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?

 

Welcome to AAC.

Your questions are not clear since they are taken out of context.

You need to provide us with more information about your system. A block diagram or a circuit diagram, for example, may help to clarify your situation.

Control systems might contain a low pass filter but that is only one building block of the complete control system.

To characterize a system, one needs to know how it would respond to various types of inputs. The response to an impulse function gives us the transfer function.

 

Thanks
i started to steady time response analysis (control system)
For example,consider the radar tracking system here the input signal vary randomly.so it is not possible to construct all the signals mathematically.But most control system are tested under standard test signals(step,impulse,ramp).How testing system under standard signals works as same for all random signals. are you getting my point sire.

 

No. You have lost me.

 

see the first paragraph,you may understand me sire

 

It sounds a little like describing the action of a servo system where the rate of acceleration and deceleration has to be calculated while observing the motor to load inertia ratio?
The article quotes standard test signals, I assume these would be unique to a particular system.
OA a little vague?
Max.

 

In general, a step function is a worst-case test input to a closed-loop control system since a step includes many frequencies as shown by its Fourier expansion. The step will show the response time of the loop and how stable it is (whether it has overshoot or ringing in the output response).

 

The step will show the response time of the loop and how stable it is (whether it has overshoot or ringing in the output response).The step will show the response time of the loop and how stable it is (whether it has overshoot or ringing in the output response).

1)so you mean that step is ONLY good for finding response and stability of system and not for any other.is it right ?

2)consider a RADAR tracking system ,the position and speed of target to be tracked may vary in random fashion so it is no possible to develope mathematical equation for all that random signals.so we are testing the system characteristics and performance with easily generatable standard signals(step.ramp,impulse )

My question is how we are sure that performance and characteristics of system evaluated by test signals would be same for the all random signals?

THank you in advance

 

Hello there,

The more general form of a common test input is t^n. The step input is the easiest to generate, and also allows us to compare systems for various performance goals like percent overshoot and steady state error.

The response to a step input shows the time response which correlates to the frequency response in the 's' plane, so it tells us a lot about the response of the system. It's also good when the system is somewhat non linear as the frequency response may be hard to develop.
But as i am sure you know, that's not the only test signal. It can depend on what the application is or what task the designer has been assigned. For example, the designer may have to be able to design the system so that the steady state error with a RAMP input is below a certain value. They are handed a specification and the circuit they design will have to be able to perform as those specifications require with the given test input specifications.

The test signals often show what happens in the real world setting where we can not always know exactly what the signals will be. For short time periods, the test signals mimic the real life signals anyway...an aircraft can not change direction in zero time for example.

The most common test signals are the step, ramp, and acceleration input types. Sine waves may also be used to test for frequency responses.

 

okay thanks ,and i have few more question regarding this topic

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

(content in my book)

1)how is this possible?

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

 

1) Any signal can be composed from a sequence of impulses.

2) For linear systems - yes. For non- linear systems - no.

 

In general, a step function is a worst-case test input to a closed-loop control system since a step includes many frequencies as shown by its Fourier expansion

so what ,if it contain many frequencies ?

 

so what ,if it contain many frequencies ?

Hi,

Well one view of this is that since it contains a lot of frequencies we can run a test with several frequencies by just applying a square wave input. Instead of seeing the effect of just one sine wave frequency input, we then see the result of lots of frequencies at the same time.

An example of this is when testing an amplifier, using a square wave input. Since the square wave itself requires many harmonics to be present, if we reduce the amplitude or even increase the amplitude of any of those harmonics we will see the square wave distort.
What this means is when we put the square wave on the input the output will look like a distorted square wave, and depending on the shape itself we can tell if the amplifier has good or bad high frequency response, or good or bad low frequency response, or even good or bad midrange. The way the square wave changes tells us right away. It's more qualitative than quantitative but still gives us some idea what the amplifier is doing, without having to sweep many frequencies (although that's a common technique too anyway).

The step input isnt exactly the same as the square wave though. It is used to show certain things about the response of the system without having to probe with a sine wave, and also tells us a lot about the time response where we usually must know the overshoot for example. If you want to see the overshoot, you have to use a step input. Even more to the point, if you want to see the overshoot with a step input then you must use a step input (almost goes without saying but that could be a requirement where the step input response is part of the specification).

And again the step input is like a 'probe' to find out where the dominate poles are located, and how bad the response is. It's a quick test that would take much longer if we had to sweep with a sine wave, and that may not even be possible with some systems so we use the step input.

An impulse on the input tells us a lot too, but that's harder to generate and perform in real life than a step input. For one thing, components are usually rated less than 100 or 200 volts so we probably cant take the chance of applying a 1000v pulse on the input.