-
1
- #1
PNachtwey
Electrical
- Oct 9, 2004
- 779
I saw a video on YouTube where the instructor said, "I can measure y so how do I get x?"
This assumed x'=A*x+B*u and y=C*x. In real life y is quantized and there may be sample jitter so estimating if x[0] is the position and velocity is x[1] and acceleration is x[2] then estimating velocity and acceleration accurately is difficult just using difference methods.
For serious control I do not like to use difference equation, I prefer state space because the position, velocity and acceleration are not quantized or suffer from sample jitter. If done properly one can estimate the state more accurately than what can be directly determined by measuring.
I have an example of control using a Luenberger Observer but unlike text books ( boo ), I try to simulate some nastiness due to modeling errors, measurement errors an noise. You can see the results are still pretty good.
Another thing I wanted to show is how simple the math is. Text books ( boo ) tend to use matrices. I think matrix math hides what is actually happening. You can see in my example finding the Luenberger gains is actually simple and does NOT require matrix math. Again, you will notice I prefer symbolic math and using differential equations. Why? Because my models don't need to be linear and my observer will still work.
If you notice, NO ROOT LOCUS REQUIRED!!!!!!!!
Difference equations, yuk.
Peter Nachtwey
Delta Computer Systems
This assumed x'=A*x+B*u and y=C*x. In real life y is quantized and there may be sample jitter so estimating if x[0] is the position and velocity is x[1] and acceleration is x[2] then estimating velocity and acceleration accurately is difficult just using difference methods.
For serious control I do not like to use difference equation, I prefer state space because the position, velocity and acceleration are not quantized or suffer from sample jitter. If done properly one can estimate the state more accurately than what can be directly determined by measuring.
I have an example of control using a Luenberger Observer but unlike text books ( boo ), I try to simulate some nastiness due to modeling errors, measurement errors an noise. You can see the results are still pretty good.
Another thing I wanted to show is how simple the math is. Text books ( boo ) tend to use matrices. I think matrix math hides what is actually happening. You can see in my example finding the Luenberger gains is actually simple and does NOT require matrix math. Again, you will notice I prefer symbolic math and using differential equations. Why? Because my models don't need to be linear and my observer will still work.
If you notice, NO ROOT LOCUS REQUIRED!!!!!!!!
Difference equations, yuk.
Peter Nachtwey
Delta Computer Systems
