alstom benchmark challenge ii on gasifier control
TRANSCRIPT
The second ALSTOM benchmark challenge on gasifier control
Alstom Benchmark Challenge II on Gasifier Control
R. Dixon and A.W. Pike
Abstract: Gasification offers a clean and efficient method for producing gas from carbon-basedfeedstock such as high-sulphur fuel oil, refinery tars, petroleum coke, coal and biomass. Theproduct gas can then be burnt cleanly and efficiently in a combined cycle gas turbine to produceelectricity. The authors introduce the second ALSTOM Benchmark Challenge on GasifierControl, in which a validated non-linear model of a coal gasifier was put forward as the subjectof a control challenge to the research community. The challenge problem includes the operatingconstraints, disturbance characteristics, control specifications and closed-loop performance tests.A baseline Proportionalþ Integral controller is provided as part of the challenge for the purposeof comparison. The design methods used and performance results obtained for the baselinecontroller are described.
1 Introduction
In the late 1990s, ALSTOM was part of a consortium ofUK companies that undertook a detailed feasibility studyfocused on the development of a small-scale powergeneration plant based on the air blown gasificationcycle (ABGC). Part of this study involved building acomprehensive dynamic model and producing a controlphilosophy for the plant [1]. The coal gasifier was onecomponent of the plant model. It was found to be a highlycoupled multivariable system with five inputs and fouroutputs and exhibiting stiff dynamics. Together, theseattributes made it particularly difficult to control. Henceit was an ideal target system for a benchmark challengeevent.In 1997 the ALSTOM Power Technology Centre issued
an open challenge to the UK academic control community,which addressed the control of a linear model of a gasifierplant. The ‘Challenge information pack’ included threelinear models (derived from ALSTOM’s comprehensivenon-linear model of the system), together with a detailedspecification comprising output limits, control input con-straints and disturbance tests. See [2] and [3] for fulldetails of the challenge and a selection of the control tech-niques that were considered.The second round of the challenge was issued in June 2002
and was the subject of a special session at the UKACCCONTROL 2004 Conference [4]. This second challengeextended the original study by providing the full non-linearmodel of a gasifier in MATLAB/SIMULINK. It included anexpanded specification to incorporate set point changes andcoal quality disturbances. The two main objectives for thebenchmark challenge were (1) to provide an opportunity
for researchers to present and compare a number of controlsystem design approaches on an industrial plant model and(2) to provide an opportunity for control engineers to evalu-ate a range of control techniques on a level footing. Themodel of a gasifier, provided by ALSTOM, is of an industrialstandard and has been validated against a set of real data fromtest facilities, making the challenge all the more relevant topractising engineers.
This paper describes the problem as posed for the secondround of the challenge. A brief introduction to the modelis given in Section 2. Section 3 gives details of the speci-fication. Section 4 discusses the design of the defaultProportionalþ Integral (PI) controller (as issued with thechallenge). Next, Section 5 presents a summary of theresults obtained with the PI controller. Finally, conclusionsare drawn in Section 6. Note that the specification, as orig-inally issued, is available from the IEE website [5].
2 The gasifier model
The coal gasifier model was developed by engineers atthe ALSTOM POWER Technology Centre. Originally itwas written in the Advanced Continuous SimulationLanguage (ACSL), before being transferred to MATLAB/SIMULINK to facilitate the design and evaluation ofcontrol laws. All the significant physical effectsare included in the model (e.g. drying processes, desulphur-isation process, pyrolysis process, gasification process,mass and heat balances) and it has been validatedagainst measured time histories taken at an experimentaltest facility that was built by British Coal’s CoalTechnology Development Division (CTDD). More detailconcerning the model can be found in [6]. Alternatively,Moreea-Taha [7] provides a comprehensive review ofgasifier modelling.
2.1 Plant description
A schematic of the plant is shown in Fig. 1. The gasifier is anon-linear, multivariable component, having five controllableinputs (coal, limestone, air, steam and char flow rates) and
# IEE, 2006
IEE Proceedings online no. 20050062
doi:10.1049/ip-cta:20050062
Paper first received 2nd March and in revised form 2nd September 2005
R. Dixon is with Loughborough University, Loughborough, Leicestershire,LE11 3TU, UK
A.W. Pike is with ALSTOMPower TechnologyCentre,Whetstone, LE8 6LH,UK
E-mail: [email protected]
IEE Proc.-Control Theory Appl., Vol. 153, No. 3, May 2006254
four outputs (pressure, temperature, bed-mass and gasquality) with a high degree of crosscoupling between them.Note that as limestone is used to absorb sulphur in the coal,its flow rate must be set to a fixed ratio of coal flow, nomin-ally 1 : 10 limestone to coal. This leaves effectively afour-input, four-output regulation problem for the controldesign.Other non-control inputs for the model include boundary
conditions (to allow manoeuvres to different operatingpoints) and two disturbance inputs: PSINK, which rep-resents pressure disturbances induced as the gas turbinefuel inlet valve is opened/closed, and Coal Quality, whichsimulates variations in the coal quality.The controllable inputs are:
1. Char flow WCHR (kg s21)2. Air flow WAIR (kg s21)3. Coal flow WCOL (kg s21)4. Steam flow WSTM (kg s21)5. Limestone flow WLS (kg s21)
The disturbance inputs are:
6. Sink pressure PSINK (N m22)7. Coal quality (%)
The controlled outputs are:
1. Fuel gas calorific value CVGAS (J kg21)2. Bed mass MASS (kg)3. Fuel gas pressure PGAS (N m22)4. Fuel gas temperature TGAS (K)
2.2 SIMULINK model
The model was formulated as a C-code s-function, whichcould be included within a SIMULINK block diagram. Twomodels were provided: one open-loop (as shown in Fig. 2)and the other with a PI multiloop controller. The PI control-ler was included to demonstrate a baseline performance. Itshould also be noted that a simple bed-mass control wasemployed in the ‘open-loop’ model to avoid the systemdrifting from steady-state.
3 Control system specification
The full specification as issued with the challenge can befound in [5]. It explains that the non-linear model shouldbe considered as the plant and the control design shouldbe carried out as it would be in practice (e.g. model theplant, perform model-based verification of the controldesign and, finally, implement on the real plant). No limit-ations were imposed on the range of control approaches thatmight be applied and the control design could be undertakenfor any or all of the operating points. However, participantsin the challenge were asked to comment on implementationissues such as stability and on the design man-hoursrequired to arrive at their results. The control specificationincludes the two pressure disturbance tests (at three differ-ent operating points), a load acceptance test (50–100%load) and a coal quality change (to simulate the effect ofvariation in the coal grade on plant performance). The spe-cifics of these tests and the constraints that must be met aredetailed in the following sections.
3.1 System specification
3.1.1 Input limits: The input actuator flow limits and therate of change limits shown in Table 1, must not be exceededduring any test, because they are associated with physicallimitations of the actuator devices (note that these ratesand limits are included in the SIMULINK model).
3.1.2 Output limits: During the sink pressure (PSINK)disturbance tests (see later), the outputs should be regulatedwithin the following constraints:
† the CV fluctuation should be minimised and shouldalways be within +10 kJ kg21;† the pressure fluctuation should be minimised and shouldalways be within +0.1 bar;† bed-mass should remain within +500 kg from the set--point;† temperature fluctuation should be kept to a minimum,always within +18C.
Gasifier System
CVVarious
Boundary
Conditions
(from look-up
tables)
Fig. 1 Gasifier schematic
IEE Proc.-Control Theory Appl., Vol. 153, No. 3, May 2006 255
At other times (during load change tests, etc.) the outputsshould be regulated as closely as possible to the demandlevel. However, there are no absolute tolerances/limits.
3.2 Performance tests
The intention was that these tests would facilitate the evalu-ation of the closed-loop system’s response to pressure dis-turbances, load changes and coal quality changes.
3.2.1 Pressure disturbance tests: The two pressuredisturbance test cases required consisted of a step disturb-ance of 20.2 bar to the system, corresponding to a step inthe gas turbine inlet valve position in reaction to a loadchange, plus a sine wave pressure disturbance of amplitude0.2 bar and frequency of 0.04 Hz, corresponding to low-fre-quency movements of the inlet valve in reaction to changesin grid frequency.
In order that a range of control system design techniquesmight be compared on a basis that was fair, the test caseguidelines were quite prescriptive:
1. (a) At the 100% operating point apply a pressure stepdisturbance (PSINK) of 20.2 bar to the system, at t ¼ 30 s.(b) Run the simulation for 5 min (i.e. until t ¼ 300 s) andcalculate the integral of absolute error for the CV andpressure outputs over the complete run.(c) Note any constraint violations.2. (a) At the 100% operating point, apply a sine wavepressure disturbance of amplitude 0.2 bar and frequencyof 0.04 Hz.(b) Over a 300 s run, calculate the integral of absolute error(IAE) as before.(c) Note any constraint violations.3. Repeat steps 1 and 2 at the 50% and 0% load operatingpoints, again calculating the integral of absolute error per-formance criterion.
Note that, if the system response seemed adequate in theinitial 300 s, but subsequently became unstable or divergedfrom the set-points (as a result of the above tests), thisshould be highlighted and commented upon.
3.2.2 Load change tests: The load change tests wereinclude because the controller must function appropriatelyacross the full operating range of the plant. Hence, theplant should be driven to a number of operating points(load changes should never be more than 5% per minuteramps) and the stability of the plant over the working
Fig. 2 SIMULINK diagram of open-loop gasifier (including empty shell for control implementation)
Table 1: Control input limits
Input Name Max, kg s21 Min, kg s21 Rate, kg s22
Coal flow WCOL 10 0 0.2
Air flow WAIR 20 0 1.0
Steam flow WSTM 6.0 0 1.0
Char flow WCHR 3.5 0 0.2
IEE Proc.-Control Theory Appl., Vol. 153, No. 3, May 2006256
range should be checked. It was also pointed out that, anyanalytical results for global stability of the plant would beof significant interest.In terms of a specific test for comparison purposes,
a ramp block was included in the model to allow the follow-ing test to be undertaken: Start the system at 50% load insteady-state and ramp it to 100% over a period of 600 s(5% per minute). The measured load should follow theload demand as closely as possible with minimal overshootat the end of the ramp. Obviously, the input constraints (rateand absolute limits) need to be adhered to at all times.
3.2.3 Coal quality/model error test: Coal quality canchange quite significantly depending on its source. Themodel includes an input that simulates changes in coalquality by, effectively, altering the amount of energy inthe coal. The coal quality should be changed incrementally(within the range+18%) and any effect on the performanceof the controller (e.g. ability to track demands, stability,etc.) should be noted.
4 Baseline controller
The baseline controller, as provided with the challengepack, used the structure of the PI control approach sug-gested by Asmar et al. [8]. The loops are illustrated inTable 2.Note that loops 1, 3 and 4 are PI, whereas loop 2 (which
determines the coal flow) has only a proportional gain onbed-mass error. This is augmented by a crosschannel gainon the char flow input (from loop 4).Rather than tuning the four sets of gains by hand, they
were designed using optimisation techniques combinedwith an identified linear model of the plant (at 100%load). The basic design steps were:
1. Obtain data from two open-loop tests with pseudoran-dom binary signals (PRBS) applied simultaneously to thesystem inputs (at 100% load).2. Identify a suitable model structure (based on the data andphysical knowledge of the plant structure) and fit the modelusing dataset 1.3. Validate the model against dataset 2.4. Using the linear identified model, run an optimisation tofind the best PI gains for rejecting the step disturbance.5. Run Monte-Carlo analysis of the closed-loop with linearmodel to assess sensitivity to model error.6. Implement and test the controller.
Naturally, there is some degree of iteration in the designprocess. Steps 1 to 3 and steps 4 to 5 are summarised inSections 4.1 and 4.2, respectively.
4.1 Identification/validation of linear model
In order to obtain the four-input, four-output system model,the four inputs of the plant were simultaneously perturbedwith independent PRBS. The input perturbation amplitudeswere set to be +10% about the full-load operating point.The input signals and the resulting output data, sampledat 5 Hz (Dt ¼ 0.2 s), were recorded and used to identifyand estimate parameters of four multi-input, single-output(MISO) models. These models are then combined to givea four-input, four-output model.
The parameters of the discrete-time MISO models wereestimated by fitting the model to the data using the simpli-fied refined instrumental variable (SRIV) method [9].Evaluation of the candidate models was carried out byvisual inspection combined with statistical measures suchas the coefficient of determination, RT
2
R2T ¼ 1�
s2
s2y
ð1Þ
where s2 is the sampled variance of the modelling error(residual) and sy
2 is the sample variance of the measureddata about its mean value. This ‘goodness of fit’ criteriontends to unity as the fit of the model to the data improves.
The PRBS inputs are shown in Fig. 3. The system outputsare compared with the outputs of the data-based model inFig. 4, together with the modelling errors (shown beloweach output). The goodness of fit measure, RT
2, is shownabove each output. The identified model comprised fourthird-order models, each with a delay of one samplegiving an overall model order of 12.
The model was validated against a second series of datagenerated with a different PRBS input set. The resultingmodel fits were similar to those shown above (i.e.RT2 ¼ 0.998, 0.994, 0.999 and 0.983, respectively), which
indicated that the model was indeed valid over the pertur-bation range of interest.
4.2 Controller design
Having obtained a representative model it is relativelystraightforward to set up an optimisation problem in
Table 2: Multiloop PI control structure
Loop Controlled output
variable
Control input
variable
Controller
structure/action
1 CVGAS, calorific
value
WAIR, air flow Pþ I
2 MASS, bed-mass WCOL, coal flow Pþ cross channel
P on WCHR
3 PGAS, gas
pressure
WSTM, steam flow Pþ I
4 TGAS, gas
temperature
WCHR, char flow Pþ I
0 50 100 150 200 250 3000.8
0.9
1
Ch
ar(k
g.s
-1)
Simultaneous PRBS Inputs
0 50 100 150 200 250 300
16
18
20
Air
(kg
.s-1
)
0 50 100 150 200 250 3007
8
9
10
Co
al(k
g.s
-1)
0 50 100 150 200 250 3002.2
2.4
2.6
2.8
3
3.2
Ste
am(k
g.s
-1)
Time (s)
Fig. 3 PRBS inputs to system
IEE Proc.-Control Theory Appl., Vol. 153, No. 3, May 2006 257
MATLAB/SIMULINK. This can be solved by a range ofoptimisation approaches; here a Nelder–Mead simplex(direct search) method was utilised (see e.g. [10, 11]).The identified linear model and the associated controller
were set up in SIMULINK to simulate rejection of a stepoutput pressure disturbance of 0.2 bar. Whereas in thenon-linear model this disturbance has dynamics (first-order type behaviour), here it is represented as a step dis-turbance added directly to the pressure output (PGAS).This means there is no need to identify a disturbancemodel and it represents a ‘worst case scenario’ where thedisturbance has a faster effect in the linear model than ithas on the real plant.The single objective function comprised a weighted sum
of output errors combined with penalty functions to penaliseany excursions of the output (controlled variables) from thedesired tolerance bounds and also to penalise overactivecontrol inputs. The optimisation problem was then startedfrom a range of initial gain values and allowed to convergein each case to the ‘optimal’ gains. Multiple local minimawere found and it was necessary to manually select theoverall best solution (clearly this procedure could be auto-mated via a genetic algorithm based search). The Monte-Carlo (sensitivity) analysis was also used to inform thisdecision, so that a controller that was robust to modelerrors could be selected.Finally, the resulting controller was implemented on the
non-linear gasifier model. The performance of the controlleron both the linear (data-based) model and the non-linearmodel is shown in Fig. 5, which also shows the output tol-erances. Note that on the non-linear system the controller
performance is better than predicted (due to the ‘worstcase’ nature of the design procedure).
5 Baseline PI results
Once a viable controller was found it was implementedfully on the non-linear simulation model and the challengetests were applied. The results for the baseline controller aresummarised in the following.
0 100 200 300–0.015
–0.01
–0.005
0
0.005
0.01
CV
(MJ/
kg)
"designed"actual
0 100 200 300
–0.4
–0.2
0
0.2
0.4
0.6M
ass
(tonnes
)
0 100 200 300–0.2
–0.1
0
0.1
0.2
Pre
ssu
re(b
ar)
0 100 200 300
–1
–0.5
0
0.5
1
Tem
p(K
)
Fig. 5 Response of optimised controller to pressure disturbance:comparison of data-based model (designed) and non-linear model(actual) responses
0 100 200 3004
4.2
4.4
4.6
4.8
CV
(MJ/
kg
)
goodness of fit, RT2: 0.99899
0 100 200 300–0.05
0
0.05E
rro
r
Time (s)
0 100 200 300–0.05
0
0.05
Err
or
Time (s)
0 100 200 30019.6
19.8
20
20.2
20.4
20.6
Pre
ssure
(bar
)
goodness of fit, RT2: 0.99946
0 100 200 3009.98
10
10.02
10.04
10.06
10.08
Mas
s(t
onn
es)
goodness of fit, RT2: 0.99979
0 100 200 300–5
0
5x 10
-3
Err
or
Time (s)
0 100 200 3001215
1220
1225
Tem
p(K
)
goodness of fit, RT2: 0.99974
0 100 200 300–1
0
1
Err
or
Time (s)
modelsystem
Fig. 4 Model fitting results for gasifier system
IEE Proc.-Control Theory Appl., Vol. 153, No. 3, May 2006258
5.1 Disturbance tests
The test results for the controller during the six disturbancetests are included in Table 3. The table shows the maximum
absolute deviation of each output from the desired value andthe integral of absolute error for the pressure and calorificvalue outputs. The units are specified and are the same asthose used in the simulation.
In summary, the controller gave good results across therange of sinusoidal and step disturbance tests (specified inSection 3.2). Only at 0% load with the sinusoidal disturb-ance does one output exceed its limit. The output in viola-tion is PGAS, shown in bold in the table. Figure 6 showsthe output response plot and Fig. 7 the corresponding inputsignals for this particular test. It is clear from the graphs andknowledge of the control loops that the saturations of thesteam flow input at zero (steam cannot be extracted) leaddirectly to the violations of the pressure limits.
5.2 Load change test
The responses for changing the demanded load are shown inFig. 8 and 9 for the outputs and inputs, respectively. It canbe seen that with the exception of the bed-mass the outputstrack their demanded levels reasonably well. It takes signifi-cant time (beyond the length of simulation shown) for thebed-mass to return to the set-point. This is due to the satur-ation of the coal feed input, which can be seen in Fig. 6 fromaround 2 min onward.
5.3 Coal variation (model error) test
A change of þ8% coal quality with the default PI controlscheme causes the controller to be unable to track thedemand temperature at 100% load steady-state. This isdue to saturation of the control input related to temperature(i.e. the char flow is reduced to its lower limit). Of course,it may be possible to mitigate this problem with a multi-variable controller where other inputs might be exploitedto manipulate the temperature.
5.4 Implementation aspects
5.4.1 Structure: The controller structure is conven-tional in nature, consisting essentially of four standard
Table 3: Summary of test output results for baselinecontroller
Test description Output Max. absolute
error
IAE
100% load step
disturbance
CVGAS, J kg21 4865 30 200
MASS, kg 6.938
PGAS, N m22 4987 39 201
TGAS, K 0.2399
50% load step
disturbance
CVGAS, J kg21 5069 32 204
MASS, kg 8.455
PGAS, N m22 5782 47 187
TGAS, K 0.2664
0% load step
disturbance
CVGAS, J kg21 5855 43 481
MASS, kg 11.05
PGAS, N m22 7712 60 197
TGAS, K 0.3223
100% load sinusoidal
disturbance
CVGAS, J kg21 4093 772 056
MASS, kg 10.89
PGAS, N m22 4975 926 115
TGAS, K 0.3800
50% load sinusoidal
disturbance
CVGAS, J kg21 4670 879 856
MASS, kg 12.87
PGAS, N m22 6231 1 149 850
TGAS, K 0.4214
0% load sinusoidal
disturbance
CVGAS, J kg21 5877 1 036 621
MASS, kg 16.36
PGAS, N m22 11 851 1 918 503
TGAS, K 0.4800
Limit violations are shown in bold
0 100 200 300–0.015
–0.01
–0.005
0
0.005
0.01
CV
(MJ/
kg
)
Dis turbance Response: Outputs and Lim its
0 100 200 300
–0.4
–0.2
0
0.2
0.4
0.6
Ma
ss
(to
nn
es
)
0 100 200 300
–0.1
–0.05
0
0.05
0.1
0.15
Pre
ss
ure
(ba
r)
Tim e (s)
0 100 200 300
–1
–0.5
0
0.5
1
Tem
p(K
)
Tim e (s)
Fig. 6 Output response to sinusoidal pressure disturbance at 0% load
IEE Proc.-Control Theory Appl., Vol. 153, No. 3, May 2006 259
single-input, single-output controllers using P and I terms.Hence, it could be implemented on a real gasifier plantwith no major difficulty.
5.4.2 Workload: The design effort was approximately40 man-hours (1 week) to obtain the results describedherein. However, it should be noted that the designerswere very familiar with this particular plant, theSIMULINK dynamic model and its associated issues (soperhaps had an advantage in this area compared to otherdesign teams).
5.4.3 Safety: For a real application it is clear that therewould be issues with regard to carrying out the open-loop system identification experiments in a safe manner.Serious consideration of all the safety issues and detailedplanning of the tests would be required to ensure thatthese tests could be carried out successfully.
6 Conclusions
The paper has described the second benchmark challengeon gasifier control. The model and control specification
0 100 200 3000
1
2
3
Dis turbance Response: Inputs and Lim its
Ch
ar
(kg
/s)
0 100 200 3000
5
10
15
20
Air
(kg
/s)
0 100 200 3000
2
4
6
8
10
Tim e (s)
Co
al(
kg
/s)
0 100 200 3000
2
4
6
Ste
am
(kg
/s)
Tim e (s )
Fig. 7 Input response to sinusoidal pressure disturbance at 0% load
0 10 20 30 40 50 60 70 800
50
100
Response to Load Change
Lo
ad
%M
CR
Actual
Demanded
0 10 20 30 40 50 60 70 804.2
4.4
4.6
CV
(MJ/
kg
)
0 10 20 30 40 50 60 70 809
10
11
Ma
ss
(T)
0 10 20 30 40 50 60 70 8015
20
25
Pre
ss
.(b
ar)
0 10 20 30 40 50 60 70 801150
1200
1250
Tem
p(K
)
Time (minutes)
Fig. 8 Load (top) and output response to a ramped load change from 50 to 100% of maximum load over 10 min
IEE Proc.-Control Theory Appl., Vol. 153, No. 3, May 2006260
have been presented. Details regarding the design of thebaseline PI controller have been given, together with aselection of the key results obtained. This controller wasprovided to give participants in the challenge somethingwith which to compare their early results.It is clear from the results that the baseline controller is
not a bad one. Indeed it only fails in its regulation taskduring one of the six pressure disturbance tests. Compa-rison of the performance of this relatively simple controllerstructure with some of the more complex approaches that arebeing proposed should be both worthwhile and interesting.
7 Acknowledgments
The authors would like to thank the management of theALSTOM Power Technology Centre for supporting boththe challenge and the publication of this paper.
8 References
1 Donne, M.S., Dixon, R., Pike, A.W., Odeku, A.J.L., andRicketts, B.E.: ‘Dynamic modelling of the ABGC prototypeintegrated plant’. DTI Coal Research and Development ProgrammeETSU Report No. COAL R143, 1998
2 Dixon, R., Pike, A.W., and Donne, M.S.: ‘The ALSTOM benchmarkchallenge on gasifier control’, Proc. Inst. Mech. Eng. I, J. Syst.Control Eng., 2000, 214, (16), pp. 389–394
3 ‘Special Issue on the ALSTOM Gasifier Control BenchmarkChallenge’, Proc. Inst. Mech. Eng. I, J. Syst. Control Eng., 2000,214, (16)
4 Dixon, R.: ‘Benchmark Challenge at Control 2004’, Comput. ControlEng. IEE, 2005, 10, (3), pp. 21–23
5 Dixon, R.: ‘Alstom Benchmark Challenge II: Control of a Non-LinearGasifier Model, ALSTOM’, 2002, http://www.iee.org/OnComms/PN/controlauto/Specification_v2.pdf
6 Pike, A.W., Donne, M.S., and Dixon, R.: ‘Dynamic modelling andsimulation of the air blown gasification cycle prototype integratedplant’. Int. Conf. on Simulation ’98, York University, IEEpublication no. 457, 1998, pp. 354–361
7 Moreea-Taha, R.: ‘Modelling and simulation for coal gasifier’ (IEACoal Research, Putney Hill, London, 2000)
8 Asmar, B.N., Jones, W.E., and Wilson, J.A.: ‘A process engineeringapproach to the ALSTOM gasifier problem’, Proc. Inst. Mech.Eng. I, J. Syst. Control Eng., 2000, 214, (16), pp. 441–452
9 Young, P.C.: ‘The instrumental variable method: A practical approachto identification and system parameter estimation’, in Barker, H.A.,and Young, P.C. (Eds.): ‘Identification and system parameterestimation’ (Pergamon, Oxford, 1985), pp. 1–15
10 Gill, P.E., Murray, W., and Wright, M.H.: ‘Practical optimization’(Academic Press, 1981)
11 Grace, A.: ‘Optimization Toolbox for Use with MATLAB’ (TheMathWorks Inc., 1994)
0 10 20 30 40 50 60 70 800
2
4Input Actuation
Ch
ar
(kg
/s)
0 10 20 30 40 50 60 70 8010
15
20
Air
(kg
/s)
0 10 20 30 40 50 60 70 806
8
10
Co
al(
kg
/s)
0 10 20 30 40 50 60 70 800
2
4
Ste
am
(kg
/s)
Tim e (m inutes)
Fig. 9 Control input responses to a ramped load change from 50 to 100% of maximum load over 10 min
IEE Proc.-Control Theory Appl., Vol. 153, No. 3, May 2006 261