Why is Gain = 1 at phase shift of 180deg drive a system to unstable state?

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I know the transfer function of feedback system, when loop gain become negative 1, denominator becomes zero, and the gain shoots up to infinity. All nice and simple on paper but I need a intuitive explanation for this thing (i.e., Barkhausen criterion ).
If any control, electronics engineers or hobbyist help to grasp the concept.
Thanks in advance 🙂

In: Engineering

3 Answers

Anonymous 0 Comments

Consider (10-s)/s(s+2) vs 0.1/(s-0.01)^2 +0.09. Both are second order gain functions one has infinite gain and unbound step response, the other has non-infinite gain and unstable step response.

Anonymous 0 Comments

Because you turn negative feedback into positive feedback. If the gain is *precisely* 1, then the feedback system will be in a metastable state.

OK, the wasn’t ELI5.

If you’re riding your bike and a cat jumps in front of you, you jam the handlebars to one side. Since the bike doesn’t move immediately, you jam it too far and you fall over.

Anonymous 0 Comments

A gain of 1 at a phase shift of 180 degrees causes the output to be equal in magnitude but opposite of the direction of the input. It’s similar to driving a car, but every time you turn the steering wheel to the right, the car goes an equal amount to the left instead.

Imagine driving a car like that and coming across an obstacle that requires you to go right slightly. You tilt the steering wheel to the right slightly, but the car goes left instead. Now you need to go right even more to correct it so you tilt the wheel more to the right and the car in turn goes more to the left. Any attempt to fix the direction you’re going only makes the problem worse. That is why the system goes into an unstable state.