Level Control of Coupled Tank System Based on Neural Network Techniques
-
B. S. Sousa
,
F. V. Silva
Abstract
The control design of coupled tanks is not an easy task due to the nonlinear characteristic of the valves, and the interactions between the controlled variables. Those features pose a challenge in the automatic control, so that linear controllers, such as conventional PID, might not work properly for regulating this MIMO system. Some advanced control techniques (e. g. control based on neural networks) can be used since neural networks are universal approximators which can deal with nonlinearities and interactions between process variables. In the present work, an experimental investigation was performed presenting a comparison between two neural network-based techniques and testing the feasibility of these techniques in the coupled tanks system. First principles simulations helped to find suitable parameters for the controllers. The results showed that the model predictive control based on artificial neural networks presented the best performance for supervisory tests. On the other hand, the inverse neural network needed a very accurate model and small plant-model mismatches led to undesirable offsets.
Nomenclature
- wk,j
Sinaptic weight of the connection between neuron “k” and neuron “j”
- bk
Bias of the layer “k”
- φ
Activation function
- xj
Neuron input
- yk
Neuron output
- ym
Predicted output
- yr
Reference trajectory
- yp
Measured output
- u’
Calculated future input value
- u
Current input
- J
Objective function
- Np
Prediction Horizon
- Nc
Control Horizon
- w
Weight of the control action in the objective function
- wy
Weight of the control error in objective function
- dk
Discrepancy between the measured value of the plant and the predicted value
- yc
Output corrected by the disturbance model
- Δt
Sample time
- ysp1
Set point of level 1
- ysp2
Set point of level 2
- yi
Level of the tank “i”
- Pi
Power of the pump “i”
- ρ
Mass Density
- Aj
Cross Sectional Area of the tank “j”
- Cvj
Valve coefficient
- Lc
Height of the tank
- T
Time to complete the volume of the vessel
- Δt
Sample time
- ts
Settling time
Acknowledgements
This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001.
Appendix
A.1 Simulink Figures
Simulink diagram used to collect identification data.
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