Control Theory -- Systems where the controller also changes with time

AI Thread Summary
The discussion centers on exploring control systems where the controller's input changes over time, specifically incorporating the derivative of the control input, ##\dot{u}##. Participants note that traditional control theory often overlooks this aspect, particularly in linear time-invariant (LTI) systems. The conversation highlights the potential for creating state variables that account for the effects of ##\dot{u}## on the output, ##y##. An example involving the "D" component of a PID controller is suggested to illustrate the concept. Overall, the discussion emphasizes the need for further exploration of time-varying control inputs in control theory.
mad mathematician
Messages
112
Reaction score
18
Usually we look at a system of ODEs of the form:
$$\dot{x}=f(x,u,t)$$
$$y=g(x,u,t)$$

Why not look at systems where the controller also changes with time, i,e functions of terms ##\dot{u}##?

I took quite a handful of Control Theory courses and yet as of yet never seen one incorporating this derivative.

Perhaps it's impractical, my pure side of me doesn't really care though... :oldbiggrin:
 
Engineering news on Phys.org
I assume you are referring to LTI systems? Because you can construct all kinds of weird #$@! otherwise.

In the very sloppiest, hand wavy way (because it's late here and it's been a long time since I did this stuff for real), you will end up with a state variable that represents the effect of ##\dot u##, if it matters to the output ##y##.

Consider the "D" part of a PID controller:
https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=9933758

Maybe try a simple example, like an RC HPF (in the EE context)? This stuff is often clearer when you work through a simple case.
 
Last edited:
  • Like
Likes mad mathematician
Hey guys. I have a question related to electricity and alternating current. Say an alien fictional society developed electricity, and settled on a standard like 73V AC current at 46 Hz. How would appliances be designed, and what impact would the lower frequency and voltage have on transformers, wiring, TVs, computers, LEDs, motors, and heating, assuming the laws of physics and technology are the same as on Earth?
I used to be an HVAC technician. One time I had a service call in which there was no power to the thermostat. The thermostat did not have power because the fuse in the air handler was blown. The fuse in the air handler was blown because there was a low voltage short. The rubber coating on one of the thermostat wires was chewed off by a rodent. The exposed metal in the thermostat wire was touching the metal cabinet of the air handler. This was a low voltage short. This low voltage...
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...
Back
Top