basic of control system

i have two basic questions

1) why control systems are low pass filter?

2) input of control system is random in nature .But why we are testing the system mostly with step signals.How does the step signal alone completely tell about the system?

1. Control system is a generalized theory and low pass filter is an application. That's the only relation between them.
2. Every random signal is composed of basic types of signal. Just like when u do Fourier transform of a signal, u fins out all the frequencies within the signal. And every signal is a sine wave, a basic building block of any type of deterministic or non-deterministic signal. Step input is a sudden discontinuous signal applied to input of system which if analysed contains array of frequencies if Fourier transformed. So, the step input response of system gives information about its rise time, fall time, settling time, overshoot, undershoot, damping factor. These time dependent factors can be easily found out just using a step input. Using impulse signal, u can find complete frequency response of system. So, u r characterizing ur system in terms of time domain response and frequency response. This is how systems are modeled in control theory. Another way to model a system is with state space representation, where u use I, O and state variables to model it using differential equations.

Hope that helps.

For the first one I think that is the general case but not including all the cases. For example if you need a closed loop control system that is because you have distrubance. Distrubances generally have high frequencies. If you have a system, you want it to be stable and not changing suddenly, therefore you eliminate the high frequency noises and make your system stable. This can be reason they are generally called as low pass filters.

Second one is another general case. For example, you have a car and you want to drive it at 80 kmph, here you were giving nothing to the system and suddenly gave a reference input like "80". It is like a 80u(t) step and your system should be stabe when you give step signal otherwise you cannot give this signal. In general you have a referance input to follow. Of course step input includes many frequencies in it.

Previous answer was very clear, I hope I didn't make your understanding worse.

Using impulse signal, u can find complete frequency response of system

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yes with step input we can analyse all the time response .But how do you say that with impulse input we can analyse all the frequency responses.please explain that

Distrubances generally have high frequencies

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i never heard it before how do u say that disturbance(noise ) are high frequency

your system should be stabe when you give step signal otherwise you cannot give this signal

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stability is depend on poles of system and not on input ,am i right

Of course step input includes many frequencies in it.

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course unit step signal have many frequencies i agree,but why do you saying this for the car example?

Thank you both and waiting for you useful reply

An impulse or simply a pulse of short duration contains two discontinuous changes. The Fourier analysis of impulse shows that it has widest spectrum of frequency contents i.e. the an impulse usually spans 0Hz to some higher MHz in all harmonics. So, the response of system to this basic signal defines its frequency response. All kinds of stimuli-response kind of modeling of system can be simply defined as
system=output/input, so if u have input of wide freq range, u can find frequency response.

@ElektrikAkar is saying, usually there are two noises that we face (not talking about additive or anything), in-band and out-band noise. The in-band noise is difficult to filter out compared to out band noise. When looking at signal on CRO, the out band noise can be seen riding on in-band as high frequency disturbances. And as a thumb rule, any compensation done to remove this noise is low pass filter. The other reason is when system is operating, any input change reflects on output and the system takes some time to produce output. This time is response time or time constant. So, if input changes at the rate faster than time constant of a system, the system will not response to change until it has finished working on previous input. So, in a way the system is filtering out any sudden or spurious changes and so low pass filter. The analogy can be a key debouncing. So, by disturbance he means, sudden changes that i explained.

Yes, stability of system is determined by poles and zeroes. So to compensate system, u may add zeroes near a dominant pole and bring it to stability as a thumb rule. So, he means for an unstable system giving input to system will not make it stable and is meaning less without any compensation. Yes u can give input, but u will only see saturated output. Just like a comparator system.

Im not sure, what question means? plz elaborate.

Hope that helps and explained what @ElektrikAkar mean.