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An \(H_\infty \) Robust Decentralized PID Controller Design for Multi-Variable Chemical Processes Using Loop Shaping Technique

  • Research Article-Electrical Engineering
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Abstract

The coupled systems with numerous interdependent variables pose considerable control and stability issues in commercial chemical processes. These systems exhibit complex interactions, time delays, parameter uncertainties and disturbances, which can lead to poor performance and reduced productivity. Conventional single-loop controllers struggle to effectively manage the interactions between variables, leading to poor disturbance rejection and tracking accuracy. A more robust and efficient control strategy is essential to tackle these limitations. Hence, a robust decentralized PID controller design is proposed to address the shortcomings of coupled industrial chemical processes. The aim is to enhance control system performance by achieving better disturbance rejection and tracking accuracy, thereby improving process efficiency and product quality. The complementary sensitivity function is exploited to attain this, and a novel graphical tuning method is proposed for obtaining optimal PID controller parameters. The use of the \(H_\infty \) robust criterion ensures robust stability and minimizes the influence of external disturbances. The proposed approach offers an efficient means to design robust decentralized controllers for complex chemical processes. The simulation results demonstrate the effectiveness of the method compared to existing controllers. Numerically, the proposed controller is able to attain almost a 20\(\%\) reduction in integral absolute error and a 30\(\%\) decrease in the settling time for all cases compared to existing controllers. The graphical tuning method enables efficient parameter optimization, resulting in faster response times and reduced settling time. This work represents a significant step toward achieving enhanced control system performance and stability in coupled industrial chemical processes.

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Abbreviations

MIMO:

Multi-input multi-output

SISO:

Single-input single-output

TITO:

Two-input two-output

PID:

Proportional integral derivative

PI:

Proportional integral

FOPDT:

First-order plus dead time

RHP:

Right half-plane

\(h_{jj}\) :

Decoupled elements

D(s):

Decoupling matrix

C(s):

Controller

\(\mathcal {K}_{\mathcal {P}}\) :

Proportional gain

\(\mathcal {K}_{\mathcal {I}}\) :

Integral gain

G :

Plant

\(\mathcal {K}_{jj}\) :

Process gain

\(\mathcal {T}_{jj}\) :

Effective dead time

\(\Theta _{jj}\) :

Time constant

\(\omega _{cjj}\) :

Phase crossover frequency

\(\mathcal {W}_{\mathcal {T}}\) :

Multiplicative weight

\(\mathcal {G}_{\delta }\) :

Perturbed plant

\(\mathcal {T}(j\omega )\) :

Complimentary sensitivity function

BLT:

Biggest logus tuning

GB:

Gershgorin-based

EOP:

Equivalent open loop

ISP:

Industrial scale polymerization

IAE:

Integral absolute error

ITAE:

Integral time absolute error

ISE:

Integral square error

WB:

Wood and berry distillation

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Author notes

  1. K. R. Achu Govind, Subhasish Mahapatra and Soumya Ranjan Mahapatro contributed equally to this work.

Authors and Affiliations

  1. School of Electronics Engineering, VIT-AP University, Amaravati, Andhra Pradesh, 522237, India

    K. R. Achu Govind & Subhasish Mahapatra

  2. School of Electronics Engineering, VIT, Chennai, Tamil Nadu, 600127, India

    Soumya Ranjan Mahapatro

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  1. K. R. Achu Govind
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  2. Subhasish Mahapatra
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Correspondence to Subhasish Mahapatra.

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Govind, K.R.A., Mahapatra, S. & Mahapatro, S.R. An \(H_\infty \) Robust Decentralized PID Controller Design for Multi-Variable Chemical Processes Using Loop Shaping Technique. Arab J Sci Eng 49, 6587–6611 (2024). https://doi.org/10.1007/s13369-023-08348-w

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