How to predict using state space model identified using system identification? (to be used in excel)
6 views (last 30 days)
Show older comments
Hello All, I am a beginner and I have used experimental data (4 inputs and 1 output) from an exothermic reactor to identify the model of the system. I used system identification tool and obtained the following state space model. However I am unable to use it effectively in excel. How do I do the step wise calculations in excel? I tried simplt substituting the values in an excel table, but I get no fit with actual values and the error keeps increasing exponentially!
x(t+Ts) = A x(t) + B u(t) + K e(t)
y(t) = C x(t) + D u(t) + e(t)
where,
A is
x1 x2 x3 x4
x1 0.99912 -0.0070421 -0.00031249 7.7892e-005
x2 -0.063971 0.83586 0.32571 -0.29828
x3 -0.021337 -0.074777 0.87549 0.53156
x4 -0.0010908 0.1197 0.061085 0.60444
B is
u1 u2 u3 u4
x1 1.7668e-007 -8.4364e-008 1.3983e-006 9.3092e-006
x2 -1.22e-005 6.8841e-005 0.0036294 0.0055134
x3 4.7894e-005 1.6459e-005 0.0055848 0.012066
x4 -3.8301e-005 8.3878e-005 -0.0018173 -0.0067679
C is
x1 x2 x3 x4
temp 866.56 -2.8526 -0.48543 0.3932
D is
u1 u2 u3 u4
temp 0 0 0 0
K is
temp
x1 0.0016648
x2 -0.2073
x3 -0.087051
x4 0.025893
and x(0) is
x1 0.088771
x2 0.27148
x3 -0.62389
x4 -1.4389
Estimated using N4SID from data set of 8 merged experiments
Loss function 0.00272453 and FPE 0.00279113
Sampling interval: 1
In Matlab the model shows a good fit of close to 92% for 1 step prediction. However when I try to manually check the same in excel I am getting no fit. The first 5 predictions are close to actual values, but the error keeps increasing exponentially.
Where am I going wrong? Please help!
0 Comments
Answers (0)
See Also
Categories
Find more on Simulation and Prediction in Help Center and File Exchange
Products
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!