For example, I have state-space of 4th order with one control input (see the attached picture).
This system describes lateral dynamics of the vehicle and there is no transfer fuction for steering. I know every state and so I can easly create LQR feedback controller.
But what to do in case when there is some transfer function for steering? For example, let it be the first-order TF. So, when I convert this system to SS representation, I will have 5th order system, where 5th state is actual steering.
I once again want create LQR controller for such system, and I have desired and actual values for all first 4 states, but I don't have one for 5th state.
How to handle it?
Michael Short Hi Michael, thank you for your answer.
Yes, you are right, steering lag in not directly measurable and more than that - I don't have a desired value for it and this seems the main problem.
For example, let's assume we observe steering lag (denote it as x5). So for LQR we will have
X = (x1,x2,x3,x4,x5) as current states values
and from my command signal I know
Xdes = (x1des,x2des,x3des,x4des) as desired state values
So for feedback LQR controller I will have residual only for 4th first states, but LQR requires all 5 to work correctly.
Thanks, Alexey
What I understand from your model is that your controller compute steering angle for given initial states.
From your state-space model dot x=Ax+Bu,
u=delta
when you compute K using K=lqr(A,B,Q,R)
u=-Kx
actually the u compute delta depending on x using control gain K.
LQR control design is a regulator type control. You can not insert a reference signal in original form. You have to modify the LQR structure to insert a reference input.
Michael Short
Well, I have something like trajectory planner component, that sends me desired values of all 4 states based on my current position. Than I make a substraction (desired - current_states) and this residuals are assumed to be zeros and goes throught LQR gains as u = -K*x.
Said another way, the part that creates desired values doesn't relate to LQR itself.
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