Analytical design 2 DOF IMC control based on inverted decoupling for non‐square systems with time delay

Jin, Qibing; Du, Xinghan; Wang, Qi; Liu, Liye

doi:10.1002/cjce.22505

Cited by 16 publications

(12 citation statements)

References 22 publications

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“…The desired open‐loop transfer functions,

l_{i} false(s false)

, must be specified to guarantee the required closed‐loop performance,

h_{i} false(s false)

and the realisability of the controller elements. Considering the H 2 optimal performance specification of IMC theory [19] with practical implementation constraints, the desired diagonal elements of the system response transfer matrix are expressed in the form of

h_{i} false(s false) = \frac{e^{- θ_{i} s}}{{false(λ_{i} s + 1 false)}^{r_{i}}} {false\prod}_{k = 1}^{q_{i}} {()(, \frac{- s + z_{k}}{s + z_{k}^{*}})}^{η_{k}}

where

λ_{i}

is an adjustable parameter set for obtaining the desirable response performance for the i th process output variable,

r_{i}

is the relative order of the numerator and denominator in

g_{i j} false(s false)

θ_{i}

is the time delay associated with this output,

z_{k}

(

k = 1, 2, . . ., q_{i}

) are the RHP zeros of the elements

g_{i j} false(s false)

in i th row vectors,

q_{i}

is their number,

z_{k}^{*}

is the complex conjugate of

z_{k}

, and

η_{k}

denotes the multiplicity of the RHP zeros. Note that by this selection, no RHP zero cancellation will happen for the transfer function matrix elements.…”

Section: Design Considerationsmentioning

confidence: 99%

“…Additional feedback filter will be needed if a disturbance dramatically deteriorates the system performance [19]. The filter for the desired closed‐loop transfer function could be

f_{i} false(s false) = \frac{φ false(s false) {false(λ_{i} s + 1 false)}^{r_{i}}}{{false(ε_{i} s + 1 false)}^{ν_{i}}}

The term

false(λ_{i} s + 1 false)^{r_{i}}

is used to cancel the specified poles of

h_{i} false(s false)

for reference tracking.…”

Section: Design Considerationsmentioning

confidence: 99%

“…The inverted decoupling maintains very simple elements for the decoupler independent of the system size, also presents several practical advantages on implementation [16]. However, when applied to non‐square processes, the decoupling controller will involve complex transfer functions including the sum of elements of the process transfer function matrix [19]. A new diagonal pre‐compensator is added to the control structure.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Compensator design based on inverted decoupling for non‐square processes

Luan

Chen

Albertos³

et al. 2017

IET Control Theory & Applications

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“…The desired open‐loop transfer functions,

l_{i} false(s false)

, must be specified to guarantee the required closed‐loop performance,

h_{i} false(s false)

h_{i} false(s false) = \frac{e^{- θ_{i} s}}{{false(λ_{i} s + 1 false)}^{r_{i}}} {false\prod}_{k = 1}^{q_{i}} {()(, \frac{- s + z_{k}}{s + z_{k}^{*}})}^{η_{k}}

where

λ_{i}

is an adjustable parameter set for obtaining the desirable response performance for the i th process output variable,

r_{i}

is the relative order of the numerator and denominator in

g_{i j} false(s false)

θ_{i}

is the time delay associated with this output,

z_{k}

(

k = 1, 2, . . ., q_{i}

) are the RHP zeros of the elements

g_{i j} false(s false)

in i th row vectors,

q_{i}

is their number,

z_{k}^{*}

is the complex conjugate of

z_{k}

, and

η_{k}

denotes the multiplicity of the RHP zeros. Note that by this selection, no RHP zero cancellation will happen for the transfer function matrix elements.…”

Section: Design Considerationsmentioning

confidence: 99%

“…Additional feedback filter will be needed if a disturbance dramatically deteriorates the system performance [19]. The filter for the desired closed‐loop transfer function could be

f_{i} false(s false) = \frac{φ false(s false) {false(λ_{i} s + 1 false)}^{r_{i}}}{{false(ε_{i} s + 1 false)}^{ν_{i}}}

The term

false(λ_{i} s + 1 false)^{r_{i}}

is used to cancel the specified poles of

h_{i} false(s false)

for reference tracking.…”

Section: Design Considerationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Compensator design based on inverted decoupling for non‐square processes

Luan

Chen

Albertos³

et al. 2017

IET Control Theory & Applications

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“…Time delay and coupling are problems that widely occur in industry, especially in the MIMO process (Jin et al, 2016). Coupling is the interaction between process variables and causes difficulties in designing MIMO controllers.…”

Section: Introductionmentioning

confidence: 99%

Inverted Decoupling 2DoF Internal Model Control for Mimo Processes

Juwari¹,

Azizah²,

Handogo³

et al. 2019

IJTech

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In general, the multiple-input-multiple-output (MIMO) system is the main method of process control in industry. However, the interaction between variables in the process is a challenge when designing controllers for the system. Strong interaction worsens system performance. Inverted decoupling plays an important role in reducing interaction in the process. Internal model control (IMC) is the controller used in this research. A one degree of freedom (1DoF) IMC controller is only able to provide a good response to set-point tracking, and has a slow response to disturbance rejection. Therefore, a controller that has a good response to set-point tracking and disturbance rejection is a two degrees of freedom (2DoF) IMC. The tuning method uses maximum peak gain margin (Mp-GM) stability criteria based on the uncertainty model. In this study, a reduction in interaction was realized by the addition of inverted decoupling to the 2DoF IMC control scheme. The Wardle & Wood and Wood & Berry column distillation models are given as illustrative examples to demonstrate the performance of the inverted decoupling 2DoF IMC control scheme. A comparison is made of the IAE values of 1DoF IMC, 2DoF IMC, decoupling 2DoF IMC, and inverted decoupling 2DoF IMC, with inverted decoupling 2DoF IMC showing the lowest IAE value.

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“…Como exemplo, pode-se citar a estrutura IMC proposta por Raja and Ali (2017) para lidar com sistemas instáveis, o controlador IMC-PID, baseado em funções equivalentes EOTF (do inglês, effective open-loop transfer function), proposto por Jin et al (2013) para sistemas não quadrados e a estrutura IMC com desacoplador invertido para sistemas quadrados apresentada em Garrido et al (2014). O trabalho realizado por Jin et al (2016) também utiliza uma estrutura IMC com desacoplador invertido, mas a ideiaé estendida para sistemas não quadrados.…”

Section: Introductionunclassified

Síntese de Controlador PI Multivariável Baseado em Controle por Modelo Interno e Otimização Multiobjetivo

Abreu

Martins

Gonçalves

2019

Anais Do 14º Simpósio Brasileiro De Automação Inteligente

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The PID controllers need the tuning of three parameters: the proportional gain, the derivative time and the integral time. With the internal model control (IMC) structure, however, it is possible to obtain PID or PI controllers by tuning only one parameter per control loop. This work presents a simple and efficient implementation of decoupled PI controllers for plants with multiple inputs and multiple outputs with delays based on IMC and multiobjective optimization. The decoupler is designed using the Differential Evolution method. Based on the decoupled system, the IMC tuning rules are used to generate the PI controllers (IMC-PI). This work proposes the application of the algorithm Differential Evolution for Multiobjective Optimization to determine the parameters of the IMC-PI controllers, which makes it possible to obtain a group of efficient solutions with different trade-offs between the set point tracking and the control effort. Resumo: Os controladores PID necessitam do ajuste de três parâmetros: o ganho proporcional, o tempo derivativo e o tempo integral. Com a estrutura de controle por modelo interno (IMC), porém,é possível obter controladores PID ou PI sintonizando apenas um parâmetro por malha de controle. Esse trabalho apresenta uma forma de implementação simples e eficiente de controladores PI desacoplados para plantas com múltiplas entradas e múltiplas saídas com atrasos, baseado no IMC e em otimização multiobjetivo. O desacopladoré projetado utilizando o método de Evolução Diferencial. Com base no sistema desacoplado, são utilizadas as regras de sintonia IMC para gerar os controladores PI (IMC-PI).É proposto nesse trabalho a aplicação do algoritmo Evolução Diferencial para Otimização Multiobjetivo para determinação dos parâmetros dos controladores IMC-PI, o que torna possível a obtenção de um grupo de soluções eficientes com diferentes compromissos entre o rastreamento da referência e o esforço de controle.

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Analytical design 2 DOF IMC control based on inverted decoupling for non‐square systems with time delay

Cited by 16 publications

References 22 publications

Compensator design based on inverted decoupling for non‐square processes

Compensator design based on inverted decoupling for non‐square processes

Inverted Decoupling 2DoF Internal Model Control for Mimo Processes

Síntese de Controlador PI Multivariável Baseado em Controle por Modelo Interno e Otimização Multiobjetivo

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