Hilbert Transform, Causality, PI Controller

AI Thread Summary
The discussion centers on the causality of the PI controller, which is defined as a causal filter with a frequency response of H(w) = Ki/(iw) + Kp. It is noted that a causal filter must satisfy the relationship H(w) = G(w) - i G_hat(w), where G_hat(w) is the Hilbert transform of G(w). Participants clarify that the gain terms Ki and Kp can be chosen freely without violating causality. Additionally, the distinction between a PID controller and its potential non-causal characteristics is mentioned, emphasizing that a standard PI controller remains causal. Ultimately, the consensus is that the selection of gain terms does not impact the causality of the filter.
angryturtle
Messages
1
Reaction score
0
TL;DR Summary
Help understanding why PI controller is causal.
I was told that PI controller is a causal filter, and has frequency response represented by H(w) = Ki/(iw)+ Kp.

I was also told that causal filter should satisfy this relationship H(w) = G(w) -i G_hat(w) where G_hat(w) is the Hilbert transform of G(w).

Does this mean that we cannot freely select gain Ki and Ki/w must be the Hilbert transform of Kp?
 
Engineering news on Phys.org
Good afternoon. I learned the theory of automatic control. But It's hard for me to understand your question. Maybe you'll give more information? Example, for which object of control you'll plan to use PI-controller?
 
angryturtle said:
Summary: Help understanding why PI controller is causal.

I was told that PI controller is a causal filter, and has frequency response represented by H(w) = Ki/(iw)+ Kp.

I was also told that causal filter should satisfy this relationship H(w) = G(w) -i G_hat(w) where G_hat(w) is the Hilbert transform of G(w).

Does this mean that we cannot freely select gain Ki and Ki/w must be the Hilbert transform of Kp?

If you mean a PID controller, it would seem to satisfy the criteria of being LTI and dependent only on current and past inputs, no? So how could it be non-causal? If the PID characteristics could be altered real-time by itself (like in Machine Learning), then it would no longer be time-invariant, but I think that is a different situation...

https://en.wikipedia.org/wiki/Causal_filter

https://en.wikipedia.org/wiki/PID_controller
 
angryturtle said:
Summary: Help understanding why PI controller is causal.

Does this mean that we cannot freely select gain Ki and Ki/w must be the Hilbert transform of Kp?
No. You can choose any gain terms and this filter will remain causal.
 
I have recently moved into a new (rather ancient) house and had a few trips of my Residual Current breaker. I dug out my old Socket tester which tell me the three pins are correct. But then the Red warning light tells me my socket(s) fail the loop test. I never had this before but my last house had an overhead supply with no Earth from the company. The tester said "get this checked" and the man said the (high but not ridiculous) earth resistance was acceptable. I stuck a new copper earth...
Thread 'Electromagnet magnetic field issue'
Hi Guys We are a bunch a mechanical engineers trying to build a simple electromagnet. Our design is based on a very similar magnet. However, our version is about 10 times less magnetic and we are wondering why. Our coil has exactly same length, same number of layers and turns. What is possibly wrong? PIN and bracket are made of iron and are in electrical contact, exactly like the reference design. Any help will be appreciated. Thanks. edit: even same wire diameter and coil was wounded by a...
Thread 'Beauty of old electrical and measuring things, etc.'
Even as a kid, I saw beauty in old devices. That made me want to understand how they worked. I had lots of old things that I keep and now reviving. Old things need to work to see the beauty. Here's what I've done so far. Two views of the gadgets shelves and my small work space: Here's a close up look at the meters, gauges and other measuring things: This is what I think of as surface-mount electrical components and wiring. The components are very old and shows how...
Back
Top