how to discretize a nonlinear model using Matlab
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I have this continuous nonlinear system and I want to discretize it using Matlab
If anyone can help me? This is the differential equations of the system
This is the state space model according to the authors of the paper that I’m studying
I want to know how to insert it in m files and how to make it discrete .. any idea??
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Alan Stevens
2020-7-14
This is a simultaneous, linear system.
You could do something like the following (replacing my arbitrary data with your actual data):
% Initial conditions
Te0 = 300; Tr0 = 300;
y0 = [Te0, Tr0];
tspan = [0 10];
[t, y] = ode45(@rates, tspan, y0);
Te = y(:,1); Tr = y(:,2);
plot(t,Te,t,Tr)
function dydt = rates(~,y)
% Data (obviously replace with the true values)
Ce = 1; Cpc = 1; Cr = 1; Cpa = 1;
Qin = 2; Qo = 2;
mdotr = 3; mdotf = 3;
en = 1;
Tinf = 273;
% Components
Te = y(1); Tr = y(2);
% Equations
dTedt = Qin/Ce - Cpc*mdotr*(Te - Tr)/Ce;
dTrdt = -Qo/Cr + Cpc*mdotr*(Te - Tr)/Cr - en*Cpa*mdotf*(Te - Tinf);
% Return rates
dydt = [dTedt; dTrdt];
end
5 个评论
F.M
2020-7-15
Alan Stevens
2020-7-15
编辑：Alan Stevens
2020-7-15
It is discretised! The solution gives discrete values of Te and Tr at discrete times.
If you want to discretise it yourself, you can set dTe/dt = (Te(i+1) - Te(i))/deltat (and a similar representation of dTr/dt), where i refers to the i'th timestep. On the right hand side you could use Te(i) and Tr(i), which would give a simple, explicit, Euler representation, or Te(i+1) and Tr(i+1), which would lead to an implicit Euler solution. Alternatively, you could use a higher order discretisation, but then you might as well use Matlab's ode45, which does just that.
It's possible I haven't fully understood what it is you want to do!
F.M
2020-7-15
Alan Stevens
2020-7-16
You mean something like this:
% Time data
endtime = 10;
N = 1000; % number of timesteps
dt = endtime/N;
% Initial conditions
Te0 = 300; Tr0 = 300;
x(:,1) = [Te0; Tr0];
t = zeros(1,N);
% Loop through timesteps
for k = 1:N-1
x(:,k+1) = x(:,k) + xdot(x(:,k))*dt; % Simple Euler integration
t(k+1) = dt + t(k);
end
Te = x(1,:); Tr = x(2,:);
plot(t,Te,t,Tr)
function dxdt = xdot(x)
% Data
Ce = 1; Cpc = 1; Cr = 1; Cpa = 1;
Qin = 2; Qo = 2;
mdotr = 3; mdotf = 3;
en = 1;
Tinf = 273;
Te = x(1); Tr = x(2); % Extract temperatures
% Define f, g and u
f = [Qin/Ce; -Qo/Cr];
g = [-Cpc/Ce*(Te - Tr) 0; Cpc/Cr*(Te - Tr) -en*Cpa/Cr*(Te - Tinf)];
u = [mdotr; mdotf];
%Calculate rates of change wrt time
dxdt = f + g*u;
end
F.M
2020-7-19
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