Capturing of System Dynamics

The output response.

ya thats obvious. But will i be able to find offset from impulse response?

In these type of cases i use a dual channel recording O scope. I measure the input and the output and record the time diff and response.

I don't think you need any kind of input to find the offset... just measure it.

OK.Will the impulse response of the system displays offset ?? I can measure the bias, but wanted to know will impulse response able to capture offset of the system?

The Fourier Transform of the impulse response gives you the frequency response of the system. The step response is the integral of the impulse response.

http://www.mathworks.com/help/control/ref/step.html

If I am understanding your question correctly:

Yes the impulse response is calculated and implemented by the circuitry to correct offset so it will include the correction value(s) required to maintain process Set Point (SP).

If the offset is negative the impulse will inject whatever positive value(s) are required to correct the output to match SP.

If the offset is positive the impulse will inject whatever negative value(s) are required to correct the output to match SP.

If the control is properly tuned the system will stabilize within three (3) cycles.

To determine offset value in the impulse response you measure the output and subtract that value from the impulse response value. The result will be negative or positive depending on the ratio of SP to PV.

It will also depend on how closely your stimulus resembles a true impulse signal. Remember an impulse signal is a theoretical waveform that cannot be realized. An infinite amplitude with no pulse width making an area of 1 is not really available from any function generator.

I always use a fast step function for the stimulus to a "plant" (any two port system). That is because it is much easier to find a very fast leading edge on many function generators. Next I differentiate the step input to get the impulse stimulus. I then compute the frequency response of the dirivative to see how flat the input is over the F range of interest. Sometimes I save that F response to use to normalize the input to a flat response.

Then I capture the I and O simultaneously, differentiate, and compute the FRF, which shows all of the resonances.

In the time domain, the step function output will show the overshoot, offset, and gain.

Exactly my point but explained a little clearer.

One can much more easily approximate a step function in real life than an impulse function to perform a empirical analysis of a system. The mathematics will (usually) be easier to apply an impulse signal to a known system transfer function to see how the output of the system should perform.

Very true. However, the differential is easy to compute with nearly any of today's scopes. This makes it easy to use a fast step to get the impulse response.

I always used a square wave with a slow rep rate (period must be long enough for the step response to damp out completely).