Why Are Control Systems Low Pass Filters and Why Use Step Input for Testing?

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?

The characteristics of a control system depend on the transfer function. So you can have systems with low pass, high pass, band pass etc characteristics. A differential controller for example has high pass characteristics. So get a grip on the mathematical principles and you will understand. You manly use the step respons to analyze a system because it tells you how your controller reacts to sudden changes. There you see how fast you reach the desired value, how much overshooting will be there and if you have a persisting devitation. Impulse responses are also often taken for analysis. If you would feed your system with a random input there is not much to see so you take a well known signal to compare different topologies.

sire,actually transient response is depend on poles of the system not the input signal ,is it not?

But if you want to visualize the transient response you have to use a defined input like a step function. For example if you want to analyze a system with an unknown transfer function or your transfer function is too complex to determine all zeros and poles.

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

I would recommend reading some Literature about control systems. There seems to be a lack of basic understanding of control systems (no offence) or I misunderstand your question. If you have for example a radar tracking system wich, let's say, should turn in the direction of some moving object. It takes a measurement of the difference between the direction of the antenna and the object. Afterwards it applies an algorithm on these value (and former values) to determine what to do, which angle to turn. To fullfill this task you need to develope a mathematical model which can be rather complex. After this process an experienced engineer can determine the quality of the model by looking at - for example - the impulse response. The gained information would be much less if you fed a random input.