllers as the centralized controllers. The result of the present method is shown to be equivalent to the empirical method proposed by Davison EJ. Multivariable tuning regulators: the feed-forward and robust control of general servo-mechanism problem. IEEE Trans Autom Control 1976;21:35–41. Three simulation examples are given. The performance of the controllers is compared with that of the reported centralized controller based on the multivariable transfer function matrix.

31 citations

Journal ArticleDOI
TL;DR: In this article, an optimal tuning procedure for design of Proportional Integral Derivative (PID) controllers for open loop unstable First Order plus Time Delay systems is given. But, the proposed method is not suitable for setpoint tracking and disturbance rejection.

17 citations

Journal ArticleDOI
TL;DR: An optimal detuning approach for designing a centralized PI control system for multi-input multi-output (MIMO) processes and a novel ETF parameterization procedure for large scale processes or systems with higher-order elements is presented.

12 citations

Journal ArticleDOI
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

References
More filters
Book
01 Nov 1990
TL;DR: This is the first text to give a comprehensive and unified view of modern multivariable feedback theory and design the feedback engineer to design real systems.
Abstract: From the Publisher: This is the first text to give a comprehensive and unified view of modern multivariable feedback theory and design the feedback engineer to design real systems.

1,464 citations


"Steady-State Gain Identification an..." refers methods in this paper

  • ...…various methods available for robustness analysis in multivariable systems (Morari and Zafiriou, 1989), the method based on the inverse of maximum singular value is one that is easy to use and to compare the different control system stabilities with (Maciejowski, 1989; Vijayakumar et al., 2012)....

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  • ...First, for a process multiplicative input uncertainty as G(s)[IþDI(s)], the closed-loop system is stable if (Maciejowski, 1989): kDI ðjxÞk 1 r f½I þ GCðjxÞGðjxÞ 1GCðjxÞGðjxÞg ð25Þ where r is maximum singular value....

    [...]

  • ...Methods of designing decentralized PI controllers for stable multiple-input multiple-output (MIMO) systems were reviewed by Luyben and Luyben (1997) and Maciejowski (1989)....

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Journal ArticleDOI
01 Dec 1975
TL;DR: In this article, a robust feed-forward-feedback controller for an unknown plant so that asymptotic tracking, in the presence of disturbances, occurs is introduced. But the only assumptions made regarding the description of the plant model are that the plant is linear and time-invariant and the uncontrolled plant is stable.
Abstract: A new notion of compensator identification, as opposed to the conventional plant identification problem, is introduced in this paper. It is assumed that it is desired to synthesize a robust feedforward-feedback controller for an unknown plant so that asymptotic tracking, in the presence of disturbances, occurs. The only assumptions made regarding the description of the plant model are that 1) the plant is linear and time-invariant and 2) the uncontrolled plant is stable. Note that it is assumed that the order of the plant model is unknown. It is assumed that the control inputs to the plant can be excited, that the outputs of the plant which are desired to be regulated can be measured, and that the class of disturbance inputs and reference inputs is known. In addition, it is also assumed in the feedforward controller case, that the disturbance inputs can be measured and be excited; this assumption is not required in the robust feedback controller case. Necessary and sufficient conditions which allow the robust feedforward-feedback compensator to be synthesized so that the controlled system is stable and so that asymptotic tracking, in the presence of both measurable and unmeasurable disturbances, occurs are obtained. An algorithm which allows the controllers to be synthesized is given. Some numerical examples are included to illustrate the results.

350 citations

Journal ArticleDOI
TL;DR: In this paper, a time-delayed process with a single right half-plane pole at s = ε is designed for proportional (P), proportional plus integral (PI), and proportional plus plus integral plus derivative (PID) controllers, and an optimum stability approach for PI controllers is based on a parameter plane study.
Abstract: Proportional (P), proportional plus integral (PI) and proportional plus integral plus derivative (PID) controllers are designed for a time-delayed process having latency L and a single right half-plane pole at s=λ, with λL < 1 Explicit designs are derived from the concept of phase margin, and an optimum stability approach for PI controllers is based on a parameter plane study An optimum gain margin design is also given for P control

182 citations


"Steady-State Gain Identification an..." refers methods in this paper

  • ...The P controller is designed for each of the scalar transfer functions by the formula given by DePaor and O’Malley (1989):...

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  • ...The P controller is designed for each of the scalar transfer functions by the formula given by DePaor and O’Malley (1989): KC ¼ ½ðs=LÞ0:5 =KP ðB2Þ Tanttu and Lieslehto’s method is used for designing the controller matrix for stabilizing the system....

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Journal ArticleDOI
TL;DR: A new notion of computer identification, as opposed to the conventional plant identification problem, is introduced and necessary and sufficient conditions which allow the robust feedforward-feedback compensator to be synthesized so that the controlled system is stable and so that asymptotic tracking, in the presence of both measurable and unmeasurable disturbances, occurs.
Abstract: A new notion of computer identification, as opposed to the conventional plant identification problem, is introduced in this paper. It is assumed that it is desired to aynthesize a robust feedforward-feedback controller for an unknown plant so that asymptotic tracking, in the presence of disturbances, occurs. The only assumptions made regarding the description of the plant model are that: (i) the plant is linear and plant-invariant, (ii) the uncontrolled plant is stable. Note that it is assumed that the order of the plant modal is unknown. Necessary and sufficient conditions which allow the robust feed-forward-feedback compensator to be synthesized so that the controlled system is stable and so that asymptotic tracking, in the presence of both measurable and unmeasurable disturbances, occurs are obtained. An algorithm which allows the controllers to be synthesized is given. Some numerical examples are included to illustrate the results.

161 citations


"Steady-State Gain Identification an..." refers background or methods in this paper

  • ...Using this SSGM, the process is first stabilized by a simple P controller matrix (Davison, 1976): KC ¼ dK 1P ð3Þ where d is considered to be from 1.0 to 2.0....

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  • ...The KC matrix is given by (Davison, 1976): KC ¼ d K 1P ð3Þ KI ¼ e K 1P ð4Þ For stable multivariable systems, Davison (1976) recommended a range of values of d from 0.1 to 0.4 and e is considered from 0.05 to 0.3....

    [...]

  • ...Using this SSGM, the process is first stabilized by a simple P controller matrix (Davison, 1976): KC ¼ dK 1P ð19Þ where d is considered to be from 1.0 to 2.0....

    [...]

  • ...Davison’s method (Davison, 1976) was modified to design single-stage multivariable PI controllers using only the steady-state gain matrix of the system....

    [...]

  • ...The KC matrix is given by (Davison, 1976) Equation (3)....

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Journal ArticleDOI
TL;DR: Explicit design formulae for proportional (P) and integral (PI) controllers for unstable first-order plus time delay processes were derived in this paper, and a stability condition for the design of a PI controller was derived.
Abstract: 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 K max 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).

105 citations


"Steady-State Gain Identification an..." refers background in this paper

  • ...For unstable FOPTD systems, typical values for these two stability limits (KC,min and KC,max) are 1 and 6 (Chidambaram, 1998; Venkatashankar and Chidambaram, 1994)....

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