A Supervised Model of Multivariable Control in Quadruple Tank System

Figures & data

Figure 1. (a): Laboratory Quadruple Tank Process Process setup – Front View. (b): Laboratory Quadruple Tank setup – Rear View.

Figure 2. Workflow diagram of QTP experimental setup of proposed RT-QTP and SVM-QTP models through regression technique.

Table 1. QTP Experimental Setup Specifications.

Inner diameter of all four tanks	9.2cm
Cross sectional area of all four tanks	A1, A2, A3, A4=66.47cm2
Maximum height of all four tanks	26.5cm
Maximum flow rate of each pump	F1, F2=55.57LPH
Inner diameter of outlet pipes of all four tanks	1.2cm
Cross sectional area of outlet pipes of all four tanks	a1, a2, a3, a4=1.13cm2

Figure 3. Regression Tree-Quadruple Tank Process (RT-QTP) Model responses for water level (h1) in Tank-1.

Figure 4. Regression Tree- Quadruple Tank Process (RT-QTP) Model responses for water level (h2) in Tank-2.

Figure 5. Support Vector Machine- Quadruple Tank Process (SVM-QTP) Model responses for water level (h1) in Tank-1.

Figure 6. Support Vector Machine- Quadruple Tank Process (SVM-QTP) Model responses for water level (h2) in Tank-2.

Table 2. Performance comparison of RT-QTP, SVM-QTP Models with conventional model performance.

Performance Comparison of Machine Learning Models and Conventional Models for Liquid Level h1
ML Regression Learner	Tank Height	RMSE	R-Squared	MSE	MAE	Prediction Speed (obs/sec)	Training Time (sec)
Fine Tree	H1	0.53	0.99	0.28	0.07	~21000	0.70
Medium Tree		0.52	1	0.27	0.09	~21000	0.51
Linear SVM		0.85	0.99	0.73	0.53	~47000	70.70
Coarse Gaussian SVM		0.79	0.99	0.62	0.46	~53000	0.65
Differential Equation Model		0.90	-	0.82	0.10	-	-
State-Space Model		0.90	-	0.81	0.10	-	-
Performance Comparison of Machine Learning Models and Conventional Models for Liquid Level h2
Fine Tree	H2	0.52	1	0.27	0.07	~53000	2.65
Medium Tree		0.49	1	0.24	0.07	~170000	0.77
Linear SVM		0.43	1	0.18	0.33	~120000	2.11
Coarse Gaussian SVM		0.70	0.99	0.49	0.50	~190000	0.48
Differential Equation Model		1.02	-	1.04	0.11	-	-
State-Space Model		0.96	-	0.92	0.10	-	-

Table.3. Comparison of Proposed and Existing algorithms for QTP system.

S.No	Algorithm	RMSE in prediction of liquid level h1	RMSE in prediction of liquid level h2
1	Tree Models – Fine Tree & Medium Tree (Proposed)	0.53 & 0.52	0.52 & 0.49
2	SVM Models – Linear SVM and Coarse Gaussian (Proposed)	0.85 & 0.79	0.43 & 0.70
3	Differential equation model [6]	0.90	1.02
4	State space model [6]	0.90	0.96
5	Fuzzy [6]	0.89	0.87