The MATLAB function ssest returns a state space model with disturbance model Ke(t). What is e(t)? is it a step, impulse, or random signal?

The MATLAB function ssest returns a state space model with disturbance model Ke(t). Since e(t) is another input to the system, I need to know what is e(t) in order to simulate the system,

˙x(t)=Ax(t)+Bu(t)+Ke(t)

y(t)=Cx(t)+Du(t)+e(t)

in simulink. So, I need to know what kind of signal e(t) is? is it a step, impulse, stochastic signal, etc...

Answer 1

[Vaibhav]

Hi Yousef,

I understand that you would like to know the type of signal "e(t)" is when using the "ssest" function.

"e(t)" represents the unmodeled dynamics or the difference between the measured output "y(t)" and the model-predicted output (Cx(t) + Du(t)).

The "ssest" function doesn't specify the type of signal for "e(t)." It can be any signal, like a step, impulse, stochastic, or others, depending on the system's characteristics and expected disturbances. For accurate modelling, choose a signal that reflects the likely disturbances. For sudden changes, a step signal works, and for random noise, a stochastic signal is suitable.

"ssest" doesn't explicitly define e(t), so assumptions or additional information is needed for proper modelling in Simulink.

You can refer to the following MathWorks documentation link to know more about "ssest" and "e(t)":

https://www.mathworks.com/help/ident/ref/ssest.html?searchHighlight=%20ssest%20function&s_tid=srchtitle_support_results_1_%20ssest%20function#mw_29865042-935e-48ba-9de6-43314dc020a5

Hope this helps!