Have a personal or library account? Click to login
Decentralized stable and robust fault-tolerant PI plus fuzzy control of MIMO systems: a quadruple tank case study Cover

Decentralized stable and robust fault-tolerant PI plus fuzzy control of MIMO systems: a quadruple tank case study

Open Access
|Sep 2019

Figures & Tables

Figure 1:

Quadruple tank level process (QTLP) scheme with fault.
Quadruple tank level process (QTLP) scheme with fault.

Figure 2:

Uncertainty domain specified by working points.
Uncertainty domain specified by working points.

Figure 3:

Open-loop response of quadruple system with non-minimum phase configuration.
Open-loop response of quadruple system with non-minimum phase configuration.

Figure 4:

Open-loop response of quadruple system with minimum phase configuration.
Open-loop response of quadruple system with minimum phase configuration.

Figure 5:

Schema of simplest decentralized control of TITO system (Schmidt, 2002).
Schema of simplest decentralized control of TITO system (Schmidt, 2002).

Figure 6:

Decentralized control structure for minimum phase system with two fuzzy and two PI controllers. fsys, fa, and fs denotes system component (leak), actuator, and sensor faults, respectively.
Decentralized control structure for minimum phase system with two fuzzy and two PI controllers. fsys, fa, and fs denotes system component (leak), actuator, and sensor faults, respectively.

Figure 7:

Stability analysis for minimum phase configuration.
Stability analysis for minimum phase configuration.

Figure 8:

Step responses: minimum phase stable system subject to process disturbances.
Step responses: minimum phase stable system subject to process disturbances.

Figure 9:

Step responses: minimum phase stable system subject to system component (leak) fault.
Step responses: minimum phase stable system subject to system component (leak) fault.

Figure 10:

Step responses: minimum phase stable system subject to actuator fault.
Step responses: minimum phase stable system subject to actuator fault.

Figure 11:

Step responses: minimum phase stable system subject to sensor fault.
Step responses: minimum phase stable system subject to sensor fault.

Figure 12:

Error comparison for minimum phase configuration.
Error comparison for minimum phase configuration.

Figure 13:

Step responses: non-minimum phase, unstable system.
Step responses: non-minimum phase, unstable system.

Figure 14:

Stability analysis for non-minimum phase configuration.
Stability analysis for non-minimum phase configuration.

Figure 15:

Step responses: non-minimum phase stable system subject to process disturbances.
Step responses: non-minimum phase stable system subject to process disturbances.

Figure 16:

Step responses: non-minimum phase stable system subject to system component fault.
Step responses: non-minimum phase stable system subject to system component fault.

Figure 17:

Step responses: non-minimum phase stable system subject to actuator fault.
Step responses: non-minimum phase stable system subject to actuator fault.

Figure 18:

Step responses: non-minimum phase stable system subject to sensor fault.
Step responses: non-minimum phase stable system subject to sensor fault.

Figure 19:

Error comparison for non-minimum phase configuration.
Error comparison for non-minimum phase configuration.

Parameters for FLC_

ParameterParameter value
No. of input variables2
No. of output variables1
No. of linguistic variables per MF7
No. of rules49
Membership function (MF)Triangular
Defuzzification methodsCenter of gravity method

Parameters of the quadruple tank level process_

Sr. no.DescriptionValue
1Area of the tanks A1, A3, A2, and A4 32 cm2
2Area of outlet pipes a1 and a3 0.071 cm2
3Area of outlet pipes a2 and a4 0.057 cm2
4Constant k 0.50 V/cm
5Gravitational constant g 981 cm/s2

Operating parameters of minimum phase and non-minimum phase system_

ParametersOperating point minimum phaseOperating point non-minimum phase
h 1 0 , h 2 0 12.76, 13.112.3, 12.7
h 3 0 , h 4 0 2.1, 1.85.1, 5.7
υ 1 0 , υ 2 0 3.33, 3.363.14, 3.31
k1, k2 3.33, 3.383.14, 3.33
λ1, λ20.7, 0.60.43, 0.34

Rule base for type-1 FLC 2 loop 2_

f2, e2 and ė2NBNMNSZRPSPMPB
NBNBNBNBNMNSNSZR
NMNBNBNMNSNSZRPM
NSNBNMNSZRPSPMPB
ZRNMNMNSZRPSPMPB
PSNMNSZRPSPMPBPB
PMNSZRPSPMPMPBPB
PBZRPSPMPBPBPBPB

Rule base for type-1 FLC 1 loop 1_

f1, e1 and ė1 e ˙ 1 NBNMNSZRPSPMPB
NBNBNBNBNMNSNSZR
NMNBNBNMNSNSZRPM
NSNBNMNSZRPSPMPB
ZRNMNMNSZRPSPMPB
PSNMNSZRPSPSPMPB
PMNSZRPSPSPMPBPB
PBZRPSPSPMPBPBPB
Language: English
Page range: 1 - 20
Submitted on: Dec 19, 2018
Published on: Sep 5, 2019
Published by: Professor Subhas Chandra Mukhopadhyay
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2019 Himanshukumar R. Patel, Vipul A. Shah, published by Professor Subhas Chandra Mukhopadhyay
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.