# Negative Feedback

## An Analogy

I have an obsession with throwing the ball of paper into the trash can from my working table. At my first attempt, I cannot score the ball into that trash can. After that, I can score the ball by decreasing or increasing the initial velocity if the ball lands behind or in front of the trash can.

Let me make the analogy complex. Instead of controlling only initial velocity let me add another variable, the direction at which I throw the ball. In the language of control theory, variables that we need to control are called control variables. Observing where the ball lands and improving in the next attempt, I can score. Though it sounds easy, this requires great determination and practice to master. Here I see the result of my initial attempt and improve the control variable in the next attempt. This type of control is called negative feedback control.

The control system has different types of sensors that convert physical entity into equivalent voltage and current rather than the biological sensors like eyes. We get the desired output by manipulating the output of such sensors.

## Negative Feedback Control System

Now I am going to apply negative feedback to the op-amp. That is we connect the output of op-amp back to negative input. If you want to understand the negative feedback control system, please read the Operational Amplifier (op-Amp) first.

Let us apply $1$ to the positive input and assume negative input is 0 in the beginning. Since the error is $1$, the input at the gain block $G$ is $1$, and the output becomes as positive as possible. But what happens after output tends to $1$? The negative input tends to $1$, and the output of the summing block tends to $0$.

Now consider a case in which negative input is higher than $1$. In this case, the input to the gain block goes negative. This means the output will be negatively railed, In this case, $0$ (Remember Operational Amplifier (op-Amp) ), and the aforementioned process repeats. The entire process continues until negative and positive input becomes equal. You see whatever you do initially, by improving the output, you get the desired output.
Writing the transfer function of this circuit is left for the reader. You can see interesting things by changing the values of $G$ and $H$ in the transfer function.

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