lsim closed controlled loop confusion

Hey, I am a bit confused regarding lsim inputs. I wish to simulate a closed loop feedback full state controller

I am using 'space state' dynamic representation

and calculated K value to ensure Controllability

basically:

x'=Ax+Bu , y=Cx

u=-Kx

when defining the ss model:

 sys_cl = ss(A-B*K,B,C,0);

but for the lsim function I need to define an already known input vector u to satisfy:

 lsim(sys_cl,u,t,x0);

So on one hand I wish "u" to be defined as -Kx (adjust itself depending on the output).

on the other hand - I define a pre-known u value for the simulation

what am I missing...?

Answer 1

[Robert U]

Hi Daniel Grebler,

In order to simulate the time response of your controlled system you need to define the system ( sys_cl), a time grid ( t ), and a target value ( u ). You define an initial state of your system by supplying ( x0 ).

See first example in Matlab documentation:

https://de.mathworks.com/help/control/ref/lsim.html?s_tid=doc_ta

Kind regards,

Robert

[Daniel Grebler]

Thank you Robert I see in the documentation that (u) is defined as the input signal and not the target value- meaning the response of the system to input u.

and not as the desired value (x) will be controlled into

[Robert U]

Hi Daniel Grebler,

Documentation is stating that ( u ) is an input of function lsim() and input of your system. Depending on the system you simulate it might be an input of dimension n >= 1 . Depending on the system model it can be any sort of input of your system.

You wrote you would like to simulate the closed-loop system response of your control system. Without having any details of the scope of your simulation I assumed, that you would like to see how system response is estimated on certain target values. Thus, your system should be described in a way that target value becomes the input of your system.

For other scopes it might be the system response on noise in your sensor path.

Kind regards,

Robert