Dynamic Modeling and Simulation of a Palm

8/6/2019 Dynamic Modeling and Simulation of a Palm

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Renewable Energy 28 (2003) 12351256

www.elsevier.com/locate/renene

Dynamic modeling and simulation of a palmwastes boiler

T.M.I. Mahlia a,, M.Z. Abdulmuin b, T.M.I. Alamsyah c,

D. Mukhlishiend

a University of Malaya, Department of Mechanical Engineering, Kuala Lumpur 50603, Malaysiab Open University of Malaysia, Centre for Engineering and Technical Studies, Block A, Level 4,

Academy of Islamic Studies Buildings, Universiti Malaya, Kuala Lumpur 50603, Malaysiac University of Syiah Kuala, Department of Mechanical Engineering, Darussalam 23111, Banda Aceh,

Indonesiad University of Syiah Kuala, Department of Chemical Engineering, Darussalam 23111, Banda Aceh,

Indonesia

Received 27 March 2002; accepted 3 October 2002

Abstract

A state-space dynamic model for a palm wastes boiler is being developed and simulated.The unique feature of this boiler is that it uses wastes in the form of fiber and shell from thepalm oil processing as its fuels. Specific characteristics of oil palm waste boilers are non-uniform fuel feed, compositions, sizes and moisture content of the fuel. These features intro-duce additional dimensions to the difficulty of boiler control. The superheated steam producedis used to generate electricity, which drives numerous motors and other equipment for palmfruit processing thus causing severe interactions between the power plant and other parts ofthe mill. The main work of this paper is the development of a dynamic model and simulation

of the boiler. The boiler unit can be divided into several sections for analysis viz., the furnace,superheater, drum, risers, and downcomer. A tenth-order, physical, linearized process modelwas developed. The linearized model consists of ten first-order simultaneous equations and isrepresented by a (10 x 10) state matrix and (4 x 10) input matrix in the state space form. 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Palm wastes boiler; Dynamic modeling; State space; Simulation; Power plant

Corresponding author. Tel.: +603-7967-6842; fax: +603-7967-5317. E-mail address: [email protected] (T.M.I. Mahlia).

0960-1481/03/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved.doi:10.1016/S0960-1481(02)00218-5


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1236 T.M.I. Mahlia et al. / Renewable Energy 28 (2003) 12351256

Nomenclature

Aw, As, Ar, Ad steam drum surface, superheater, riser, and downcomer flowareas (m2, ft2)

A, B, C, D matrices of constant coefficients of the systemCp, Cg, Cst, Crt heat capacitance of superheated steam, flue gas, superheater,

and riser tubes (J/kg C, Btu/lb F)Dr, Ds, Dd riser, superheater, and downcomer tube diameters (m, ft)

fs, fr, fd superheater, riser, and downcomer friction coefficientshi, hw, hv, hr, hs, hf enthalpy of liquid, saturated liquid, vapor, liquidvapor

mixture, and superheated (J/kg, Btu/lb)

kec drum liquid mass evaporation rate constant (kg/s C, lb/s F )

kF gas temperature/fuel rate constant (C s/kg, F s/lb)ks, kr, kgs, kgr heat transfer coefficients for superheater and riser tubes to

steam and boiling liquid and from flue gas to superheater and risertubes (J/kg C, Btu/lb F)

Ls, Lr, Ld superheater, riser, and downcomer tube lengths (m, ft)

Ms,Mr, Mw superheater tubes, riser tubes, and steam drum liquid mass (kg,

lb)

ps, pv, pw superheater, steam, and water-drum pressures (bar, psig)

Qg,Qgs,Qs,Qgr,Qr,Qf steady-state heat release and heat input rates from fluegas and calorific value (J/s Btu/s)

Tg, Tgs, Tgr flue gas temperatures (C, F)Ts, Tv, Tw superheated steam, saturation, and liquid temperatures (C, F)Tst, Trt superheater and riser tube-wall temperatures (C, F)Vw, Vv liquid and vapor-phase volume of steam drum (m

3, ft3)

wA/wF air/fuel ratio

ws, wv, wr, wd, we, wi, wF, wec mass flows of steam or water at superheater,riser, downcomers, feed water, fuel, and drum liquid evaporation

(kg/s, lb/s)

x riser outlet mixture quality (%)

x(t) state variable vector of process system

y water-level displacement (m, ft)

y(t) system input or control vector [ws, wi, wf, Te]

rs, rv, rr, rw steam, saturated vapor, liquidvapor mixture and liquiddensities (kg/m3, lb/ft3)

1. Introduction

Electricity is now viewed as a necessity. The basic principle functions of powergeneration are to convert energy from any kind of resource to electrical energy and

to transmit this energy to the consumers. Steam boilers today range in size from


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1237T.M.I. Mahlia et al. / Renewable Energy 28 (2003) 12351256

those required to heat a small-size home to the very large ones used in electric power

generating stations. The fundamental requirement for the power plant system is how

to ensure the smooth and continuous energy flow. To satisfy this requirement, it is

desirable that the power generation units be properly controlled so that the productionand consumption of energy can be maintained in equilibrium at all times. To reach

this requirement, many ways of modeling and controls have been applied. Simulation

of the operation of the system is achieved by the utilization of computers. Modeling

and simulation provides key information as to the characteristics that are vital for

the investigation and prediction of the plant. It enables the modeler to measure theperformance of existing or proposed systems under different operating schemes.

The model developed in this research is intended for further research to understand

the behavior of palm wastes boilers under steady state and transient operations, and

can be used in control system and operational optimization studies. This boiler uses

a different type of fuel from conventional boilers, using fiber and shell waste productsfrom oil palm processing. It has commonly been taken for granted that this energy

is free in the palm oil mills industry. Specific characteristics of the boiler are non-uniform fuel feed and moisture content in fiber and shell. These features result inadditional dimensions to the difficulty of controlling palm waste boilers. The natureof fuels, stoichiometric air-to-fuel ratio, and mass balance of a palm waste boiler

are discussed in Ref. [1].

2. Plant description

Parameters of the model equations are either computed using construction data or

identified using the steady state operation test data. Since a large number of variablesare required to describe the boiler system, it is necessary to devise a systematic

convention for naming the variables. The boiler is modeled based on the follow-

ing subsystems:

Furnace,

Superheater,

Drum,

Downcomer,

Risers.

The simplified block diagram of oil palm wastes boiler process is presented inFig. 1.

For simulation purposes, two types of data are required. First, data that will not

change while the plant is operating physical data. Second, data that will experi-ence small changes when the plant is operating steady state operating data. Thereare many data needed to simulate the systems, and they are obtained by several

methods given below:

On-line reading from the boiler plant,


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Fig. 1. Simplified block diagram of oil palm wastes boiler.

Design specifications of the boiler, Published work on oil palm waste boiler,

Calculations from available data,

Polynomial Curve Fitting (PLCF).

2.1. Physical data

Complete physical data of the boiler that is used for simulation are shown in

Table 1.

2.2. Steady state operating data

The steady state operating data have been collected with on line reading from the

plant. These data are then used to calculate other necessary data together with dataavailable in the design specification of the boiler and steam tables. Steady stateoperating data that are used for the simulation are shown in Table 2.

3. Methodology

The important basic equations used in the analysis and developments of the boiler

model are the following equations [26]:


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Table 1

Physical data of the boiler

Description Values

Amount of superheater tubes 65

Outlet diameter of superheater tubes 0.0381 m

Tick of superheater tubes 0.003505 m

Superheater tube lengths 2.6 m

Amount of riser tubes 560

Outlet diameter of riser tubes 0.0762 m

Tick of riser tubes 0.003505 m

Riser tube lengths 4.5 m

Amount of downcomer tubes 24

Outlet diameter of downcomer tubes 0.1016 m

Tick of downcomer tubes 0.003988 mDowncomer tube lengths 5.25 m

Drum diameter 1.203 m

Lengths of drum 5.29 m

Steel boiler and superheater tubes densities 7850 kg/m3

Table 2

Steady-state operating data

Description Values

Drum outlet pressure 17.24 Bar

Superheater outlet pressure 16.41 Bar

Enthalpy of superheated steam 592 kJ/kg

Liquid vapor mixture density 558.46 kg/m3

Air temperature 30 CFlue-gas temperature in the furnace 1575 CFeedwater temperature 60 CSuperheated steam temperature 234 CRiser tubes temperature 206 CSuperheater tubes temperature 242 CFuel mass flow 4.51 kg/s

Steam mass flow 18.8 kg/s

Riser friction coefficient 0.0531

Air:fuel ratio 8.036

Low heating value of fuel 2373 kJ/kg

Flow equations: NavierStokes-type equations for one-dimensional non-turbulentflow are used in this study. Viscous friction is neglected so that the velocity profileacross the flow is constant. However, a friction loss term proportional to the squareof velocity is included in the momentum equation. Continuity, momentum, and

energy conservation equations are applied with certain simplifying assumptionsthat will be mentioned in the following section.

Heat transfer equations: these are empirical equations used to determine the rate


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of heat transfer from hot gases to tube banks in turbulent flow, from tube wallto steam and to boiling liquid. The tube wall temperatures are determined by the

heat capacitance of the walls.

State equations: these equations are obtained from steam tables at saturated andsuperheated steam for the steady state operating conditions. The relations are

assumed to be linear for a given range of values of the variables.

Some fundamental physics laws are reviewed in the time-dependent form, and the

process model is established using the following fundamental equations:

3.1. Conservation of mass

The mass balance equation or conservation of mass is expressed by:d(Vr)

dt win wout. (1)

3.2. Conservation of energy

The conservation of energy is the first law of thermodynamics and can beexpressed in terms of the relationship:

d(Vrhout)

dt winhin wouthout Q W. (2)

3.3. Conservation of momentum

The law of conservation of momentum is expressed in terms of the following[3]:

PinPout Ln

gAn

d wout

dt fn

Ln

g

w2out

rout(An)2Dn

Lnrout 1

2g(An)2

w2out

rout(3)

w2out

rout(An)2g

w2in

rin(An)2g.

3.4. Heat transfer

The risers and superheater are assumed to receive heat from the flue gas by con-vection only. The heat is assumed to be transferred from the flue gas to the metaland from the metal to the fluid by convection only. The equations used are [7]:

Gas to metal:

Qg kg w0.6g (Tg Tm) (4)

Metal to fluid (one phase flow)


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Q k w0.8 (Tm T) (5)

Metal to fluid (two phases flow)

Q k (Tm T)3 (6)

3.5. Method for model linearization

The model of a boiler represented by a large number of non-linear partial differen-

tial equations. Most of the equations are related to fluid flow and heat transfer involv-ing partial derivatives of time and space. Solutions of a set of these equations are

very difficult and therefore some simplifying assumptions have to be made. In theanalysis, the boiler is divided into a number of sections and for each lumped para-

meter section, the steam and gas are assumed to vary only in the axial directions

and linearly with space. Linearizing the partial differential equations reduces theseequations to ordinary linear differential equations by applying small perturbation and

difference equation techniques. Suppose an equation of the general form:

fx,y,z,...,xt,xl

,yt

,yl

,... 0 (7)where

t

indicates time derivative andl

is the derivative with respect to the space

variable. It is assumed that for small space intervals L, the variables x, y, z,... may

be written in linear functions of the variable l, so that:

xl

x2x1

L,yl

y2y1

L,zl

z2z1

L,..., (8)

where x2,y2,z2,..., and x1,y1,z1,..., denote the value of the variable x, y, z,... at the end

and at the beginning, respectively, of the space interval L. Even though x1,y1,z1,...,

x2,y2,z2,..., are no longer functions of l, they are still functions of time .

x,y,z,...,xt

,yt

,zt

,... are now assumed to be the value of variables at the beginning of

the space interval, hence Eq. (8) can be written as:

fx1,y1,z1,..., x1t,x2x1

L,

y1

t,y2y1

L,

z1

t

z2z1

L,..., 0. (9)

Eq. (9) is then perturbed at steady state operating conditions to eliminate the non-

linearities, giving the following equation:

fx1

x1 fy1

y1 ... fx2

x2 fy2

y2 f

(x1)t

(x1)t

... (10)

0

where (x1)t

, (y1)t

, .... can be replaced byd

dt(x1),

d

dt(y1),... for small pertur-


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bations. It is seen from the equations above that time-derivative terms

dx1

dt,dy1

dt,dz1

dt, ... are treated as independent variables and second or higher order terms

in perturbed variables are neglected. The partial differentials fx1,fy1

,fz1

,, whichare the coefficients of the perturbed variables, are evaluated at initial steady stateoperating conditions about the dynamic behavior of the boiler to be analyzed. As a

result of these simplifications, Eq. (10) becomes linear first order ordinary differentialequations with constant coefficients in the perturbed variables written asx1, x2, y1, y2, z1, z2.

4. Model development

4.1. General assumptions and abbreviations

The following general assumptions are made in deriving the dynamic model for

the boiler. Additional assumptions are listed under each section:

Feed water temperature is assumed to be constant. State equations for vapor phase are determined from steam tables and estimation

of the actual pressure, temperature, and density relation within a given range of

value of the variables.

Linear relations between the mentioned variables are obtained from steam tables

both for saturated and superheated steam.

No rate of change of stored mass in the gas path.

Turbulent heat transfer rates from hot gas to tube banks or from the superheater

tube to the steam are obtained from empirical relations.

The heat transfer coefficients are determined from the steady state operating con-

dition. A lumped parameter approach with ordinary differential equations is used to

describe the system.

Water and steam in the drum and in the risers are in saturation equilibrium.

Mixture of fiber and shell in the fuel is constant. No mass and momentum transfer at the tube side.

The following abbreviations are used in the model development:

COM: Conservation of Mass COT: Conservation of Momentum

COE: Conservation of Energy


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4.2. Model development

4.2.1. Furnace

The following assumptions are made in deriving the dynamic model for the fur-

nace:

The fuel (fiber and shell) consumption is assumed to be constant. Calorific value and moisture content of the mixture of palm fiber and shell are con-

stant.

The airfuel ratio is assumed to be constant. Temperature of combustion gases in furnace is proportional to the fuel rate.

In each tube bank the heat transfer rate is determined by the tube wall temperature,

the average gas temperature is a function of the temperature of incoming gasesand the amount of the heat loss of that particular bank.

Inertia of the hot gases is neglected and the velocity changes take place instan-

taneously.

Delay due to the heat capacitance of the hot gases is neglected; that is, temperature

changes take place instantaneously in combustion gases.

Turbulent heat transfer is assumed throughout the process.

COM:

VF d rFdt

VAdrAdt

(wF wA) wg (11)

from point 3 of the general assumptions, it is known that VFd rF

dt 0,

VAd rA

dt 0, therefore (wF wA) wg where Airfuel ratio

wA

wF, wA

wA

wFwF, wg wF

wA

wFwF

wg 1 wA

wF wF (12)COT:Not relevant.

COE:

Vgd(rghg)

dt (wFhF wAhA) wghg Qg (13)

where Vgd(rghg)

dt 0, wg 1 wA

wF wF , hg hF hA, therefore

Qg wg hg, Qg wg Cg Tg

Qg wg . LHV (14)


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Tg Qg

Cg (1 wA/ wF) wF(15)

4.2.2. Superheater

The following assumptions are made in deriving the dynamic model for the super-

heater:

Inertia term in the flow equation is neglected. Load disturbance is a change in the steam flow rate. To calculate superheater section average gas temperature, both risers are con-

sidered as one lumped section.

Gas side

COM:

Vgsdrgs

dt wg wgs (16)

where Vgsdrgs

dt 0 therefore

wg wgs. (17)

COT:Not relevant.

COE:

Vgsd(rgs hgs)

dt wghg wgshgs Qgs (18)

where Vgsd(rgshgs)

dt 0 therefore wghg wgshgs Qgs 0, Qgs

wghg wgshgs , Qgs wg Cg Tg wgs Cgs Tgs where wg wgs , Cg

Cgs then Qgs wg Cg (Tg Tgs), Qgs Cg (1 wA/ wF) wF (Tg Tgs)

Therefore the flue gas temperature leaving superheater banks and entering riserbanks is as follows:

Tg1 Tg Qgs


Tube Bank

COE:

Ms Cstd Tst

dt Qgs Qs (20)

where

Qgs kgs w0.6F (Tgs Tst) (21)

Tgs Tg 1

2

Qgs

Cg (1 wA/ wF) . wF(22)


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Qs ks w0.8v (Tst Ts). (23)

Water/Steam Side

COM:

As Lsdrs

dt ws wv. (24)

COT:

pvps fsw2v

rv. (25)

COE:

As Ls drs hsdt

wv hv ws hs Qs. (26)

4.2.3. Riser

The following assumptions are made in deriving the dynamic model for the risers:

Only natural circulation exists.

Vapor and liquid velocities in the risers are identical.

Heat transfer rate to boiling liquid from tube wall is proportional to the cube ofthe temperature difference between the wall and the liquid.

Liquid temperature is always the same as the saturation temperature correspondingto the drum pressure; that is, instantaneous evaporation takes place in the riser

when the drum pressure changes.

Both risers are considered as one lumped section.

Gas side

COM:

Vgrdrgr

dt wgs wgr (27)

where Vgrdrgr

dt 0 therefore wgs wgr.

COT:Not relevant.

COE:

Vgrd(rgr hgr)

dt wgshgs wgrhgr Qgr (28)

where Vgrd(rgrhgr)

dt 0 therefore wgshgs wgrhgr Qgr 0, Qgr

wgshgs wgrhgr , Qgr wgs Cgs Tgs wgr Cgr Tgr where, wgs wgr ,Cgs Cgr then Qgr wg Cg (Tg Tgr), Qgr Cg (1

wA/ wF) wF (Tg Tgr).


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Therefore the flue gas temperature leaving the riser is as follows:

Tg2 Tg Qgr

Cg (1 wA/ wF) wF. (29)

Tube BankCOE:

Mr Crtd Trt

dt Qgr Qr (30)

where

Qgr kgr w0.6F (Tgr Trt). (31)

Rewriting Eq. (9); Tg1 Tg Qgs

Cg (1 wA/ wF) wFtherefore,

Tgr Tg1 1

2

Qgr

Cg (1 wA/ wF) wF. (32)

Substituting Eq. (9) into Eq. (32) results in the following equation:

Tgr Tg Qgs

Cg (1 wA/ wF) wF

1

2

Qgr


Qr kr (Trt Tv)3. (34)

Water/Steam side

COM:

Ar Lrdrr

dt wd wr. (35)

COT:

pwpv Lr

gAr

dwr

dt fr

Lr

g

w2r

rrA2rDr

Lrrr w2r

2g rrA2r

w2rrrA

2rg

w2d

rwA2g (36)

COE:

ArLrd(rr hr)dt

wdhw wrhr Qr (37)

1

rr

x

rv

(1 x)

rw(38)

hr xhv (1x) hw (39)

hr xhfg hw. (40)

4.2.4. Drum

The following assumptions are made in deriving the dynamic model for the drum:

There is no temperature gradient in the vapor phase in the drum and the tempera-

ture is always the saturation temperature corresponding to the drum pressure.


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The liquid phase has no temperature gradient except through a very thin layer at

the liquid surface because of the turbulence in the drum.

Evaporation or condensation rate in the drum is proportional to the difference of

liquid and saturation temperatures. Liquid level changes due to bubble formation in the drum are neglected.

Feed water temperature is assumed to be constant.

Gas side

Not relevant.

Tube bank

Not relevant.

Water/Steam side

COM:Water

d

dt(Vwrw) wi (1 x) wr wd wec. (41)

Steam

d

dt(Vvrv) wec x wr wv (42)

y Vv

Aw

Vw

Aw(43)

M Aw rw y. (44)

COT:

Not relevant.COE:

d

dt

(Vwrwhw) (1 x) wrhv wihi wdhwwechv. (45)

4.2.5. Downcomers

The following assumptions are made in deriving the dynamic model for downco-mers:

Only natural circulation exists.

No boiling takes place in downcomers.

Downcomers liquid temperature is the same as the drum liquid temperature.

Gas SideNot relevant.

Tube bank


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conditions, which is between 17.2 bar (250 psig) and 22 bar (320 psig) of drum

pressure. The dynamic physical model can be summarized as follows:

Type of model: state space

Number of input variables: four

Steam flow-rate (ws) Feed water flow rate(wi) Fuel flow rate (wF) Feed water temperature flow rate (Ti)

Number of output variables: ten

Superheated steam density (s) Superheated steam temperature (Ts) Superheater tube wall temperatures (Tst)

Quality of mixture leaving riser (x)

Riser mass flow rate (wr) Drum pressure (Pv)

Riser tubes wall temperatures (Trt)

Drum and downcomers liquid temperature (Tw)

Drum liquid level (y)

Superheater pressure (Ps)

The main difficulty in this work is the size and complexity of the boiler unit.When the model was formulated and linearized it was found that many manipulationsteps were required before arriving at the final form of the model. The reason wasthat a set of ten simultaneous differential equations together with large number of

the steady-state ones needed to be suitably rearranged and solved.

In simulation, the set of equations developed and linearized in the previous section

are reduced and rearranged in order to obtain a suitable model for simulation in

state-space form. This palm wastes boiler model has been simulated using MATLAB.Before the simulation can be performed it is necessary that all the unknown constants

and parameters are made available to the model. These unknowns include steady-state balance equations and operating points, boiler physical data, and curve fittingrelationship if data extracted from the steam tables. The set of linearized equations

may be written in the following matrix form:

x(t) Ax(t) Bu(t) (52)

y(t) Cx(t) Du(t) (53)

where A is a (10 x 10) state matrix, B (10 x 4) input matrix, C output matrix and

direct transmission matrix D are constant matrices. The value of the matrices is

presented in Appendix A.The response of the output variables for 10% step inputs of steam, feed water,

flow rate, temperature, and fuel are shown in Figs. 25.


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Fig. 2. Response with 10% steam flow rate step.


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Fig. 3. Response with 10% feedwater flow rate step.

Validation of the model was done by on-line reading of drum pressure from the

plant using HP 3497A Data Acquisition and Control Unit and HP BASIC as the

programming language. This data was transferred to a MATLAB file. Pneumaticcylinders were used as mechanisms (actuators) for adjusting the amount of the input

fuel (fiber and shell) to the furnace of the boiler plant. The responses model for


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Fig. 4. Response with 10% fuel flow rate step.


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Fig. 5. Response with 10% feedwater temperature step.


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drum pressure (Pv) with respect to fuel flow rate (wF) is presented in Fig. 6. Fromvalidation it can be seen that the result obtained is quite encouraging and the simu-

lated model of drum pressure matches fairly well with the experimental plot.

6. Conclusion

In the reduction of the system order, it is important to select dependent variables

to give the best reduced system. For control studies, it is suggested that the dependentvariables can be reduced to several significant output variables such as:

superheated steam temperature (Ts)

quality of mixture leaving riser (x)

drum pressure (Pv)

drum liquid level (y)

superheater pressure (Ps)

with system inputs:

feed water flow rate(wi) fuel flow rate (wF) feed water temperature flow rate (Ti)

and consider the steam flow rate (ws) as a disturbance. In a more simplified structurethe output variables can be reduced to Pv and y only while the input variables arereduced to only one, i.e., wF.

The model has been developed with certain assumptions that might make the

model less accurate. The number of assumptions can be reduced especially in the

riser part, where a more accurate representation can be expected if the riser could

be derived separately. However, from the validation shown, the result matches fairlywell with the experimental plot. Finally, this model should be useful as a basis for

further studies of the two following purposes:

To be a basis for a linearized model to be used for design of a multivariablecontrol system of a palm wastes boiler.

Fig. 6. Steam drum pressure response with 20% fuel flow rate step.


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To be a basis for a reduced order linearized transfer function model for related

control applications.

Acknowledgements

The authors would like to acknowledge the financial support from the Ministryof Science, under the IRPA financing scheme. The research was carried out underIRPA research Project No. 03-02-03-0353.

Appendix A

Rewriting Eq. (25), pvps fsw2v

rv or in perturbed form can be written as:

pvps fs2 wv

rvpv fs

w2v

r2v rv wv

rv

fs 2 wvpv

rv

fs 2 wvps

wv

2 rv rv. Then in simplified form, wv z1 pv z2 ps z3 rv

where z1 rv

fs 2 wv, z2

rv

fs 2 wv, z3

wv

2 rv rv.

Input matrices A (10 x 10) and B (10 x 4) and output matrix C and D:

A

0.85972 0.00092 0 0 0

15.93825 0.22675 0.15181 0 0

42.04492 0.14517 0.10124 0 0

0.00441 4.7223 10-6 0 0.17506 3.02126 10-8

5264.27236 0.96792 2.91963 1.00392 106 0.92565

1285.64960 1.37760 0 0 0

0 0 0.00044 0 0

0 0 0 3.51597 0.00035

6.80509 0.00729 0 269.36171 4.64881 10-5

56620.34223 78.22541 10.93006 0 0

1.33932 10-5 0 0 0 0

0.00025 0 0 0 0

0.00066 0 0 0 0

2.24703 10-7 4.12171 106 0.00013 0 0

4.31077 1830.09555 157.59312 0 0

0.55027 209.41783 24.49676 0 0

0.19445 87.82094 0 0 0

0.00160 0 0.7277 4 0 0

0.00031 0.00879 0.19556 0 0

0.88206 0 0 0 0

B

0.00339 0 0 0

0 0 0 0

0 0 1.49170 0

0 1.77767 10-7 0 0

60.69606 23.94852 530.97106 1.16471

0 0.05186 0 0

0 0 22.98759 0

0 0.02530 0 0.00229

0 2.17627 10-6 0 0

228.02653 0 0 0


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C

1.000 0 0 0 0 0 0 0 0 0

0 1.000 0 0 0 0 0 0 0 0

0 0 1.000 0 0 0 0 0 0 0

0 0 0 1.000 0 0 0 0 0 0

0 0 0 0 1.000 0 0 0 0 0

0 0 0 0 0 1.000 0 0 0 0

0 0 0 0 0 0 1.000 0 0 0

0 0 0 0 0 0 0 1.000 0 0

0 0 0 0 0 0 0 0 1.000 0

0 0 0 0 0 0 0 0 0 1.000

D

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

References

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