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# Step Response & Impulse Response

05/20/2016 5:44 AM

I want to know the significance of both impulse & step response. I know that both the responses are just a different representations of the process; I wanted to know which response is better for studying the process at different conditions. Essentially I have two kinds of systems that I am working with 1. loops with set point changes (I have used ARX structure to find out the model of the closed system) 2. Loops without set point changes (I have used AR noise model to find out the closed loop system model). We are using step response to find the process characteristics for loops having set point changes & impulse response for loops without set point changes; I wanted to know the theory behind this (why impulse response cannot be used for loops having set point changes & step response cannot be used for loops without set point changes) Experts please help.

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#1

### Re: Step response & impulse response

05/20/2016 8:42 AM
Guru

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#2

### Re: Step response & impulse response

05/20/2016 8:44 AM

Step response is the integral of impulse response. Step response gives you directly the response to a set point change, scaled appropriately. The Fourier transform of the impulse response gives you the frequency response of the loop.

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#3

### Re: Step response & impulse response

05/20/2016 9:07 AM
• The impulse input is a hypothetical concept that can be used to determine the frequency response of the loop by calculation. A pure unit impulse is not achievable in the real world.
• The step input is a real concept that can be used to determine the stability of the loop and the adequacy of the controller terms, either by calculation or by experiment.
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Guru

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#4

### Re: Step response & impulse response

05/20/2016 9:13 AM

Step response is what you do when you discover that you have dog poop on your shoe.

Impulse response is wanting to kick the dog that is responsible for your having dog poop on your shoe.

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#5

### Re: Step response & impulse response

05/20/2016 4:22 PM

That's the funniest thing I've read all week. Thanks for the much needed laugh on this Friday afternoon.

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#6

### Re: Step response & impulse response

05/20/2016 4:23 PM

"Impulse response is wanting to kick the dog that is responsible for your having dog poop on your shoe."

Or wanting to kick the neighbor who didn't pick up their dog's poop.

I don't blame the dog. They don't realize we can't smell those things the way they can and that we don't want to smell it the way that they do.

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#9

### Re: Step response & impulse response

05/31/2016 4:00 PM

Yeah - we can update this a bit:

Step response: what you do quickly when you are texting and walking and realize the screech of tires is for you as you've stepped into the path of a car.

Impulse response: what your body gets from the car as it sends you flying through the air.

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#7

### Re: Step Response & Impulse Response

05/23/2016 10:10 AM

Heh, this is the stuff I was learning when going for my BS degree.

You use a Step input to a system to determine its reaction to change: either a change in the control variable, or an external force that changed the output. It does not matter where the change came from; at t<0 The output is in balance with the input and the system is stable, at t=0 the input and output are out of balance, at t>0 the output either returns to balance with the input, oscillates around the value it should be achieving, or grows exponentially. Those responses describe a stable system with proper feedback, a stable system with overcompensating feedback, or an unstable system, respectively.

Doing this in the math before setting up the system in reality is Very Important. If the system is, for example, a control for a multi-ton, multi-million dollar satellite dish, you want to know the aiming dial will aim the dish properly, instead of trying to swing it back and forth 'near' were it's supposed to point, or try spinning it like a top.

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#8

### Re: Step Response & Impulse Response

05/27/2016 5:19 PM

As you are using them the difference comes down to where in the loop you are introducing the change, aside from the difference in the nature of the perturbation. A step change to the setpoint basically measures the system response to a change in the control variable between two distinct steady state limits, while an impulse basically measures the response to a transient that is introduced via a process variable. The difference is whether it is introduced internal or external to the control loop.

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