I am trying to discretize a continuous time state space model using the following code
s=tf('s');
G=1/(Iyy*(s^2))
Gs=ss(G)
Gd=c2d(Gs,0.01,'zoh');
Now, when i use this discretized model 'Discrete State-space Model' in simulink, my close loop system goes unstable. Same is happening with observer, like discretized observer is making close loop system unstable. Can someone help me here?
Hello Adeel Ahsan .
In order to help you, it would be convenient if you shared the transfer function of the continuous model. Because in your explanation you don't know what "lyy" is. Knowing the continuous model I think it is possible to help you.
Regards.
https://www.mathworks.com/matlabcentral/answers/246861-how-to-convert-model-from-continuous-state-space-with-disturbance-to-discrete
Make sure you set the sampling rate on simulink to match what you've used in the c2d function.
A reason might be the "warping" of the z-plane, that occurs when transforming a continuous tf into a discrete one. Depending on your values of lyy, your poles might end up in a region that is warped very strongly, so that small numerical errors might destabalize the system. You might want to try using the "LTI-System" block in simulink and see if that makes a difference. Brian Douglas has a great video series on the topic of discrete control:
https://www.youtube.com/watch?v=NRbGPgcLhU0&t=943s
Hello everyone!
Thanks for reaching me out. The value of Iyy=0.00842865. I have tried using the small value of sampling time, it is still unstable. Can anyone now check and help me out please?
Manuel Widdel
Henry Mariña
I suggest you to see these links and on topic.
https://math.stackexchange.com/questions/3281767/discrete-state-space-representation-of-a-second-order-system
https://www.springer.com/gp/book/9783319772189
https://folk.ntnu.no/skoge/prost/proceedings/ifac11-proceedings/data/html/papers/1346.pdf
Please see the book
Franklin, G.F., Powell, J. D., and Emami-Naeini, A., Feedback Control of Dynamic Systems, 6th ed., Prentice-Hall 2010
Your system is basicly a double integrator, so a borderline stable system. If you look at your phase value of the bode plot for the continious system (bode(G)), you will see that it has a phase of -180° over all frequencies. Since any kind of delay causes the phase of a system to drop, if you introduce an arbitrarily small amount of delay on your continious tf G, and use the command "margin(G)", you will find that your system will always have a negative phase margin. And since discretizing will always introduce delay into your system, closing the loop on it will automatically destabalize it. You can use 'tustin' as you discretizing method, which essentialy uses trapezoidal integration, a more stable integration algorithm, and simulink should probably get your discrete system stable this way.
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