Design of a multivariable internal model controller based on singular value decomposition

Jin, Qibing; Zhao, Liang; Feng, Hao; Liu, Si‐wen

doi:10.1002/cjce.21735

Cited by 10 publications

(17 citation statements)

References 17 publications

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“…The controller tuning parameter α of 1.1 is designed to give

γ

of 0.98, which is equivalent to the IMC controller. The performance of the proposed scheme is compared with the IMC controller designed based on the singular value decomposition (SVD) proposed by Jin et al The IMC controller parameters for the shell standard control problem are given by:

G_{c I M C} (s) = true[\begin{matrix} left \\ center \frac{- 2.9733 s + 0.0791}{5.7412 s^{2} + 7.0541 s + 1} e^{- 0.4878 s} \frac{7.8971 s - 0.0032}{1.5885 s^{2} + 17.4078 s + 1} e^{- 7.8553 s} \\ center \frac{- 1.2497 s - 0.336}{0.3524 s^{2} + 15.0875 s + 1} e^{- 11.769 s} \frac{- 2.4715 s + 0.2751}{1.1188 s^{2} + 11.1794 s + 1} e^{- 12.3746 s} \\ center \frac{- 0.9954 s + 0.2167}{1.2501 s^{2} + 3.2418 s + 1} e^{- 5.4051 s} \frac{- 0.5132 s - 0.0806}{5.3295 s^{2} + 2.2549 s + 1} e^{- 4.1735 s} \end{matrix} true]

…”

Section: Simulation Studiesmentioning

confidence: 99%

“…Most control design methods for non‐square processes usually realize a square controller by adding or deleting variables, which might cause degradation in system performance due to the loss of system information, especially for the minimum phase non‐square systems . Many research methods focusing on non‐square systems are based on matrix computation, if the transfer function matrix is non‐square, then the issue of inversion will often emerge …”

Section: Introductionmentioning

confidence: 99%

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Model based multivariable control scheme in a reset configuration for stable multivariable systems

Pathiran¹,

Prakash

2017

Can J Chem Eng

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The multivariable control scheme is a widely used advanced process control methodology to control key process variables in chemical engineering processes. However, successful implementation of multivariable control requires a simplified control structure, a lower number of tuning parameters, and an appropriate tuning method. In this work, a model based multivariable control scheme is realized in reset configuration for the control of stable multi‐input and multi‐output systems. This control scheme utilizes the process transfer function matrix and the inverse of the steady state gain matrix for its implementation. The control scheme has a single tuning parameter and also inherently takes into account the interaction that exists between process inputs and outputs. This scheme is easy to implement and apply in multivariable systems with multiple delays, high‐dimensional systems, non‐square systems, and systems with RHP zeros. Simulation examples from process system engineering such as industrial scale polymerization reactor system, quadruple‐tank system, temperature control for the four room process, and shell control problem are presented to show the efficacy of the proposed multivariable control scheme.

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“…The controller tuning parameter α of 1.1 is designed to give

γ

G_{c I M C} (s) = true[\begin{matrix} left \\ center \frac{- 2.9733 s + 0.0791}{5.7412 s^{2} + 7.0541 s + 1} e^{- 0.4878 s} \frac{7.8971 s - 0.0032}{1.5885 s^{2} + 17.4078 s + 1} e^{- 7.8553 s} \\ center \frac{- 1.2497 s - 0.336}{0.3524 s^{2} + 15.0875 s + 1} e^{- 11.769 s} \frac{- 2.4715 s + 0.2751}{1.1188 s^{2} + 11.1794 s + 1} e^{- 12.3746 s} \\ center \frac{- 0.9954 s + 0.2167}{1.2501 s^{2} + 3.2418 s + 1} e^{- 5.4051 s} \frac{- 0.5132 s - 0.0806}{5.3295 s^{2} + 2.2549 s + 1} e^{- 4.1735 s} \end{matrix} true]

…”

Section: Simulation Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Model based multivariable control scheme in a reset configuration for stable multivariable systems

Pathiran¹,

Prakash

2017

Can J Chem Eng

View full text Add to dashboard Cite

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“…The integral square error (ISE) values were used to quantitatively evaluate the performance of closed‐loop systems . However, Jin has adopted another method to measure overall ISE values for a TITO system . For a unit step in

R_{1}

in Figure , the ISE corresponding to the

Y_{1}

I S E_{Y_{1} - R_{1}} = {\int_{0}^{\infty} false(1 - Y_{1} false)}^{2} d t

, and the ISE corresponding to the interaction response is

I S E_{Y_{2} - R_{1}} = {\int_{0}^{\infty} false(0 - Y_{2} false)}^{2} d t

.…”

Section: Simulation Examplesmentioning

confidence: 99%

“…Here, to illustrate stability, robustness of the proposed control system, input, and output uncertainties are considered. For a process

G (s)

with an input uncertainty of

G (s) [I + {normalΔ}_{I} (j w)]

, the closed‐loop is stable if the following is true:

true∥ {normalΔ}_{I} true(normalj normalw true) true∥ < 1 true/ σ_{\max} true{- {[I + D false(normalj normalw false) C false(normalj normalw false) G false(normalj w false)]}^{- 1} D (j w) C (j w) G (j w) true}

…”

Section: Simulation Examplesmentioning

confidence: 99%

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PI controller design for a TITO system based on delay compensated structure and direct synthesis

Jin

Zhu

Wang³

et al. 2016

Can J Chem Eng

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The present study suggests a new scheme to design a decentralized PI controller for two‐input two‐output (TITO) processes. The decentralized controller is obtained from the direct synthesis method. The decoupler is derived from a modified decoupler and minimizes the interaction between the loops. Then a new reduced method based on equivalent transfer function (ETF) with relative gain array concept and relative normalized relative gain array concept reduces the decoupled process transfer functions to first‐order plus time delay (FOPTD) forms. Further, two PI controllers are obtained in the proposed delay‐compensated configuration in terms of the only parameter in every individual loop for the FOPTD transfer functions. Three illustrative examples demonstrate that the performance is verified on the original interactive system and show the effectiveness of the proposed design method. The results confirm the superior performance of the proposed compensation configuration in nominal and robust cases. The proposed method also offers several important advantages compared to other previous methods.

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Artificial neural network based identification of process dynamics and neural network controller design for continuous distillation column

Gizaw

Periyasamy

Kumar

et al. 2023

Sustainable Energy Technologies and Assessments

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Design of a multivariable internal model controller based on singular value decomposition

Cited by 10 publications

References 17 publications

Model based multivariable control scheme in a reset configuration for stable multivariable systems

Model based multivariable control scheme in a reset configuration for stable multivariable systems

PI controller design for a TITO system based on delay compensated structure and direct synthesis

Artificial neural network based identification of process dynamics and neural network controller design for continuous distillation column

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