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

Patel, Himanshukumar R.; Shah, Vipul A.

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

Himanshukumar R. Patel

Patel, Himanshukumar R.

and

Vipul A. Shah

Shah, Vipul A.

Sep 05, 2019

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

International Journal on Smart Sensing and Intelligent Systems

Volume 12 (2019): Issue 1 (January 2019)

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Article Category: research-article

Published Online: Sep 05, 2019

Page range: 1 - 20

Received: Dec 19, 2018

DOI: https://doi.org/10.21307/ijssis-2019-004

Keywords
Actuator fault, Fuzzy control, PI controller, Sensor fault, System component fault, Decentralized control, Robust stability, Robust performance

© 2019 Himanshukumar R. Patel et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Quadruple tank level process (QTLP) scheme with fault.

Uncertainty domain specified by working points.

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

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

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

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.

Stability analysis for minimum phase configuration.

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

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

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

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

Error comparison for minimum phase configuration.

Step responses: non-minimum phase, unstable system.

Stability analysis for non-minimum phase configuration.

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

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

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

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

Error comparison for non-minimum phase configuration.

Parameters for FLC_

Parameter	Parameter value
No. of input variables	2
No. of output variables	1
No. of linguistic variables per MF	7
No. of rules	49
Membership function (MF)	Triangular
Defuzzification methods	Center of gravity method

Parameters of the quadruple tank level process_

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

Operating parameters of minimum phase and non-minimum phase system_

Parameters	Operating point minimum phase	Operating point non-minimum phase
$h_{1}^{0}$ , $h_{2}^{0}$	12.76, 13.1	12.3, 12.7
$h_{3}^{0}$ , $h_{4}^{0}$	2.1, 1.8	5.1, 5.7
$υ_{1}^{0}$ , $υ_{2}^{0}$	3.33, 3.36	3.14, 3.31
^k₁^{, k}₂	3.33, 3.38	3.14, 3.33
^λ₁^{, λ}2	0.7, 0.6	0.43, 0.34

Rule base for type-1 FLC 2 loop 2_

^f₂, e₂ and ė₂	NB	NM	NS	ZR	PS	PM	PB
NB	NB	NB	NB	NM	NS	NS	ZR
NM	NB	NB	NM	NS	NS	ZR	PM
NS	NB	NM	NS	ZR	PS	PM	PB
ZR	NM	NM	NS	ZR	PS	PM	PB
PS	NM	NS	ZR	PS	PM	PB	PB
PM	NS	ZR	PS	PM	PM	PB	PB
PB	ZR	PS	PM	PB	PB	PB	PB

Rule base for type-1 FLC 1 loop 1_

^f₁, e₁ and ė₁ ${\dot{e}}_{1}$	NB	NM	NS	ZR	PS	PM	PB
NB	NB	NB	NB	NM	NS	NS	ZR
NM	NB	NB	NM	NS	NS	ZR	PM
NS	NB	NM	NS	ZR	PS	PM	PB
ZR	NM	NM	NS	ZR	PS	PM	PB
PS	NM	NS	ZR	PS	PS	PM	PB
PM	NS	ZR	PS	PS	PM	PB	PB
PB	ZR	PS	PS	PM	PB	PB	PB

Language:: English

Publication timeframe:: 1 times per year
Journal Subjects:: Engineering, Introductions and Overviews, Engineering, other

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

Article Category: research-article

Published Online: Sep 05, 2019

Page range: 1 - 20

Received: Dec 19, 2018

DOI: https://doi.org/10.21307/ijssis-2019-004

Keywords
Actuator fault, Fuzzy control, PI controller, Sensor fault, System component fault, Decentralized control, Robust stability, Robust performance

© 2019 Himanshukumar R. Patel et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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Figure 18:

Figure 19:

Parameters for FLC_

Parameters of the quadruple tank level process_

Operating parameters of minimum phase and non-minimum phase system_

Rule base for type-1 FLC 2 loop 2_

Rule base for type-1 FLC 1 loop 1_

^f₂, e₂ and ė₂	NB	NM	NS	ZR	PS	PM	PB
NB	NB	NB	NB	NM	NS	NS	ZR
NM	NB	NB	NM	NS	NS	ZR	PM
NS	NB	NM	NS	ZR	PS	PM	PB
ZR	NM	NM	NS	ZR	PS	PM	PB
PS	NM	NS	ZR	PS	PM	PB	PB
PM	NS	ZR	PS	PM	PM	PB	PB
PB	ZR	PS	PM	PB	PB	PB	PB

^f₁, e₁ and ė₁ ${\dot{e}}_{1}$	NB	NM	NS	ZR	PS	PM	PB
NB	NB	NB	NB	NM	NS	NS	ZR
NM	NB	NB	NM	NS	NS	ZR	PM
NS	NB	NM	NS	ZR	PS	PM	PB
ZR	NM	NM	NS	ZR	PS	PM	PB
PS	NM	NS	ZR	PS	PS	PM	PB
PM	NS	ZR	PS	PS	PM	PB	PB
PB	ZR	PS	PS	PM	PB	PB	PB

^f₂, e₂ and ė₂	NB	NM	NS	ZR	PS	PM	PB
NB	NB	NB	NB	NM	NS	NS	ZR
NM	NB	NB	NM	NS	NS	ZR	PM
NS	NB	NM	NS	ZR	PS	PM	PB
ZR	NM	NM	NS	ZR	PS	PM	PB
PS	NM	NS	ZR	PS	PM	PB	PB
PM	NS	ZR	PS	PM	PM	PB	PB
PB	ZR	PS	PM	PB	PB	PB	PB

^f₁, e₁ and ė₁ ${\dot{e}}_{1}$	NB	NM	NS	ZR	PS	PM	PB
NB	NB	NB	NB	NM	NS	NS	ZR
NM	NB	NB	NM	NS	NS	ZR	PM
NS	NB	NM	NS	ZR	PS	PM	PB
ZR	NM	NM	NS	ZR	PS	PM	PB
PS	NM	NS	ZR	PS	PS	PM	PB
PM	NS	ZR	PS	PS	PM	PB	PB
PB	ZR	PS	PS	PM	PB	PB	PB

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

Himanshukumar R. Patel

Vipul A. Shah

Article Category: research-article

Published Online: Sep 05, 2019

Page range: 1 - 20

Received: Dec 19, 2018

DOI: https://doi.org/10.21307/ijssis-2019-004

KeywordsActuator fault, Fuzzy control, PI controller, Sensor fault, System component fault, Decentralized control, Robust stability, Robust performance

© 2019 Himanshukumar R. Patel et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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Figure 9:

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Figure 13:

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Figure 19:

Parameters for FLC_

Parameters of the quadruple tank level process_

Operating parameters of minimum phase and non-minimum phase system_

Rule base for type-1 FLC 2 loop 2_

Rule base for type-1 FLC 1 loop 1_

Keywords
Actuator fault, Fuzzy control, PI controller, Sensor fault, System component fault, Decentralized control, Robust stability, Robust performance

^f₂, e₂ and ė₂	NB	NM	NS	ZR	PS	PM	PB
NB	NB	NB	NB	NM	NS	NS	ZR
NM	NB	NB	NM	NS	NS	ZR	PM
NS	NB	NM	NS	ZR	PS	PM	PB
ZR	NM	NM	NS	ZR	PS	PM	PB
PS	NM	NS	ZR	PS	PM	PB	PB
PM	NS	ZR	PS	PM	PM	PB	PB
PB	ZR	PS	PM	PB	PB	PB	PB

^f₁, e₁ and ė₁ ${\dot{e}}_{1}$	NB	NM	NS	ZR	PS	PM	PB
NB	NB	NB	NB	NM	NS	NS	ZR
NM	NB	NB	NM	NS	NS	ZR	PM
NS	NB	NM	NS	ZR	PS	PM	PB
ZR	NM	NM	NS	ZR	PS	PM	PB
PS	NM	NS	ZR	PS	PS	PM	PB
PM	NS	ZR	PS	PS	PM	PB	PB
PB	ZR	PS	PS	PM	PB	PB	PB