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国外经典书籍MULTIVARIABLE FEEDBACK CONTROL-多变量反馈控制 的源码

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Date: Wed, 03 Dec 1997 18:47:32 +0100
From: Erik Mikkelsen <[e-mail]>
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Hei!

Sender deg filene til kjoering av destillasjonskolonnen.


Hilsen
Erik M m.fl.

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function xprime=cola4p(t,X) 
% sample usage:   [t,x]=ode15s('cola4p',[0 5000],Xinit);
%
% cola4p  - Subroutine for simulation using MATLAB integration routine
%           It calls the distillation model colamodp 
%
%            SYNTAX: [t,x]=ode15s('cola4p',tspan,Xinit);
%
%            tspan -   [t_start,t_stop]
%            Xinit -   column vector containing initial liquid composition
%                      for stages 1-NT and initial liquid hold up for stages
%                      1-NT.
%
%            Disturbances are feedrate, feed composition and feed liquid fraction
%            These are set by directly altering 'cola4p.m'.


% Number of stages in column

NT=41;


% Feed	

F  = 1.0;				% Feedrate (kmol/min)
zF = 0.5;				% Feed composition light comp.
qF = 1.0;				% Feed liquid fraction


% Termodynamic data			

TBL= 272.65;				% Boilingpoint light comp.(K)
TBH= 309.25;				% Boilingpoint heavy comp.(K)
CpL=96;					% Heatcapasity light comp. (kJ/kmol*K)
CpH=121;				% Heatcapasity heavy comp. (kJ/kmol*K)
HvapL=19575;				% Hvap for light comp. (kJ/kmol)
HvapH=28350;				% Hvap for heavy comp. (kJ/kmol)
p0L=1.013e5;				% Vapor pressure of pure light liquid comp.(Pa)
p0H=1.013e5;				% Vapor pressure of pure heavy liquid comp.(Pa)
R=8.314;				% Universal gasconstant (kJ/kmol*K)


% Get actual values

xD=X(NT);xB=X(1);			% Actual composition in reboiler and condenser
MB=X(NT+1);  MD=X(2*NT); 		% Actual reboiler and condenser holdup
TD=X(3*NT);				% Actual temperature in reboiler


% Calculates the right top pressure for cooling control

pL= p0L*exp(-HvapL/R*(1/TD-1/TBL));
pH= p0H*exp(-HvapH/R*(1/TD-1/TBH));
p = xD*pL + (1-xD)*pH;


% P-Controllers for control of reboiler, condenser hold up and condenser cooling

% Setpoints

xDs=0.99; 				% Composition top
xBs=0.01;				% Composition bottom
ps=1.013e5;				% Pressure in condenser (Pa)


% Bias values and controller gains

KcB=7;KcD=7; KcP=10;KcXB=50;KcXD=33;	% Controller gains
MDs=0.7; MBs=0.7;			% Holdups  
D0=0.5; B0=0.5;				% Flow (kmol/min)
LT0=2.70629; VB0=3.20629;		% Reflux and boilup
VD0 = VB0;				% Condensation heat(kJ/min)


% P-Controllers

D=D0+(MD-MDs)/MDs*KcD;			% Distillate flow
B=B0+(MB-MBs)/MBs*KcB;			% Bottoms flow     
VD=VD0+((p-ps)/ps)*KcP;			% Pressure
LT=LT0-(xD-xDs)/xDs*KcXD;		% Destillat
VB=VB0+(xB-xBs)/xBs*KcXB;		% Bottoms		


% Store all inputs and disturbances

U(1)=LT; U(2)=VB; U(3)=D; U(4)=B; U(5)=VD; U(6)=F; U(7)=zF; U(8)=qF; U(9)=TBL;
U(10)=TBH; U(11)=CpL; U(12)=CpH; U(13)=HvapL; U(14)=HvapH; U(15)=p0L; U(16)=p0H;
U=U(:);


xprime=colamodp(t,X,U);


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function xprime=colamodp(t,X,U) 
%
% Written by S. Skogestad, L. Westskogen, E. Mikkelsen and S. Helland
% November 1997
%
% colamodp - included pressure variations
%           This is a nonlinear model of a distillation column with
%           NT-1 theoretical stages including a reboiler (stage 1) plus a
%           total condenser ("stage" NT). The liquid flow dynamics are
%           modelled by a simple linear relationship.
%           Model assumptions: Two components (binary separation); constant
%           relative volatility; no vapor holdup; one feed and two products;
%           constant molar flows (same vapor flow on all stages); 
%           total condenser
%
%           The model is based on column A in Skogestad and Postlethwaite
%           (1996). The model has 3x41 states.
%
% Inputs:    t    - time in [min].
%            X    - State, the first 41 states are compositions of light
%                   component A with reboiler/bottom stage as X(1) and 
%                   condenser as X(41). State X(42)is holdup in reboiler/
%                   bottom stage and X(82) is hold-up in condenser. 
%                   states x(83) and on are temperatures
%            U(1) - reflux L,
%            U(2) - boilup V,
%            U(3) - top or distillate product flow D,
%            U(4) - bottom product flow B,
%            U(5) - flow condensated, VD, 
%	     U(6) - feed rate F,
%            U(7) - feed composition light comp., zF.
%            U(8) - feed liquid fraction, qF.
%	     U(9) - boilingpoint light comp. ,THL,
%	     U(10)- boilingpoint heavy comp. ,TBH,
%	     U(11)- Cp light comp., CpL,
%	     U(12)- Cp heavy comp., CpH,
%	     U(13)- Hvap for light comp., HvapL,
%	     U(14)- Hvap for heavy comp., HvapH,
%	     U(15)- Vapor pressure of pure light liquid comp., p0L,
%	     U(16)- Vapor pressure of pure heavy liquid comp., p0H,
%
%
% Outputs:   xprime - vector with time derivative of all the states 
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%------------------------------------------------------------
% The following data need to be changed for a new column.
% These data are for "column A".
% Hvap and Cp given in cola4p.m are also data for "column A", and need to be changed.


NT=41;					% Number of stages (including reboiler and total condenser)
NF=21;					% Location of feed stage (stages are counted from the bottom)
alpha=1.5;				% Relative volatility

M0(1)=0.5;         			% Nominal reboiler holdup (kmol)
i=2:NT-1; M0(i)=0.5*ones(1,NT-2);	% Nominal stage (tray) holdups (kmol)
M0(NT)=0.5;	         		% Nominal condenser holdup (kmol)


% Data for linearized liquid flow dynamics (does not apply to reboiler and condenser):

R=8.314;				% Universal gasconstant (kJ/kmol*K)
taul=0.063;				% Time constant for liquid dynamics (min)
F0=1.0;					% Nominal feed rate (kmol/min) 
qF0 = 1.0;				% Nominal fraction of liquid in feed 
L0=2.70629;				% Nominal reflux flow (from steady-state data)
L0b=L0 + qF0*F0;			% Nominal liquid flow below feed (kmol/min)
lambda=0;				% Effect of vapor flow on liquid flow ("K2-effect")
V0=3.20629;V0t=V0+(1-qF0)*F0;		% Nominal vapor flows - only needed if lambda is nonzero 
k=2.4288e-4;				% Valve equation constant


% End data which need to be changed
%------------------------------------------------------------


% Splitting the states

x=X(1:NT)';				% Liquid composition from btm to top
M=X(NT+1:2*NT)';			% Liquid hold up from btm to top
T=X(2*NT+1:3*NT)';			% Temperatures


% Inputs and disturbances

LT 	= U(1);                       	% Reflux
VB 	= U(2);                       	% Boilup
D  	= U(3);                       	% Distillate
B  	= U(4);                       	% Bottoms
VD 	= U(5);			      	% Condensation heat and cooling	
F  	= U(6);                       	% Feedrate
zF 	= U(7);                       	% Feed composition light comp.
qF 	= U(8);                       	% Feed liquid fraction
TBL	= U(9);		       	      	% Boilingpoint light comp.
TBH	= U(10); 		      	% Boilingpoint heavy comp.
CpL 	= U(11);		      	% Cp for light comp
CpH 	= U(12);		      	% Cp for heavy comp
HvapL	= U(13);		      	% Hvap for light comp.
HvapH	= U(14);		      	% Hvap for heavy comp.	 
p0L	= U(15);		      	% Vapor pressure of pure light liquid comp.(Pa)
p0H	= U(16); 	  	      	% Vapor pressure of pure heavy liquid comp.(Pa)


% Assume linearity between Havp, Cp and composition

Cp   = zF*CpL + (1-zF)*CpH;	      % Heatcapasity for feed
Hvap = zF*HvapL + (1-zF)*HvapH;	      % Heat of vaporization for feed


% THE MODEL


% Vapor-liquid equilibria

i=1:NT-1;   
y(i)=alpha*x(i)./(1+(alpha-1)*x(i));


% Vapor pressures of the two components (Clausius-Clapeyron)

i=1:NT;
pL(i)= p0L*exp(-HvapL/R*(1./T(i)-1/TBL));
pH(i)= p0H*exp(-HvapH/R*(1./T(i)-1/TBH));


% Stage Pressure (Raoults law)

i=1:NT;  
p(i) = x(i).*pL(i) + (1-x(i)).*pH(i);


% Vapor flows (valve equation)

i=1:NT-1;
if (p(i+1)-p(i))<0
  V(i) = k*sqrt(p(i).^2-p(i+1).^2);
else;
  V(i) =0.1*VB;
end;  


% Liquid flows assuming linearized tray hydraulics with time constant taul
% Also includes coefficient lambda for effect of vapor flow ("K2-effect").

i=2:NF;      
L(i) = L0b + (M(i)-M0(i))./taul + lambda.*(V(i-1)-V0);

i=NF+1:NT-1; 
L(i) = L0  + (M(i)-M0(i))./taul + lambda.*(V(i-1)-V0t);
L(NT)=LT;


% Time derivatives from  material balances for 
% 1) total holdup 
% 2) component holdup
% 3) enrgy holdup (temperature)