MATLAB: How to build a matrix with “sum” function in its elements

MATLABmpc

Hello everyone, I am building an mpc controller in matlab rather than using the built in 'mpc command'. I am facing some difficulties in building the mpc's matrices I thought about using for loop.my question is how to use for loop to generate these matrices? …thanks in advance

Best Answer

Outline, not checked in detail against Su,b matrix requirements

CAn = Cb;
TCAn = 0;
TCAB = 0;
for K = 1 : p
    %Sub
    CAB = CAn * Bu;
    TCAB = TCAB + CAB;
    %now store TCAB into appropriate locations in Sub
    insert storage code here
    %Sxb
    CAn = CAn * A;
    TCAn = TCan + CAn;
    %now store TCAN into appropriate locations in Sxb
end

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MATLAB: Can’t figure out how to finalize the code

%V1=volume of first reactor in L
%V2=volume of second reactor in L
%V3=volume of third reactor in L
%V4=volume of forth reactor in L
 
%k1=first order reaction rate in units of (L^3)(M^-1)(T^-1)
%k2=second order reaction rate in units of (L^3)(M^-1)(T^-1)
%Each reactor has different reaction rate
 
%M=mass in units of M
%Qin=inflow in units of (L^3)(T^-1)
%Qout=outflow in units of (L^3)(T^-1)
%Qxy=the flow from reactor x to reactor y (x&y can be 1,2,3..)
%UNITS
%The unit for V1, V2, V3 & V4 is L
%The unit for k1 is hr^-1
%The unit for k2 is L/(mg*hr)
%The unit for M is mg
%The unit for Qin, Qout,Q12, Q23, Q34, Q32, Q43 & Qxy is L/hr
%Given and calculated values  
Qin=10;
Q12=10;
Q23=10+5; %Q23=Q12+Q32
Q34=15-5+3; %Q34=Q23-Q32+Q43
Qout=10;
Q32=5;
Q43=3;
 
Cain=1;
Cbin=0;
 
V1=25;
V2=75;
V3=100;
V4=25;
 
k11=0.05;
k12=0.1;
k13=0.5;
k14=0.1;
 
k21=0.04;
k22=0.08;
k23=0.4;
k24=0.08;
 
%% PARTA
 
%Mass Balance Eqns for Chemical Species A
 
%For reactor 1

%(Qin*Cain)-(Q12*Ca1)-(k11*Cain*V1)==0  %for first order reaction
%(Qin*Cain)-(Q12*Ca1)-(k21*(Cain)^2*V1)==0  %for second oreder reaction
 
%For reactor 2

%(Q12*Ca1)+(Q32*Ca3)-(Q23*Ca2)-(k12*Ca2*V2)==0 %for first order reaction
%(Q12*Ca1)+(Q32*Ca3)-(Q23*Ca2)-(k22*(Ca2)^2*(V2))==0 %for second oreder reaction
 
%For reactor 3

%(Q23*Ca2)+(Q43*Ca4)-(Q32*Ca3)-(Q34*Ca3)-(k13*Ca3*V3)==0  %for first order reaction
%(Q23*Ca2)+(Q43*Ca4)-(Q32*Ca3)-(Q34*Ca3)-(k23*(Ca3)^2*(V3))==0  %for second order reaction
 
%For reactor 4

%(Q34*Ca3)-(Q43*Ca4)-(Qout*Ca4)-(k14*Ca4*V4)==0  %for first order reaction
%(Q34*Ca,3)-(Q43*Ca,4)-(Qout*Ca,4)-(k24*(Ca4)^2*V4)==0  %for second order reaction
 
%Mass Balance Eqns for Chemical Species B
 
%For reactor 1
%(Qin*Cbin)-(Q12*Cb1)+(k11*Ca1*V1)==0  %for first order reaction
%(Qin*Cbin)-(Q12*Cb1)+(k21*(Ca1)^2*V1)==0  %for second oreder reaction
 
%For reactor 2
%(Q12*Cb1)+(Q32*Cb3)-(Q23*Cb2)+(k12*Ca2*V2)==0 %for first order reaction
%(Q12*Cb1)+(Q32*Cb3)-(Q23*Cb2)+(k22*(Ca2)^2*(V2))==0 %for second oreder reaction
 
%For reactor 3
%(Q23*Cb2)+(Q43*Cb4)-(Q32*Cb3)-(Q34*Cb3)+(k13*Ca3*V3)==0  %for first order reaction
%(Q23*Cb2)+(Q43*Cb4)-(Q32*Cb3)-(Q34*Cb3)+(k23*(Ca3)^2*(V3))==0  %for second order reaction
 
%For reactor 4
%(Q34*Cb3)-(Q43*Cb4)-(Qout*Cb4)+(k14*Ca4*V4)==0  %for first order reaction
%(Q34*Cb3)-(Q43*Cb4)-(Qout*Cb4)+(k24*(Ca4)^2*V4)==0  %for second order reaction
 
syms Ca1 Ca2 Ca3 Ca4 Cb1 Cb2 Cb3 Cb4
Eqns_1st_Order=[(Qin*Cain)-(Q12*Ca1)-(k11*Cain*V1)%=0















(Q12*Ca1)+(Q32*Ca3)-(Q23*Ca2)-(k12*Ca2*V2)%=0
(Q23*Ca2)+(Q43*Ca4)-(Q32*Ca3)-(Q34*Ca3)-(k13*Ca3*V3)%=0
(Q34*Ca3)-(Q43*Ca4)-(Qout*Ca4)-(k14*Ca4*V4)%=0
(Qin*Cbin)-(Q12*Cb1)+(k11*Cain*V1)%=0
(Q12*Cb1)+(Q32*Cb3)-(Q23*Cb2)+(k12*Ca2*V2)%=0
(Q23*Cb2)+(Q43*Cb4)-(Q32*Cb3)-(Q34*Cb3)+(k13*Ca3*V3)%=0
(Q34*Cb3)-(Q43*Cb4)-(Qout*Cb4)+(k14*Ca4*V4)]%=0
Eqns_1st_Order = 
 
Eqns_2nd_Order=[(Qin*Cain)-(Q12*Ca1)-(k21*(Cain)^2*V1)%=0
(Q12*Ca1)+(Q32*Ca3)-(Q23*Ca2)-(k22*(Ca2)^2*(V2))%=0
(Q23*Ca2)+(Q43*Ca4)-(Q32*Ca3)-(Q34*Ca3)-(k23*(Ca3)^2*(V3))%=0
(Q34*Ca3)-(Q43*Ca4)-(Qout*Ca4)-(k24*(Ca4)^2*V4)%=0
(Qin*Cbin)-(Q12*Cb1)+(k21*(Cain)^2*V1)%=0
(Q12*Cb1)+(Q32*Cb3)-(Q23*Cb2)+(k22*(Ca2)^2*(V2))%=0
(Q23*Cb2)+(Q43*Cb4)-(Q32*Cb3)-(Q34*Cb3)+(k23*(Ca3)^2*(V3))%=0
(Q34*Cb3)-(Q43*Cb4)-(Qout*Cb4)+(k24*(Ca4)^2*V4)]%=0
Eqns_2nd_Order = 
sol = solve(Eqns_2nd_Order, [Ca1 Ca2 Ca3 Ca4 Cb1 Cb2 Cb3 Cb4])
sol = struct with fields:
    Ca1: [8×1 sym]
    Ca2: [8×1 sym]
    Ca3: [8×1 sym]
    Ca4: [8×1 sym]
    Cb1: [8×1 sym]
    Cb2: [8×1 sym]
    Cb3: [8×1 sym]
    Cb4: [8×1 sym]
sol.Ca1
ans = 
sol.Ca2
ans = 
vpa(sol.Ca2, 3)
ans =

MATLAB: Output of previous command into input

If those variables are in the workspace, it should run without any problems.

Ca1 = ...;
Ca2 = ...;
Ca3 = ...;
Ca4 = ...;
Cb1 = ...;
Cb2 = ...;
Cb3 = ...;
Cb4 = ...;
x0 = [Ca1 Ca2 Ca3 Ca4 Cb1 Cb2 Cb3 Cb4];
x = fsolve(@functiondescription, x0)

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MATLAB: Can’t figure out how to finalize the code

MATLAB: Output of previous command into input

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