If positive feedback makes output exponentially increase and cause instability in an opamp then why doesn't negative feedback make output extremely small and cause the system to collapse?
Negative feedback does make the overall output less.
Consider a voltage follower. Typical open-loop opamp gains are over 100,000. But, you are putting multiple volts in and getting the same out. That is "extremely small".
For more on negative feedback, see https://electronics.stackexchange.com/a/50472/4512.
Consider the following control system: -
- You set a "position" demand
- The error amplifier measures the difference between demand and actual
- The amplified output of the error amplifier drives the motor
- The error gets smaller
- And smaller
- And smaller
- Until the amplified difference between demand and actual is too small to turn the motor any more.
If you had infinite gain in your error amplifier then the motor would setle at a position where demand = actual. The perfect controller!
This is negative feedback but, in a real system, the error amplifier has non-infinite gain and so there will be a litle error.
Now imagine that instead of a motor and potentiomenter you directly connected the error-amp output back to -Vin. If you analyse things correctly then you'll see that you have a unity gain amplifier. In other words, the error-amp (aka op-amp) drives its output to virtually match the demand set at the +Vin input. The slight error you will see will be due to the non-infinite gain of the op-amp.
Most op-amps have open-loop gains exceeding 100,000 so this is trivial.
See also this answer.