Self-tuning fuzzy logic PID controller, applications in ...

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Int. J. Intelligent Systems Technologies and Applications, Vol. 14, No. 1, 2015

Self-tuning fuzzy logic PID controller, applications in nuclear power plants Harsh Deol and Hossam A. Gabbar* Faculty of Energy Systems and Nuclear Science, University of Ontario Institute of Technology (UOIT), 2000 Simcoe Street North, Oshawa, L1H 7K4 ON, Canada Fax: 1–905–721–3046 Email: [email protected] Email: [email protected] *Corresponding author Abstract: This paper presents intelligent control design using self-tuning fuzzy logic control technique. The proposed adaptive control design is used to maintain system parameters to be within design limits, which provided means to improve the efficiency of the overall control system. The proposed self-tuning control system is applied on breathing air control systems in nuclear power plant which was recommended to maintain system pressure within design limits. System dynamics were studied, transfer functions were built and controlling parameters were established to develop system model in Simulink. Relationship to system pressure, steady-state error, Kp, Ki and Kd was studied and used to build fuzzy controller. Controller was implemented and simulation results demonstrated that self-tuning fuzzy PID controller has better control, precision and performance in maintaining system pressure with reduced overshoot, rise time, settling time and steady state error compared against conventional PID controller. Fuzzy PID controller also proved to be huge cost saver for the company in long run. Keywords: PID controller; fuzzy logic controller; control system design in nuclear power plants; air breathing system. Reference to this paper should be made as follows: Deol, H. and Gabbar, H.A. (2015) ‘Self-tuning fuzzy logic PID controller, applications in nuclear power plants’, Int. J. Intelligent Systems Technologies and Applications, Vol. 14, No. 1, pp.70–89. Biographical notes: Harsh Deol is a Graduate student with University of Ontario Institute of technology (UOIT) since 2011. He got his Bachelor degree in Nuclear Engineering in 2008 and is currently pursuing Masters degree (MASc) in the same field. Hossam A. Gabbar is a Professor in the Faculty of Energy Systems and Nuclear Science and the Faculty of Engineering and Applied Science at the University of Ontario Institute of Technology. Since 2004, he was an Associate Professor in the Division of Industrial Innovation Sciences, Okayama University, Japan.

Copyright © 2015 Inderscience Enterprises Ltd.

Self-tuning fuzzy logic PID controller, applications in nuclear power plants

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Introduction

Nuclear power plants meet more than 50% Ontario electricity demand (OPG, n.d.). It is imperative to run them reliably and safely at all times. This is partly done by executing plant outages wherein, a unit is taken offline and personnel enter reactor building to execute maintenance. Airborne radiation levels in the reactor building can be high, therefore, personnel require breathing air supply to perform work inside these buildings. Hence, pressure to the breathing air system at Nuclear Plant becomes crucial to execute work during outage and could lead to outage delays if not maintained within design limits (OPG, 1989). As shown in Figure 1, typical breathing air system at nuclear generating plant in Ontario is supplied by “three, two stage, water cooled and oil free rotary screw compressors, ZR3B type manufactured by Atlas Copco” (OPG, 1989). Each compressor discharges air at 650 scfm at 860 kPa into air receiver that further discharges air to 4 inch diameter common header (OPG, 1989). Figure 1

Schematics of breathing air compressor

Source: OPG (2011)

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H. Deol and H.A. Gabbar

The compressor internals (i.e., oil coolers, intercoolers, aftercoolers etc.) are cooled by service water supplied to each compressor to maintain its key parameters under acceptable limits. Each compressor also has a water separator at the aftercooler drain trap to extract moisture from breathing air before it’s supplied to station. In addition, it also contains air filter to remove dust and foreign materials from air that is fed downstream. After compressors and receivers, breathing air is fed to common header that contains two pressure control valves (Pressure CVs) with operating alignment as one valved in and one standby to reduce operating pressure from 860 kPa to 620 kPa to be compliant with system design pressure. Drain traps exist to air receivers, piping and stations to remove excess moisture from breathing air to keep its air quality within compliance of Z180.1-00 standards (CSA Compressed Breathing Air and Systemsstd). The control problem investigated involves Pressure CVs not operating reliably to maintain design pressure of 620 kPa. Typically, in Nuclear Generation plants, preventative maintenance practices exist to maintain functionality of Pressure CVs. Due to accumulation of dirt (ex rust), they could get stuck closed to further reduce pressure maintaining capability in the system. Consequences include, CVs not regulating system pressure properly and incurring extra costs to the company (e.g., during plant outages, when increased maintenance activities are carried out in the RB (reactor building), breathing air demand goes high but the CVs do not regulate to allow more air to pass through and maintain system pressure at 620 kPa. Therefore, breathing air pressure reduces beneath 550 kPa initiating alarm to the control room and all maintenance activities get stopped resulting in outage delays.)

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Literature review

Focus of the paper is to investigate breathing air control problem at nuclear generating plant in Ontario using self-tuning fuzzy logic PID controllers since it provides optimised control in maintaining system design pressure involving complicated and uncertain system parameters. Review of the following references demonstrated self-tuning fuzzy-logic controller is a better choice compared against conventional PID controllers. “Fuzzy immune PID control in VVVF Hydraulic system” (Beitao et al., 2009) paper proved that conventional PID controller had difficulty maintaining precise pressure in the system whereas, biologically immune and principal adjusted amalgamated fuzzy controller is more effective to maintain system desired pressure to VVVF hydraulic system. “Fuzzy PID control of intelligent pump” (Lu et al., 2011) also showed field pressure control problems to aerial hydraulic system solved via designing an intelligent pump. Non linear mathematical model for the pump was developed since load to aerial hydraulic system was complex. A fuzzy PID controlled algorithm was developed to raise output of the load. Simulation was performed and compared against PID controller. Results demonstrated fuzzy PID controller having better accuracy and rapidity than conventional PID controller in maintaining pressure to the hydraulic system. “Application of self-tuning fuzzy PID controller on industrial hydraulic actuator using system identification approach” (Zulfatman and Rahmat, 2012) also demonstrated that a


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self-tuning fuzzy PID controller is better to optimise electro-hydraulic actuator performance. System Identification technique was used for investigating and estimating mathematical model of the system. Discrete transfer functions were developed, Matlab was used for simulation and fuzzy logic was used to tune parameters of PID controller. Results indicated improved performance of hydraulic system with fuzzy PID compared to conventional PID controller. “The pump house constant pressure fuzzy self-tuning PID control system simulation” (He and Song, 2012) also showed that keeping constant pressure to the water supply system using conventional PID controller produced large delay times and often was not reflective of the working condition parameters. A self-tuning fuzzy PID led controller showed better real-time tuning of PID parameters to maintain pressure to the water supply system. Modelling to the system developed in Matlab/Simulink proved that by using fuzzy led PID controller, short output response is attained and strong robustness was achieved in steady state, PID parameters with no overshoot. It was concluded again that fuzzy led PID controllers were better solution for complicated pump delay system issues. “Predictive fuzzy PID control: theory, design and simulation” (Jialiang et al., 2012) also reiterated same results. Controller was developed to improve time-delay systems using fuzzy led PID logic. Predictive control concepts and fuzzy PID control were used to develop a structure of a controller based on, online model identification, fuzzification, defuzzification, rule base and optimal cost index. Many simulations were performed and advantages to the controller were confirmed. Results indicated predictive fuzzy PID control methods providing better control to complex linear/nonlinear and uncertain systems.

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Proposed design

The new proposed design at a nuclear generating station in Ontario involves replacing CVs with fuzzy + PID controllers as shown in Figure 2. Figure 2

Proposed design of breathing air system

CP → Air Compressor, RC → Receiver, RB → Reactor Building.


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Following process was used to conclude proposed control design in Simulink (Zhong, 2006). •

Control goals established → Maintain breathing air system pressure at 620 kPa and never below 550 kPa.

•

Variables to be controlled identified → System pressure, steady-state error, fuzzy/PID parameters Kp, Ki and Kd.

•

Specifications written → modelling to PID done repeatedly to understand system behaviour to develop fuzzy rules and establish Kp, Ki and Kd numerical ranges.

•

System configuration established → Block diagram developed with fuzzy matrix and rules to drive PID controllers.

•

Process model developed in Simulink (Figure 3).

•

Control problem analysed, controllers developed and key parameters adjusted for simulation.

•

Simulation performance analysed and parameters adjusted to produce optimum results.

•

Simulation performance adjured to specifications and process repeated to reach control goal (of maintaining system pressure at 620 kPa and never below 550 kPa). Control design finalised in the end (Figure 3).

Figure 4 demonstrates sample system configuration of breathing air controlling valves at a nuclear generating station in Ontario (OPG, 2011). Figure 3

Model of breathing air using fuzzy + PID controller in Simulink

Self-tuning fuzzy logic PID controller, applications in nuclear power plants Figure 4

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Breathing air flowsheet (see online version for colours)

Source: OPG (2011)

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Datasets

Modelling and building transfer functions of the system in Simulink consisted of four parts. Part 1: Valve input signal to open or close the valve. Generated from an electrical controller, the electrical input signal range is kept between 4–20 ma and relative output pressure range is 3–15 psi (g). Therefore equation (1) calculates the slope. G ( Ax) =

20 − 4 16 = = 1.33 = K 0 15 − 3 12

G ( Ax) = K 0.

(1) (2)

Part 2: Valve travel due to signal input. This includes the movement of valve stem including friction. Following equation was used to drive the transfer functions. m × y = − F = ( P × S ) − ( K1× y ) − ( K 2 × y )

m: y :

mass of the valve acceleration of valve movement

y :

velocity of valve stem

(3)

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y: F: P: S: K1–K8:

friction displacement of valve force pressure imposed on the valve area of valve diaphragm constants.

Simplifying the equation gives: (m × y ) + ( K1× y ) + ( K 2 × y ) = ( P × S )

(4)

§ § K1 · § K 2 ·· § S · × y ¸ + ¨ × y¸¸ = ¨ × P¸ ¨ ( y) + ¨ m m m © ¹ © ¹ © ¹ © ¹

(5)

y + ( K 3 × y ) + ( K 4 × y ) = ( K 5 × P ).

(6)

Laplace Transform to equation (6) gives: P(s) K5 = G (CV ) = 2 Y (s) S + (K 3× S ) + K 4 G (CV ) =

K5 . S + (K 3× S ) + K 4 2

(7) (8)

Part 3: Air flow through the valve and into breathing air system. q = y×

∆P ∂

y:

Displacement of calve

∆P: q:

Pressure difference across the valve Air flowrate across the valve

∂:

Density of air

(9)

Simplifying the equation gives: q = K6× y G (flow) = K 6.

(10)

Adding all three transfer functions will produce final function to be used in Simulink for the valve. G (total) =

q(s) = G ( Ax) × G (CV ) × G (flow) u ( s)

G (total) =

q( s) K5 = K0× 2 × K6 u ( s) S + (K 3× S ) + K 4

(11)


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K S + (K 3× S ) + K 4 K . G (total) = ( S + K 7) × ( S + K 8) G (total) =

2

For simplicity purposes, assume K8 >> K7 K K K8 = S + K8 S +1 K8 K K8 = (T × S ) + 1

G (total) =

T=

1 . K8

From various experiments and for simplicity purposes, the time constant (T) has been derived to be 0.0013 and K/K8 assumed to be 1. Hence, T = 0.0013, K/K8 = 1 Therefore, complete transfer function for the valve is derived to be, Valve transfer function =

1 . 0.00135 + 1

(12)

Part 4: Breathing air system. Breathing Air System at PNGS was thought of as volume of air into a system. Therefore, t

Q = Qo + ³ q(t )dt 0

Q: Q 0: q(t):

(13)

total volume of breathing air in the system initial volume of breathing air in the system air flow going into the system.

Derivative of equation (13) gives us. Q = q (t ).

(14)

Laplace transform to equation (14) gives SQ = q.

(15)

Q( s) 1 = GBA = . q(s) S

(16)


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Control system implementation

Please refer to newly proposed breathing air model (Figure 3) developed using PID + fuzzy logic controllers in Simulink. In order to prove effectiveness of the new model, it was compared against conventional PID controllers (Figure 5). Figure 5

Model of breathing air using conventional PID controller in Simulink

5.1 Building fuzzy rules Fuzzy rules were incorporated to fuzzy logic in order to develop Simulink model (Figure 3). This involves using fuzzy controller to support simulation of control model (Figure 6). Figure 6

Fuzzy logic controller with rule-viewer in Simulink (see online version for colours)


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Input to the fuzzy model was kept as error (i.e., SP-actual pressure) to the breathing air system. Furthermore, PID controller (Figure 7) was built to control positioning of the valves involving Kp, Ki and Kd parameters driven by the fuzzy controller (Figure 6). Figure 7

Conventional PID controller developed in Simulink (see online version for colours)

To formulate fuzzy rules, simple PID controller was run numerous times to understand the pattern of Kp, Ki and Kd in relation with system pressure and steady state error (Figure 8). Using this data, ranges to error, Kp, Ki and Kd were established in fuzzy controller to reach optimum results (Figures 9–12). Figure 8

Graph showing relationship between PID parameters, system pressure and error (see online version for colours)

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Error range was chosen from –620 to 620. Figure 9

Error range for fuzzy logic controller (see online version for colours)

Kp range was chosen from 0 to 50. Figure 10 Kp range for fuzzy logic controller to drive PID controller (see online version for colours)

Self-tuning fuzzy logic PID controller, applications in nuclear power plants Ki range was chosen from 1 to 3. Figure 11 Ki range for fuzzy logic controller to drive PID controller (see online version for colours)

Kd range was chosen from 4 to 40. Figure 12 Kd range for fuzzy logic controller to drive PID controller (see online version for colours)

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Results

Simulation with fuzzy + PID was run for 60 s and demonstrated following results (Figure 13). Figure 13 Simulation results for fuzzy PID controller for 60 s (see online version for colours)

Tables 1 and 2 are used as references to explain how better system performance is when using fuzzy logic. Table 1

Simulation results for fuzzy + PID controller

Rise time

Approx. 2.5 s (90% of 620 kPa = 558 kPa)

Over-shoot

640 kPa

Settling time

50 s

S-S error

0.907

To prove the model’s effectiveness, simulation was run with simple PID controller (Kp = 3, Ki = 2, Kd = 30) for 60 s. Results demonstrate that pressure in the system did not settle for 60 s (Figure 14). PID Simulation was repeated for 150 s with following results (Figure 15). Therefore, reduced rise-time, overshoot and settling time were noted with amalgamated fuzzy PID controller.

Self-tuning fuzzy logic PID controller, applications in nuclear power plants Figure 14 Simulation results for conventional PID controller for 60 s (see online version for colours)

Figure 15 Simulation results for conventional PID controller for 120 s to understand system stability (see online version for colours)

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Simulation results with simple PID controller

Rise time

Approx 6 s (90% of 620 kPa = 558 kPa)

Over-shoot

990 kPa

Settling time

130 s

S-S error

0.907 (approx)

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Cost comparison

Average cost for delaying an outage is estimated to be $20,000/h (Canadian dollar) at a nuclear power plant in Ontario. When pressure in breathing air system reaches below 550 kPa, alarm is initiated in PNGS control room and personnel in the RB building are directed to evaluate building to restore system pressure back to 620 kPa. Therefore, this results in delay in performing critical work in the Reactor Building. A comparator was implemented to Simulink models to calculate area of running model beneath 550 kPa. Following were the results. Both controllers were run for 150 s to understand their cost relation with respect to model stability. Conventional PID controller results are shown in Figure 16. Figure 16 Graph depicting area underneath 550 kPa using PID controller (see online version for colours)


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Total area underneath 550 kPa = 5750 (approx). Judging by simulation graph, we know system pressure reached below 550 kPa after rise time at 20 s. In running plant, this would initiate breathing air pressure low alarm and personnel will be asked to evacuate from RB building. All critical work be stopped resulting in outage delay of approx 3hrs. Therefore, predicted outage delay cost with PID controller. 3 h×

$20, 000 = $60, 000 (Canadian dollars) h

(17)

Results for fuzzy + PID controller for 150 s are shown in Figure 17. Figure 17 Graph depicting area underneath 550 kPa using fuzzy + PID controller (see online version for colours)

Total area underneath 550 kPa = 428 (approx). This area is only calculated during the initial rise time when operators would not sending people into the RB building until system has reached pressure above 550 kPa (i.e., no alarms be initiated into the control room). Confirmed by simulation results in Figure 18, the system pressure never reaches below 550 kPa after the initial rise time. Hence, predicted delay cost using fuzzy + PID controller 0 h×

$20, 000 = $0(Canadian dollars). h

(18)

Results to system pressure using fuzzy + PID are shown underneath (Figure 18) with rule-viewer in Figure 19 and implied fuzzy rules in Figure 20.

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Figure 18 Simulation result of fuzzy + PID controller for 120 s to perform cost analysis (see online version for colours)

Figure 19 Rule-viewer for fuzzy controller (see online version for colours)

SS error = 0.00551 (with fuzzy + PID controller).


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Figure 20 Please refer to fuzzy rules built to run simulation (see online version for colours)

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Conclusions

This paper investigated using fuzzy PID controller to resolve control problem at PNGS station. Simulink was used to develop system model with fuzzy rules. Results were compared against conventional PID controller and demonstrated that fuzzy PID controller has superior control and precision in maintaining system design pressure with reduced rise-time, overshoot, settling time and steady-state error when compared against conventional PID. It was also shown that using PID conventional controller will cost extra $60,000 for losses incurred due to instability in the system. Hence, it is recommended that fuzzy PID controller be implemented to breathing air systems at nuclear power stations in Ontario for optimised system air pressure control.

References Beitao, G., Hongyi, L., Yang, J., Cao, Y. and Honghai, T. (2009) Fuzzy Immune PID Control in VVVF Hydraulic System, School of Mechanical Engineering & Automation, Northeastern University/Shenyang Institute of Chemical Technology. He, L. and Song, L. (2012) The Pump House Constant Pressure Fuzzy Selftuning PID Control System Simulation, School of Electronic and Information Engineering, Chongqing University of Science and Technology, 29 March, 2012.

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Jialiang, L., Guanrong, C. and Hao, Y. (2012) Predictive Fuzzy PID Control: Theory, Design and Simulation, Department of Electrical and Computer Engineering, University of Houston, 15 March, 2012. Lu, Z., Tang, Z., Li, H. and Pei, Z. (2011) Fuzzy PID Control of Intelligent Pump, School of Automation Science and Electrical Engineering. Ontario Power Generation (OPG) (1989) Breathing Air System Design Manual, NK30-75140. Pickering B Nuclear Generation Station, Ontario Power Generation, Pickering. Ontario Power Generation (OPG) (2011) Breathing Air System Flowsheet, 30-058-O-75140-FS-01. Pickering B Nuclear Generation Station, Ontario Power Generation, Pickering, 03 May, 2011. Ontario Power Generation (OPG) (n.d.) Nuclear Power, Ontario Power Generation, Ontario Power Generation, 21 February, 2015, http://www.opg.com/generating-power/nuclear/Pages/ nuclear.aspx Zhong, J. (2006) PID Controller Tuning: A Short Tutorial, Purdue University, http://wwwdsa. uqac.ca/~rbeguena/Systemes_Asservis/PID.pdf (Accessed 3 April, 2012). Zulfatman and Rahmat, M.F. (2012) Application of Self-Tuning Fuzzy PID Controller on Industrial Hydraulic Actuator using System Identification Approach, Faculty of Electrical Engineering, 1 April.

Websites Are We Living in a Computer Simulation – USAHM Conspiracy News, USAHM Conspiracy & Alternative News, http://usahitman.com/human-sim (Accessed 3 April, 2012). Artificial Neural Networks – A Neural Network Tutorial, http://www. learnartificialneuralnetworks.com/ (Accessed 10 February, 2012). Control (Wet) Storage – A Misunderstood Concept, Compressed Air Best Practices, Atlas Copco Compressors LLC, December, 2011, http://www.airbestpractices.com/sites/default/ files/CABP_2011_12December_LR3.pdf (Accessed 22 January, 2012). Instrumentation and Control (I&C) Systems in Nuclear Power Plants: A Time of Transition, IAEA, http://www.iaea.org/About/Policy/GC/GC52/GC52InfDocuments/English/gc52inf-3att5_en.pdf (Accessed 21 January, 2012). The System Assessment – Comprehensive Compressor Air Audits – 5 Step Process, Compressed Air Best Practices, Atlas Copco Compressors LLC, December 2011, http://www.airbestpractices. com/sites/default/files/CABP_2011_12December_LR3.pdf (Accessed 22 January, 2012).

Bibliography De Carvalho, E., Rixey, R.A., Shepley, J.P., Gomes, J.O. and Guerlain, S. (2006) Design of a Nuclear Power Plant Supervisory Control System, http://www.sys.virginia.edu/students/ nuclearcontrol.pdf (Accessed 22 January, 2012). Dorf, R.C. and Bishop, R.H. (2001) Modern Control Systems, 9th ed., Prentice-Hall, Upper Saddle River, NJ. Gabbar, H.A. (2012) NUCL 5285G: Advanced Process Control Systems, Lec 2,3,4. Gershenson, C. (2003) Artificial Neural Networks for Beginners, Cornell University. Haque, M.T. and Kashtiban, A.M. (2005) Application of Neural Networks in Power Systems; A Review, World Academy of Science, Engineering and Technology, http://www.waset.org/ journals/waset/v6/v6-12.pdf (Accessed 22 January, 2012). Jayaprakash, A. (2009) Fault Tolerance System, SlideShare, http://www.slideshare.net/ prakashjjaya/fault-tolerance-system (Accessed 12 March, 2012).


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Jin, J. (2010) ‘Why does one need fault-tolerant control systems anyway?’, 2010 Conference on Control and Fault Tolerant Systems, France, p.118. Martínez, M., Molina, M.G. and Mercado, P.E. (2012) Dynamic Performance of Compressed Air Energy Storage (CAES) Plant for Applications in Power Systems, IEEE, 25 March, Sao Paulo. Maxwell, G. and Rivera, P. (2012) Dynamic Simulation of Compressed Air Systems, Iowa State University, Department of Mechanical Engineering, Sveavägen Stockholm, Sweden, 8 April. Mehrotra, K., Mohan, C.K. and Ranka, S. (1997) Elements of Artificial Neural Networks, MIT, Cambridge, MA. Rabunal, J.R. and Dorado, J. (2006) Artificial Neural Networks in Real-life Applications, Idea Group Pub., Hershey, PA. Shreyas, S. (2012) Fault-Tolerant and Secure Control Systems, Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario. Škutová, J. (2012) Adaptive Control with Inverse Model of a Compressed-Air Aggregate, Department of Control Systems and Instrumentation, Velké Karlovice, Czech Republic, 29 February. Sojoudi, S., Lavaei, J. and Murray, R.M. (2011) Fault-Tolerant Controller Design with Applications in Power Systems and Synthetic Biology, http://www.cds.caltech.edu/~lavaei/ ACC11_Fault.pdf Wei, J. (2010) Intelligent Building Control of Water Tank Based On Fuzzy Theory, Zhongnan University of Economics and Law, China. Zhang, Y. (2012) FP9-1: Fault Tolerant Control Systems, http://users.encs.concordia.ca/ ~ymzhang/courses/FTC/FTC06_LN1_Intro.pdf (Accessed 11 March, 2012). Zhang, Y., Jin, J. and Theilliol, D. (2008) ‘Incorporating performance degradation in fault tolerant control system design with multiple actuator failures’, International Journal of Control, Automation, and Systems, June, http://www.ijcas.com/admin/paper/files/IJCAS _v6_n3_pp.327-338.pdf (Accessed 25 January, 2012).