Table 4 Performance comparison of PID, FOPID, SMC and LQR controllers for RO desalination.

From: A smart single stage solar battery driven desalination system with hybrid MPPT and optimal control for brackish water treatment

 

Rated from the permeate flow rate

Qpref and Product

Evaluated performance

Techniques used for RO

Water Salinity Cpref

PID

FOPID

SMC

LQR

step 0–7 h

 

Rise time(h)

0.25

0.27

0.24

0.23

0.02 m3/h

Settling time(h)

2.5

2.2

2.05

1.56

5.2 mg/l

Overshoot (%)

12

9

7

1

 

Peak time (h)

2.2

2.1

2.05

1.56

step 7–11 h

 

Rise time(h)

0.59

0.50

0.48

0.43

0.24 m3/h

Settling time(h)

3.384

3.25

2.1

0.5

5.2 mg/l

Overshoot (%)

30

21

12

2

 

Peak time (h)

0.55

0.52

0.5

0.48

step 11–15 h

 

Rise time(h)

0.62

0.6

0.58

0.50

0.35m3/h

Settling time(h)

2.62

2.25

2.25

1.82

5.2 mg/l

Overshoot (%)

32

25

25

2

 

Peak time (h)

1.74

1.33

1.2

0.64

step 15–19 h

 

Rise time(h)

0.44

0.41

0.41

0.34

0.198m3/h

Settling time(h)

3.90

3.68

3.18

2.1

5.2 mg/l

Overshoot (%)

22

17

13

2

 

Peak time (h)

0.44

0.42

0.41

0.27

step 19–22 h

 

Rise time(h)

0.36

0.32

0.31

0.24

0.118m3/h

Settling time(h)

3

2.62

2.62

1.43

5.2 mg/l

Overshoot (%)

52

18

18

2

 

Peak time (h)

0.66

0.62

0.62

0.43

step 22–24 h

 

Rise time(h)

0.47

0.44

0.44

0.34

0.032m3/h

Settling time(h)

2

1.96

1.85

1.2

5.2 mg/l

Overshoot (%)

28

19

15

2

 

Peak time (h)

1.37

1.30

0.92

0.37

Control effort

  

Low

Moderate-Low

Moderate

High

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