TwoRoomHouse.m

% This m-file generates the state space model for the 2-Room house heating
% system model in Chapter 6 of NCS.

%  The Thermal Cpacitance Data:

CR1     = 62.67;
CR2     = 83.03;
CHE1    = 62.5;
CHE2    = 62.5;

% The Thermal Resistance Data:

RHE1    = 0.01*3600;
RHE2    = 0.01*3600;
RHE3    = 0.01*3600;
Rwall1  = 0.0264*3600;
Rflceil1= 0.1*3600;
Rwind1  = 0.0417*3600;
Rwall2  = 0.0242*3600;
Rflceil2= 0.075*3600;
Rwind2  = 0.0167*3600;
RL1     = 0.1*3600;
RL2     = 0.5*3600;
RL3     = 0.5*3600;

% The Values in the Model:

Req2    = 1/(1/Rwall1+1/Rflceil1+1/Rwind1);
Req1    = 1/(1/Req2+1/RHE1);
Req4    = 1/(1/Rwall2+1/Rflceil2+1/Rwind2);
Req3    = 1/(1/Req4+1/RHE2);
Req5    = 1/(1/RL1+1/RL2+1/RL3);
alpha1  = 1-Req5/RL2;
alpha2  = 1-Req5/RL3;

% The C Matrix:
C   = diag([CR1 CR2 CHE1 CHE2]);
G   = [-1/Req1    0             1/RHE1               0
          0    -1/Req3            0                1/RHE2
        1/RHE1    0     -(1/RHE1+alpha1/RL2)         0
          0     1/RHE2            0         -(1/RHE2+alpha2/RL3)];
A   = C\G;

%  Heat Lost to the Outside Ambient Temperature:
B1  = C\[1/Req2 1/Req4       0         0   ]';
%  Heat Flow into Zone for Room 1:
B2  = C\[  0      0     Req5/RL2       0   ]';
%  Heat Flow into Zone for Room 2:
B3  = C\[  0      0          0    Req5/RL3 ]';

%  Sources in the model:

Eff     = 0.8;              % Boiler Efficiency
HperGal = 100000;           % BTU per gallon for Oil 
FlowRate= 1/3600;           % Combustion Nozzle flow rate (Gal/Sec.) 
Qf = Eff*HperGal*FlowRate;  % Maximum Heat flow from the furnace
Ta = 10;                    % Outside Temperature oF

% Linear Control System with Integral Gain:

delt         = 5;
Control_Gain = 1;
Ki           = 1/(2*Qf*3600);
Kd           = 1000;

% Simulation Data

Tend = 3;                  % Simulationn stop time in Hours
Tend = 3600*Tend;          %  --- Converted to Seconds.