# Control systems

1. Mar 25, 2013

### Daifa

Why should the input follow the exact output in control systems (Transfer function). What if my system is an amplifier ? shouldn't that means that the output is the input * gain ?
I cant understand the differences between dealing with a real system ( such as an amplifier) of dealing with a transfer function ( transient response)....

2. Mar 25, 2013

### milesyoung

It's often desirable to have unity gain in closed loop but you're certainly not restricted to it. Consider the closed-loop transfer function T(s):
$$T(s) = \frac{G(s)}{1 + H(s) G(s)}$$
where G(s) is the open-loop transfer function of your system and H(s) is the transfer function of whatever dynamics you have in your feedback path.

For a unity feedback system with high open-loop gain, G(s) >> 1, H(s) = 1, you'll have unity gain in closed-loop, but notice how you're able to control the closed-loop gain by adjusting H(s). For H(s) = 0.5, you'd have a closed loop gain of approximately 2 (if you have high open-loop gain).

Adjusting H(s) is exactly what you're doing when you select resistor values etc. for the feedback path of your opamp amplifier.

A transfer function is just a mathematical model that hopefully approximates the behavior you're interested in of your actual system. It might not encapsulate every minor detail of how your amplifier works, but then again, you might not be interested in every aspect of its functionality.

3. Mar 26, 2013

### Daifa

So you mean that : R(s) is a command signal which is responsible to start the amplification process for example ?
So what we measure on the output is how fast the system start the amplification when the command ask it to do ? And thats why Y(s) should follow R(s) ????
Because my question was kinda why Y(s) should follow the input R(s) !

4. Mar 26, 2013

### milesyoung

It doesn't have to, that was the point I was trying to make.

As I wrote in my previous post, a transfer function is a mathematical model that can, to some extent, describe the behavior of an actual physical system, be it an amplifier, a control system or some other device. Your posts read a bit like you see transfer functions as something unique to control systems.

A controller could make some system respond with a high gain, like an amplifier, or it could try to make it track some reference command, it's up to you really.

Last edited: Mar 26, 2013
5. Mar 30, 2013

### engineeringtub

control System

hey buddy, you seem to be quite confused with exact output in respect to input as in control system we generally want system to be stable, linear, distortion less, etc. that is why we generally say we want exact output in terms of input i.e. for system to be linear we should have following equation Ax1+Bx2=Cy1+Dy2.
here in comparsion with linearity there should be also negative feedback in system in order to have less distortion. That's why we need exact output in comparsion to input.

Last edited by a moderator: May 6, 2017
6. Mar 30, 2013

### milesyoung

I can't make sense of any of this. What is your definiton of 'exact output' and 'distortion'?

Last edited by a moderator: May 6, 2017
7. Mar 30, 2013

### jim hardy

Hey, buddy there's no need for condescension in these parts..

I don't think you know a lot about control systems.

Original question was not clearly worded.
I guess OP was referring to feedback in audio amplifiers?

Audio amp wants output to be a larger version of input, right?
That transfer function would be just K or A+B, the gain, with no frequency dependent terms.
Well maybe, unless the tone controls are not set "flat" in which case A and B sprout frequency dependent terms.
The transfer function becomes some complex function of frequency.
Control systems generally have frequency terms in them so as to shape frequency response of a system.
That's exactly what a tone control does as well.

Control systems we test with step and ramp signals.
Audio gets tested with sine waves.

Try it - feed an audio amp with a square or triangle wave then tweak the tone controls and you'll see a non-square or non-triangle wave at output. It's no longer a replica of the input.
But it's experienced a quite linear multiplication by some function of frequency.

Sinewave is a mathematical oddity - its derivative and its integral have exactly same shape.
So when it goes through a transfer function with frequency terms it just moves ahead or behind by a little bit. It keeps its shape so it is not apparent that it has been multiplied by anything other than simple "gain".
So you tend to not notice that an audio amp with tone controls indeed changes the frequency content of its input .
If that's not "distortion", what is?

I think that's OP's confusuion.

Last edited: Mar 30, 2013