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. 2020 Jun 11;20(11):3335.
doi: 10.3390/s20113335.

A Non-linear Model Predictive Control Based on Grey-Wolf Optimization Using Least-Square Support Vector Machine for Product Concentration Control in L-Lysine Fermentation

Bo Wang  1 , Muhammad Shahzad  1 , Xianglin Zhu  1 , Khalil Ur Rehman  1 , Saad Uddin  2
Affiliations

A Non-linear Model Predictive Control Based on Grey-Wolf Optimization Using Least-Square Support Vector Machine for Product Concentration Control in L-Lysine Fermentation

Bo Wang et al. Sensors (Basel). .

Abstract

L-Lysine is produced by a complex non-linear fermentation process. A non-linear model predictive control (NMPC) scheme is proposed to control product concentration in real time for enhancing production. However, product concentration cannot be directly measured in real time. Least-square support vector machine (LSSVM) is used to predict product concentration in real time. Grey-Wolf Optimization (GWO) algorithm is used to optimize the key model parameters (penalty factor and kernel width) of LSSVM for increasing its prediction accuracy (GWO-LSSVM). The proposed optimal prediction model is used as a process model in the non-linear model predictive control to predict product concentration. GWO is also used to solve the non-convex optimization problem in non-linear model predictive control (GWO-NMPC) for calculating optimal future inputs. The proposed GWO-based prediction model (GWO-LSSVM) and non-linear model predictive control (GWO-NMPC) are compared with the Particle Swarm Optimization (PSO)-based prediction model (PSO-LSSVM) and non-linear model predictive control (PSO-NMPC) to validate their effectiveness. The comparative results show that the prediction accuracy, adaptability, real-time tracking ability, overall error and control precision of GWO-based predictive control is better compared to PSO-based predictive control.

Keywords: L-Lysine fermentation; grey-wolf optimization; least-square support vector machine; machine learning; model predictive control.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
The Basic Structure of MPC.
Figure 2
Figure 2
GWO-LSSVM prediction model.
Figure 3
Figure 3
GWO-LSSVM-NMPC to control l-Lysine product concentration.
Figure 4
Figure 4
Product concentration prediction and error curve.
Figure 5
Figure 5
GWO-NMPC controlled product concentration output with hypothetical reference.
Figure 6
Figure 6
GWO-NMPC controlled inputs with hypothetical reference
Figure 7
Figure 7
GWO-NMPC controlled product concentration output with optimal reference.
Figure 8
Figure 8
GWO-NMPC controlled agitation rate u1 with optimal reference.
Figure 9
Figure 9
GWO-NMPC controlled airflow rate u2 with optimal reference.
Figure 10
Figure 10
GWO-NMPC controlled ammonia flow rate u3 with optimal reference.
See this image and copyright information in PMC

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