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Applying hybrid genetic–PSO technique for tuning an adaptive PID controller used in a chemical process

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Abstract

The conventional PID controller has static parameters that cannot be changed at different operating conditions. As a result, the term ‘adaptive PID controller’ has appeared to solve this problem. This controller can be tuned using intelligent techniques such as Fuzzy Logic Control, Neural Network Control, or Adaptive Neuro-Fuzzy Inference Systems. However, the choice of the suitable parameters for these intelligent controllers has a direct effect on their performance. Metaheuristics algorithms—with their powerful performance, speed, and optimal parameter selection—can be applied for choosing controller parameters efficiently. In this paper, a hybrid of genetic algorithm and particle swarm optimization is proposed to tune the parameters of different adaptive PID controllers. To evaluate the performance of the proposed hybrid optimization method on the different adaptive PID controllers, these controllers are applied to control the operation of one of the most difficult chemical processes, the divided wall distillation column. The proposed column used in this work separates a ternary mixture of ethanol, propanol, and n-butanol. Our proposed hybrid optimization technique is compared with the genetic algorithm, and simulation results show that our proposed hybrid genetic-particle swarm technique outperforms genetic algorithm for different disturbances.

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(Khanam 2014)

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Abbreviations

B :

Bottom product flow rate (kmol/min)

D :

Distillate product flow rate (kmol/min)

l :

Reflux flow rate (kmol/min)

F :

Feed flow rate (kmol/min)

S :

Side stream flow rate (kmol/min)

V :

Boilup flow rate (kmol/min)

R L :

Liquid split ratio

R V :

Vapor split ratio

M i :

Total liquid holdup on the ith tray (kmol)

L i :

Liquid flow rate from the ith tray (kmol/min)

V i :

Vapor flow rate from the ith tray (kmol/min)

x i,j :

Mole fraction of the jth component in the liquid phase at the ith tray

y i,j :

Mole fraction of the jth component in the vapor phase at the ith tray

\( \alpha_{j} \) :

Relative volatility of the jth component

q :

Feed condition

\( T_{{{\text{B}},j}} \) :

Boiling point temperature of the jth component

\( T_{i} \) :

Temperature of the ith tray

N :

Number of trays

\( x_{\text{A}} \) :

Top composition, component A

\( x_{\text{B}} \) :

Side composition, component B

\( x_{\text{C}} \) :

Bottom composition, component C

\( z_{1} \) :

Feed composition, component A

\( z_{2} \) :

Feed composition, component B

Subscript \( i \) :

Tray number \( i \in \left\{ {1, \ldots , N} \right\} \)

Subscript \( j \) :

Component \( j \in \left\{ {1, 2, 3} \right\} \)

\( u\left( t \right) \) :

The control signal

\( K_{\text{p}} \) :

Proportional gain

\( K_{\text{i}} \) :

Integral gain

\( K_{\text{d}} \) :

Derivative gain

\( e\left( t \right) \) :

Error between reference and actual temperatures

\( \omega_{k + 1} \) :

The inertia factor

\( c_{1} \) :

The cognitive scaling factor

\( c_{2} \) :

The social scaling factor

\( r_{1,k}^{i} , r_{2,k}^{i} , r_{3,k}^{i} \) :

Random numbers uniformly distributed in the interval \( \left[ {0 \,1} \right] \)

\( p_{k}^{i} \) :

The best previously obtained position of the ith particle

\( p_{k}^{g} \) :

The best obtained position in the entire swarm at the current iteration \( k \)

\( k \) :

Iteration number

\( v_{k + 1}^{i} \) :

The velocity update of a particle \( i \)

\( v_{k}^{i} \) :

The current velocity of a particle \( i \)

\( x_{k + 1}^{i} \) :

The position update of a particle \( i \)

\( x_{k}^{i} \) :

The current position of a particle \( i \)

\( N \) :

Dimension of the problem

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Correspondence to Eman M. El-Gendy.

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El-Gendy, E.M., Saafan, M.M., Elksas, M.S. et al. Applying hybrid genetic–PSO technique for tuning an adaptive PID controller used in a chemical process. Soft Comput 24, 3455–3474 (2020). https://doi.org/10.1007/s00500-019-04106-z

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Keywords

  • Divided wall distillation column
  • Genetic algorithm
  • PID controller
  • Particle swarm optimization
  • Fuzzy gain scheduling PID
  • Neural PID tuner
  • ANFIS PID tuner
  • Hybrid GA-PSO