Solving Block diagram in Different way.

Basic concepts :

Let us start with control system .

The first question that we should ask ourself , why we are studying this subject . The answer is very simple everything in this world will be like where we have a input and system and based on that there is output.







you can understand this with any basic thing , like simple FAN , which takes the electrical input  and then system will process that i,e nothing but the coil and result is nothing but the rotation of the fan.

Let go further and understand what is feedback in control system.

We can understand this feedback with a example. Suppose you have pick up a object that is lying somewhere on floor provided your eyes are closed. This task would be very diffcult to do it .
if the same exercise you have to do while keeping your eyes open , that would be pretty easy.

Now what we can understand here , in first scenrio as eyes are closed you don,t know how close you are with the objects . here your eyes work as the feedback , so as you can see that in second situation as your eyes are open u can do it pretty easy.  so the feedback helps in reducing the difference between the hand and the objects.

Feedback is not helping in reducing the error , but it also help in stability, noise reduction , sensitivity etc.

There are 2 type of feedback .

1. Positive feedback
This is kind of feedback which is used when you need the saturation. For eg remember OSCILLATOR which will be used in positve to ocsillate in +ive and -ive real axxis ( like sine wave).

2. Negative Feedback
It is used when you want to stabilize the output. For eg OP_AMP in inverting mode , as you would be knowing that as temperature increases , the open loop gain will increase in a faster rate.( from 10pow(3) to 10pow(6)  ). And output will try to go towards the positive or the negative saturation.

But because of the feedback , that will not happen.

 BLOCK DIAGRAM REDUCTION :

The technique that i am going to tell that will not require any remembering

So in order to solve this you should know that gain of two blocks in cascasde will be get multiplied.

Lets analyise the above one. We can see that postion 1 , we don,t know the what is coming so i will take it as K1 , now K1 and G2 are in cascade so the C will be K1G2, which is my first equation.

Similarly in order know what is coming at postion 2 so i will take as K2 so i will get the first equation.

And we  will solve further to get the transfer function.