PI Fuzzy Gain-Scheduling Speed Control at Startup of a Gas-Turbine Power Plant

310 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 26, NO. 1, MARCH 2011

PI Fuzzy Gain-Scheduling Speed Control atStartup of a Gas-Turbine Power Plant

Arnulfo Rodriguez-Martinez, Raul Garduno-Ramirez, Senior Member, IEEE, and Luis Gerardo Vela-Valdes

Abstract—Speed control during startup is one of the most crit-ical tasks of gas turbine power plant operation. This paper intro-duces the PI fuzzy gain-scheduling (PI-FGS) controller to solve theforemost speed-control problems, including tracking of the accel-eration pattern and rejection of disturbances caused by operationevents throughout startup. Fundamentally, the PI-FGS synthesizesa GS controller from multiple locally tuned generalized propor-tional integral (PI) algorithms by means of a fuzzy system. ThePI-FGS structure permits independent tuning of the tracking andrejection responses at any operating point. In addition, tuning canbe carried out on-site based on the operator experience and inspec-tion of the current plant response. Simulation experiments showthat the PI-FGS may improve speed-control performance well overthat provided by commercially available speed controllers, whichare based on a single conventional PI algorithm.

Index Terms—Fuzzy systems, gain scheduling (GS), gas turbine,generalized PI, PI control, speed control.

I. INTRODUCTION

NOWADAYS, power generation by means of gas turbinepower plants (GTPPs) is playing a major role worldwide.

Also, most power plants to be built in the next 20 years will becombined cycles based on topping GTPPs due to their advan-tages over other technologies. Most relevant advantages include:relatively low commissioning, maintenance and operation costsper unit of power, fast startup and response to load change, ca-pability to use diverse fuel (diesel, oil and biomass), as well asversatility to integrate high-performance combined cycles andcogeneration systems [1].

GTPPs operate at relatively higher speeds, pressures and tem-peratures, with wider variation ranges and faster changes ofpoints of operation, than other plants. Moreover, operation ofGTPPs has a very high level of automation, which includes thestages of startup, synchronization, loading in different modesand stop. All these characteristics set very tight requirementsfor the control system; the startup very probably being themost demanding stage for the control system [2]. At startup,the speed-control loop is responsible to take the plant up to syn-chronization speed in a safe, reliable and efficient way. With thisaim, the speed control has to provide the right control actions

Manuscript received December 3, 2007; revised March 30, 2009; acceptedJuly 24, 2010. Date of publication December 30, 2010; date of current versionFebruary 18, 2011. Paper no. TEC-00483-2007.

A. Rodriguez-Martinez and R. Garduno-Ramirez are with the Division ofControl Systems, GCI 29–1, Electrical Research Institute, Cuernavaca, Mor62490, Mexico (e-mail: [email protected]; [email protected]).

L. G. Vela-Valdes is with the Departments of Electronics Mechatronics, Na-tional Research and Technology Development Centre, Cuernavaca, Mor 62490,Mexico (e-mail: [email protected]).

Digital Object Identifier 10.1109/TEC.2010.2081991

to follow, with the highest fidelity, the established accelerationpattern and to compensate the effects of disturbances producedby normal operation events and other external forces.

Currently, speed-control schemes of GTPPs consist of a sim-ple feedback loop, where a PI or PID algorithm with fixed gainscalculates the control signal from the difference between thespeed reference, obtained from the acceleration pattern, and thespeed measurements [3]–[5]. Such algorithms may be tuned tosatisfy, at a single point of operation, either the speed referencetracking or the disturbance rejection requirements, but both atthe same time, as required by GTPPs at startup. In this regard,a generalized PI was introduced by the authors to improve in-dependently and simultaneously both requirements in [6]. Nev-ertheless, having fixed gains, this strategy is also valid at onlyone point of operation, and GTPP speed response may deteri-orate throughout startup. Then, the authors have demonstratedthe feasibility to extend the advantages of the generalized PIalgorithm to the whole startup operating space using a fuzzysystem [10]. This approach allows independent satisfaction ofthe tracking and rejection requirements all through the speed-control operating region.

This paper provides a detailed explanation of the design ofthe PI fuzzy gain-scheduling (PI-FGS) algorithm for speed con-trol of a GTPP at startup. Shows how a preliminary designcan be modified to achieve even higher performance in track-ing the acceleration pattern and in compensating disturbancesall over the speed range at startup of a particular GTTP. Alsoshows that trial-and-error tuning can yield performance as goodas simulation-based optimized tuning, making it feasible foron-site tuning in actual power plants. Section II presents thegeneralized PI algorithm and some relevant aspects of multi-mode and GS control, which are used to extend its range ofapplication. Section III presents the PI-FGS design as a fuzzysystem that completely solves the problems of detection of op-erating conditions, controller switching, and gain scheduling.Section IV shows the application of PI-FGS to GTPP speedcontrol, including partitioning of the speed operating space.Section V describes the tuning procedure for the partition con-trollers. Section VI shows the results of simulation experimentsof PI-FGS control against conventional PI control. Section VIImakes a few relevant comments and draws the conclusion.

II. GENERALIZED PI, MULTIMODE

CONTROL, AND GS CONTROL

The control action u(t) generated by the generalized PI algo-rithm is given by

u(t) = Kprr(t) − Kpf y(t) + Ki

∫e(t)dt (1)

0885-8969/$26.00 © 2010 IEEE

RODRIGUEZ-MARTINEZ et al.: PI FUZZY GAIN-SCHEDULING SPEED CONTROL 311

Fig. 1. Discrete-time generalized PI control algorithm.

where r(t) is the reference signal, y(t) is the output signal,e(t) = r(t) − y(t) is the error signal, Kpr and Kpf are propor-tional gains for the reference and output, respectively, and Ki

is the integral gain. Note that when Kpr and Kpf are equal, thegeneralized PI algorithm reduces to the conventional PI algo-rithm. A discrete-time recursive version of the generalized PIcan be obtained with the following approximations for time andthe error time integral

t ↔ kT ,

∫ t

0e(t)dt ↔

k∑i=1

ei (2)

where k is a natural integer index and T is the sampling period.The control signal in the kth instant is

u(k) = Kprr(k) − Kpf y(k) + Ki

k∑i=1

ei. (3)

The change of the control signal is

Δu(k) = u(k) − u(k − 1)

= KprΔr(k) − Kpf Δy(k) + KiTe(k) (4)

where Δr(k) = r(k) − r(k − 1) and Δy(k) = y(k) − y(k −1) are changes of reference and output, respectively. Therefore,

u(k) = Δu(k) + u(k − 1)

= KprΔr(k) − Kpf Δy(k) + KiTe(k) + u(k − 1) (5)

is the desired recursive version of the generalized PI control law,as shown in Fig. 1.

In a previous work [6], the authors showed that the structureof the generalized PI allows for simultaneous optimization ofboth the reference signal tracking and the disturbance rejectionresponses. In conventional PI control, it is always necessary tomake a compromise between both responses.

One way to extend the advantages of the generalized PI allover the GTPP operating space is to build with it a multimodecontrol scheme. In this scheme, the plant operating space isdivided into a number of subspaces or partitions, assigning ageneralized PI controller to each one of them. Each controlleris tuned taking into account the plant dynamics in its partition.Once in service, controllers are switched with the change ofthe plant-operating conditions as it moves from one partitionto another. A major problem with this control scheme is the

design and implementation of the switching logic to have asoft plant response, despite transitions among either partitionsor controllers. Moreover, when all controllers in a multimodescheme have the same structure, the multimode scheme yieldsa GS scheme.

A GS control scheme produces a nonlinear global controllerfrom a series of local controllers tuned at specific points ofoperation. Parameters of the global controller are continuouslyupdated with the change of the plant-operating conditions. Suchchange is detected through the change of a suitable variable,selected to be the scheduling variable. In comparison to otheradaptive control strategies, GS control does not require any on-line parameter estimation, and then, can provide a relativelyfast response to the changes of operating conditions. A majordrawback is the selection of the scheduling variable, since ithas to capture the nonlinearities of the plant and has to varyslowly [7]. Another difficulty is the design of the schedulingfunction to modify the controller parameters in terms of thescheduling variable.

Commonly, realization of GS controllers is made with numer-ical methods that are not intuitive and many times very hard tomaintain. In contrast, the characteristics of fuzzy systems sug-gest that the detection of operating conditions, local controllerswitching logic, and parameter interpolation or global controllerGS, may be intuitively realized using natural language propo-sitions, allowing for integration of operation staff experience.Blending of the generalized PI structure with the multimode andGS control schemes by means of a fuzzy system, to produce thePI-FGS controller and to employ it to control the GTPP speedduring startup, is described in the following sections.

III. PI FUZZY GS CONTROLLER

Basically, the PI-FGS controller is composed of a series ofgeneralized PI controllers working in parallel. Each one of thesecontrollers corresponds to one partition of the operating space(startup speed range), it is tuned to satisfy the tracking and re-jection requirements of its partition, and it is put into serviceaccording to the plant operating conditions. The PI-FGS con-troller is assembled by means of a fuzzy system. Fuzzificationimplements the mechanism to detect the plant current operatingconditions. Inference rules implement the generalized PI localcontrollers, one per rule. The inference process implements theswitching logic and the interpolation or GS function.

The PI-FGS controller is based on a Takagi–Sugeno–Kan(TSK) fuzzy system with four inputs and one output. The firstinput enters the scheduling variable α. The remaining inputsenter the previously defined signals Δr(k), e(k), and Δy(k),required by the generalized PI to calculate the control signal.The output of the TSK fuzzy system is the change in the controlsignal Δu(k). Structure of the PI-FGS controller and the TSKfuzzy system are depicted in Fig. 2. The TSK fuzzy system hasthe following main characteristics [8]. The scheduling variablemembership functions are trapezoidal and triangular. Singletonfuzzification is used to simplify calculations by the inferencemechanism. Inference mechanism is based on individual rules.


Fig. 2. Structure of PI-FGS controller.

The total output is the weighted average combination of all ruleoutputs.

Each rule of the fuzzy system is associated to a single par-tition of the operating space and implements a generalized PIcontroller. Rules have the form

IF α is Ai THEN Δui(k)

= KpriΔr(k) − Kpf iΔy(k) + KiiTe(k) (6)

where i = 1, 2, . . . , R is the rule number, Ai is the fuzzy setdefining the ith partition of the operating space, Kpri , Kpf i ,and Kii are the generalized PI parameters or gains of the ithrule or controller, and Δui(k) is the control signal generatedby the ith rule or controller. The total control signal change,generated by the TSK fuzzy system, is the weighted average ofthe control signals generated by each rule or controller

Δu(k) =∑R

i=1 wiΔui(k)∑Ri=1 wi

(7)

where the weights wi are calculated as the product of the mem-bership values of the inputs being fuzzified. Since only the firstinput is being fuzzified

wi = μAi(α). (8)

From (6), (7), and (8), the control signal change Δu(k) is

Δu(k)

=∑R

i=1 μAi(α) (KpriΔr(k) − Kpf iΔy(k) + KiiTe(k))∑R

i=1 μAi(α)

.

(9)

Finally, the control signal is obtained recursively as in (5)

u(k) = Δu(k) + u (k − 1) . (10)

IV. APPLICATION OF PI-FGS TO GTPP

The PI-FGS speed controller is designed for a 24-MW GTPP.The gas turbine is open cycle and rotates at 5100 r/min develop-ing 25980 KW of useful output peak power. The air compres-sor is 17 stages axial flow. The three-phase, two-poles, 60-Hz,13.8-kV electric generator rotates at 3600 r/min. The startingdevice is a 500-hp diesel engine. Fig. 3 shows both the speed

Fig. 3. Relevant points of operation during GTPP startup.

TABLE IPOINTS OF OPERATION SELECTED TO DEFINE PARTITIONS

reference signal and the measured speed signal during startup.Acceleration of GTPP from 0 r/min through 1900 r/min, ap-proximately, is carried out by the starting diesel engine. At thispoint, the speed-control loop is activated to regulate the fuelflow into the combustion chamber to accelerate up to nominalspeed (5100 r/min). The startup stage ends when the generatoris synchronized to the grid.

The first relevant issue to design the PI-FGS controller is toselect the scheduling variable, which must be strongly related tothe change of the GTPP operating conditions. In this case, thespeed reference signal is chosen since its evolution is highly cor-related to plant operation. The speed-control range of operationspans from 1946 r/min through 5100 r/min.

The second relevant design issue is that of partitioning theoperating space, which must be based on the analysis of op-erating conditions and control requirements throughout startup.One possibility is to define partitions in terms of plant dynamics,as determined by variation of its dominant poles [9]. Althoughprecise, this approach requires the plant mathematical modelthat could be very difficult to obtain in practice. In this paper, itis proposed to define partitions using a set of operating pointsthat are selected by their impact on the GTPP speed response.Advantages of this approach include no need of a plant mathe-matical model; can be done by inspection of the speed responseand makes use of operation staff experience.

As a first approximation to PI-FGS design [10], considerthe points listed in Table I, which are also shown in Fig. 3.Partition of operating space is done through fuzzy sets. Forsimplicity, fuzzy sets are chosen trapezoidal or triangular, withcenter and base corners at the said points (see Fig. 4). Therefore,detection of the operating conditions is given by the degree of


Fig. 4. Definition of fuzzy sets for operating space partition.

membership of the scheduling variable to each one of the fuzzysets or partitions just defined.

Subsequently, a generalized PI controller is assigned to eachpartition through the inference rules of the fuzzy system. From(6) and the definition of fuzzy sets Ai , in Fig. 4, the followinginference rules are obtained:

IF α is A1 THEN Δu1(k)

= Kpr1Δr(k) − Kpf 1Δy(k) + Ki1Te(k)






= Kpr4Δr(k) − Kpf 4Δy(k) + Ki4Te(k). (11)

V. TUNING OF LOCAL PI CONTROLLERS

The parameter values of the local generalized PI controllersof the PI-FGS were determined both by trial and error andautomatically by means of an optimization routine, taking intoaccount the tracking and rejection requirements in each selectedoperating point, knowing that Kpr determines the tracking re-sponse, while Kpf and Ki determine the disturbance rejectionresponse. Search was initiated from the conventional PI gainvalues, Kp = 3.5 and Ki = 0.7. Manual tuning is carried outas follows.

1) Initial values of the local controller parameters are setequal to the parameters of the conventional PI controller asKpr = Kpf = Kp = 3.5 and Ki = 0.7. A first simulationis run with these parameters to obtain the IAE performanceindex and the control effort (CE).

2) Next, parameters of controller 1 (partition1) are tuned,keeping constant the parameters of controllers 2, 3, and 4:

a) First, parameters Kpf and Ki are tuned to improvedisturbance rejection through simulation until thelowest value of IAE index is attained.

b) Second, parameter Kpr is tuned to improve trackingresponse through simulation until the lowest valueof IAE index is obtained.

3) Using the parameter values obtained for controller 1, pa-rameters of controller 2 are tuned keeping constant theparameters of controllers 1, 3, and 4. This process is ap-plied to controllers 3 and 4.

TABLE IIPARAMETERS OF GENERALIZED PI CONTROLLERS OF PI-FGS

4) Once all local controllers are tuned, a final tuning is carriedout for all parameters together, using the parameters justobtained as initial values.

Later on, an automatic tuning algorithm was implementedbased on the fminunc optimization function of MATLABsoptimization toolbox. Function fminunc performs a nonlinearoptimization without constraints providing the minimum of ascalar function, starting at an initial value, as follows:

[x, fmin] = fminunc(fobj, x0, options) (12)

where fmin is the minimum value of the objective function,and fobj evaluated at the solution x. The initial value is x0, andoptions specifies the parameters to be used for optimization.Steps for automatic tuning are the same as for manual tuning,taking into account that the objective function to be minimizedis the IAE performance index. Table II reports the parametervalues obtained for the generalized PI controllers of the PI-FGSwith four partitions and four inference rules or controllers.

VI. SIMULATION EXPERIMENTS

Performance of the PI-FGS controller is demonstratedthrough simulation experiments in a regular 2 MB RAM, 2 GHz,dual-core PC platform. All programming is developed in theMATLAB/Simulink graphical simulation software [11]. ThePI-FGS controller, developed with MATLAB’s Fuzzy LogicToolbox, is tied to the model of the 24-MW GTPP specified inSection IV, which is a full-scope model that has been used forreal-time factory acceptance tests (FATs) of actual GTPP con-trol systems [12]. The simulation software considers separatemodules for controls, plant models, communication links, andoperator interfaces. Software modules are separated that wayto ease transition of control software applications from the PCplatform to real-time hardware-in-the-loop laboratory platformand finally to double or triple-redundant target platforms at thepower station.

In all the tests, responses with the PI-FGS controller arecompared to the responses with the conventional PI controllerused by commercially available digital speed controllers. Fig. 5shows startup speed responses obtained with both the conven-tional PI and the PI-FGS (trial and error, and automatic tuning)controllers. Responses are closed up at the regions of majorinterest to get a better appreciation. Fig. 6 shows that bothPI-FGS controllers respond a little better after activation ofthe speed-control loop (Point 1). On the other hand, Fig. 7clearly shows a better response of both PI-FGS at the acceler-ation pattern corner (Point 4), but have larger deviations afteropening the compressor inlet guide vanes (IGVs) and closing its


Fig. 5. Speed response of conventional PI and PI-FGS controller with fourpartitions.

Fig. 6. Close-up to speed responses after activation of speed control loop andstarting engine shut-off.

Fig. 7. Close-up to speed responses at IGVs opening, bleeding valves closing,and final change of acceleration.

Fig. 8. Control signals of conventional PI and PI-FGS controllers.

TABLE IIISPEED RESPONSE PERFORMANCE

bleeding valves (Point 3). Complementarily, Fig. 8 shows thecontrol signals issued by the three controllers. The PI-FGS tunedby trial and error has smaller amplitude oscillations at the majorinterest regions of Figs. 6 and 7. This provides softer controlactions and less thermal stress.

Table III reports the integral of the absolute value of error(IAE) index and the CE to visualize more precisely the perfor-mance of the controllers. Data in Table III show that the PI-FGScontroller has better IAE performance than the conventional PIcontrol for both manual and automatic tuning. Furthermore, trialand error tuning provided better response than automatic tuningthat can be trapped in a local optimum. This result is relevant inthe sense that trial and error tuning can provide results as goodas those given by the optimization routines, since the formermethod is the one used on site, at the power plant.

Additionally, although results summarized in Table III showthat the PI-FGS controller with four partitions already outper-forms the conventional PI controller, even better performancemay be obtained taking into account more partitions. Such extrapartitions can be directly defined by inspection of the GTPPspeed response using the operators’ experience and knowledge.To illustrate this approach, cases with six and seven partitionsare demonstrated. By inspection of Figs. 6 and 7, extra pointsfor speed response improvement can be selected between cur-rent Points 1 and 2, and 3 and 4, as listed in Tables IV and Vfor the six and seven partitions cases, respectively. These tablesalso include the list of parameter values of the generalized PIcontroller for each partition as obtained by trial and error andautomatic tuning.

Responses of PI-FGS controllers with six partitions are closedup in Figs. 9 and 10, in addition to the response of the conven-tional PI controller. In these figures, both responses of PI-FGS


TABLE IVSELECTED OPERATING POINTS AND CONTROLLER PARAMETERS

OF PI-FGS WITH SIX PARTITIONS

TABLE VSELECTED OPERATING POINTS AND CONTROLLER PARAMETERS

OF PI-FGS WITH SEVEN PARTITIONS

Fig. 9. Close-up of speed responses after activation of speed control loop andstarting engine shut-off for PI-FGS with six partitions.

controllers are quite similar. Fig. 9 shows responses at the be-ginning of the startup ramp. Clearly, responses of PI-FGS con-trollers outperform that of the conventional PI controller. Theyalmost eliminate disturbances produced by the starting deviceshut-off. On the other hand, Fig. 10 shows responses at the endof the startup ramp. Again, both PI-FGS controllers outperformthe conventional PI controller. Also, responses with six parti-tions are better than that using four partitions. The extra parti-tions allowed reshaping the speed response to improve trackingand disturbance rejection at regions, where PI-FGS with fourpartitions was close to the conventional PI.

Control signals of PI-FGS controllers with six partitions areprovided in Fig. 11. Large oscillations at the beginning of startupramp have been drastically reduced, as compared to the cases

Fig. 10. Close-up of speed responses at IGVs opening, bleeding valves clos-ing, and final change of acceleration for PI-FGS with six partitions.

Fig. 11. Control signals of PI-FGS controllers with six partitions.

with four partitions and the conventional PI. Also, control signaloscillations are reduced at the end of the startup ramp, but reduc-tion is less spectacular. Although not evaluated, this behaviorgreatly reduces thermal stress at startup.

Figs. 12 and 13 close-up responses at points of interest of thestartup speed obtained with both the conventional PI and thePI-FGS controllers with seven partitions, one manually tunedby trial and error and the other automatically tuned. Fig 13shows that the PI-FGS with seven partitions is also better thanthe PI-FGS with six partitions. It almost eliminates disturbancesproduced by the closing of bleeding valves and opening of IGVs,and reduced oscillations at synchronizing speed. Control signalsare shown in Fig. 14, where it can be seen that at the endof startup, the manually tuned PI-FGS presents more abruptoscillations than the automatically tuned PI-FGS controller.

Table VI provides the measures of performance of thePI-FGS controllers with six and seven partitions. IAE perfor-mance shows again that the PI-FGS controllers, tuned by trialand error provide better performance than those tuned automati-cally. These results show improvement of 69.9%, 62.2%, 74.5%,


Fig. 12. Close-up of speed responses after activation of speed control loopand starting engine shut-off for PI-FGS with seven partitions.

Fig. 13. Close-up of speed responses at IGVs opening, bleeding valves clos-ing, and final change of acceleration for PI-FGS with seven partitions.

Fig. 14. Control signals of PI-FGS controllers with seven partitions.

TABLE VISPEED RESPONSE PERFORMANCE WITH SIX AND SEVEN PARTITIONS

and 70.5% on speed response for PI-FGS controllers with sixand seven partitions, respectively.

VII. COMMENTS AND CONCLUSION

This paper explained application of the PI-FGS controller togovern the speed response of a GTPP during startup, from fuelignition at 1946 r/min, through to nominal speed at 5100 r/min,just before synchronization to the electrical grid. The PI-FGScontroller amalgamates the characteristics of multimode con-trol, GS control, and fuzzy systems to extend the advantages ofthe generalized PI controller all over the speed-control operat-ing range. Detection of the operating condition, implementationof the switching logic (multimode control), and interpolation ofparameters (GS) are nicely solved using a TSK fuzzy system.Thus, the application of fuzzy logic to design the PI-FGS con-troller yields a practical solution that makes use of operationstaff’s experience.

Partitioning of the operating space, as dictated by experienceand knowledge of the GTPP speed response, together with usageof the generalized PI structure for each partition controller of thePI-FGS, allow independent adjustment of controller parametersto improve the speed reference tracking and disturbance rejec-tion responses simultaneously and in the required amount ateach partition. Results of simulation experiments demonstratethat the PI-FGS algorithm may improve the performance ofspeed control at startup of GTPPs, well beyond that obtainedwith speed controllers based on the conventional PI algorithm.Hence, the PI-FGS proposed approach makes it possible to eas-ily build high-performance tailor-made speed controllers for anyspecific GTPP.

Comparing the performance of GTPP responses obtainedthrough trial and error tuning against those obtained withsimulation-based automatic tuning, one can be certain that val-ues obtained by trial and error are very close to those that canbe obtained through numerical optimization. This fact is veryimportant since trial and error tuning can be carried out on-siteand on-line, with the plant working, while automatic tuning iscarried out off-line and requires lots of simulation iterations.Thus, application of PI-FGS to an actual GTPP may be eas-ily accomplished starting with the current controller parametersand following the procedure outlined in Sections IV and V.

ACKNOWLEDGMENT

The authors would like to thank Dr. S. Gonzalez-Castro andMr. R. Chavez-Trujillo, at the Electrical Research Institute (IIE),for their support to this research project.


REFERENCES

[1] J. H. Horlock, Advanced Gas Turbine Cycles. Malabar, FL: Krieger,2007.

[2] R. Garduno and M. Sanchez, “Control system modernization: Turbogasunit case study,” in Proc. 1995 IFAC Symp. Control Power Plants PowerSyst., 2011, vol. 2, pp. 245–250.

[3] R. Uram, “Computer control in a combined cycle power plant—Part II:The digital gas turbine system,” in Proc. 1977 IEEE Power Eng. Soc.(PES) Winter Meet., Paper A 77, pp. 078–079.

[4] SPEEDTRONIC Mark VI, Industrial Steam Turbine Control, GeneralElectric Co., Fairfield, Connecticut, GEI-100473, 2001.

[5] 2301D-GT Digital Electronic Load Sharing and Speed Control for SmallGas Turbines, Woodward Governor Co., Fort Collins, CO, Manual26144B, 2002.

[6] A. Rodriguez, R. Garduno, and G. Vela, “Speed control of a turbogasunit with generalized PI,” presented at the IEEE RVP/AI Conference,Acapulco, Mexico, 2004. (In Spanish).

[7] W. J. Rugh, “Analytical framework for gain scheduling,” IEEE ControlSyst. Mag., vol. 11, no. 1, pp. 79–84, Jan. 1991.

[8] W. Li-Xing, A course in Fuzzy Systems and Control. New York: PrenticeHall, 1997.

[9] R. Garduno and K. Y. Lee, “Fuzzy scheduling control of a power plant,”in Proc. 2000 IEEE Power Eng. Soc. Winter Meet., vol. 1, Singapore,pp. 441–445.

[10] A. Rodriguez and R. Garduno, “Speed control of a turbogas unit withgain-scheduling fuzzy PI,” presented at the IEEE RVP/AI Conference,Acapulco, Mexico, 2005. (In Spanish).

[11] H. Klee, Simulation of Dynamic Systems with MATLAB and Simulink.Boca Raton, FL: CRC Press, 2007.

[12] R. Garduno, S. De Lara, and M. Carretero, “Environment for developmentand validation of control algorithms for gas turbines,” Electrical Res. Inst.,Cuernavaca, Mexico, Technical Report IIE/11983/I002/P/DC/AX/VX ver1.0, Apr. 2001. (In Spanish).

Arnulfo Rodriguez-Martinez received the Commu-nications and Electronics Engineer degree from theEscuela Superior de Ingenierıa Mecanica y Electrica,Instituto Politecnico Nacional, Mexico, in 1987, andthe M.Sc. degree in control engineering from theNational Research and Technological DevelopmentCentre, Mexico, in 2004.

Since 1987, he has been with the Division of Con-trol Systems, Electrical Research Institute, Mexico.He has taken part and led several projects to designand develop instrumentation and control systems for

process industry. His current areas of interest include intelligent and digitalcontrol.

Mr. Rodriguez-Martinez is a member of International Society of Automation.

Raul Garduno-Ramirez (S’96–M’00–SM’03) re-ceived the Electrical Engineer degree from the Es-cuela Superior de Ingenierıa Mecanica y Electrica,Instituto Politecnico Nacional, Mexico, in 1985, theM.Sc. degree from the Centro de Investigacion y deEstudios Avanzados, Instituto Politecnico Nacional,in 1987, and Ph.D. degree from the PennsylvaniaState University, PA, in 2000 as a Fulbright Scholar.

In 1986, he was at the National Laboratory ofMechanical Engineering, Japan, developing indus-trial robot controls. Since 1987, he has been at the

Division of Control Systems, Electrical Research Institute, Mexico, workingon power plant automation and control. His areas of interest include intelligentcontrol systems, control software engineering, and multiobjective optimizationof power plant operation. He is author or coauthor of more than 70 publishedtechnical papers, five book chapters, and is author of the book Fossil-Fuel PowerPlant Control: An Intelligent Hybrid Approach.

Dr. Garduno is member of the Mexican National Research System.

Luis Gerardo Vela-Valdes received the degree of In-dustrial Engineer in electronics and the M.Sc. degreein electrical engineering, in 1986 and 1989, respec-tively, both from the La Laguna Institute of Technol-ogy, and the Ph.D. degree from the Universite HenriPoincare, Nanci I, France in 1998.

He is currently a Professor and Researcher inthe Departments of Electronics and Mechatronics,National Research and Technological DevelopmentCentre, Mexico. His areas of research include controland diagnosis of electrical machines, robotics, and

adaptive control. He was a Technical Reviewer of the Israel Science Foundationin 2010.

PI Fuzzy Gain-Scheduling Speed Control at Startup of a Gas-Turbine Power Plant

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