simulating state space model with disturbance

just a supposedly simple question:

how can one simulate a state space model with external disturbance in simulink / with the lsim-command in matlab, that is given a system

with v being a disturbance wich I would like to simulate...

In order to be able to use lsim or the state space simulink block, repectively, how about modelling the disturbance as

but that would lead to a B of a different dimension. As a consequence, a simple state feedback controller wouldn't fit dimensionwise...

How could I in a simple way simulate a system with disturbance? Using a block-model in Simulink with a dedicated disturbance is not an option, as systems of different designs shall be simulated, i.e. the "model structure" changes (e.g. sensor placement, etc).

[David Wilson]

You seem to have the right idea. To include the disturbance, just pretend it is another input, so the augmented B matrix now has an extra column at the right hand side. You now stack the disturbance input on the bottom of the origial u vector.

A statefeedback controller u = -K*x can be designed in the same way, just use the original (un-augmented) B matrix.

In summary, you need to be careful about:

1. The original system, G = ss(A,B,C,D)
2. The augmented system: Ga = ss(A, [B, B2], C, Da) with ua = [u; v].

[Daniel]

Hi David,

thanks for your reply - that seems logical, don't know why I didn't think of that myself :-) I'll try and get back to you in case it doesn't work as intended.

[Raghav Gopal Rao Netrakanti]

Hi Daniel,

I'd appreciate it if you could tell me if this approach has worked for you.

Thanks,

Gopal