Circuit's Time Constant

yes. even same elevator function or escalator function is used.

Well the use of a switch closing step function into a real world circuit mimics the unity step function (u(t)) which has a La Place transform pair of 1/s. The ease of such a simple input S domain waveform allows the analysis of the output waveform to determine exactly the circuit transfer function. The theoretically easiest input signal to back calculate the transfer function would be a δ(t) spike. This has the ideal S domain value of 1. But an infinitely narrow pulse that has an infinite amplitude so that the area is 1 is clearly only a mathematical concept that cannot be even closely approximated in real life. Now a true ramp function will have to incorporate the slope of the ramp into the transformation. Also a true ramp must be capable of an eventual infinite amplitude. So while one most certainly can derive an S transform of a ramp that starts at 0 value at 0 time and rises at a fixed slope (m), it will not be such a simple transform as a step function nor easy to replicate as a test signal.

I do recommend though that the student derives a Laplace transform for a ramp function from the definition of a Laplace transform. F(s)≡∫f(t)e^-st dt with this over the time interval of t=0 to ∞.

Yo Kameel

circuit time constant is the plc's runtrough of the ladder

When you use Ramping , this is for the Analog/Digital circuits, those run separately from the laddercircuits.

They are separate timing indexes they have in principle nothing to do with each other, except when you make the one dependent of the other.

T L.

PID loop

ladderdiagram

Ladder

My circuit is linear one, only contains resistors and inductances(no capacitors)

I expect the time constant with Ramp function will be much less than if Step function is used.

Kameel

The time constant of the circuit's transfer function will be exactly the same regardless of the input signal. This should be obvious because one has not changed the circuitry at all. However, when you use an input waveform that differs from a step function, a sine wave or a very few other well defined shapes then it gets difficult to calculate the circuit's time constant from the output response. Review your circuit theory, La Place transforms and particularly the mathematics of a convolution.

I wish to emphasize again that you cannot generate a true ramp function, because as time goes to infinity your voltage goes to infinity. You are probably actually using a triangle wave that repeats after a certain amount of time.

To identify what the waveform you will get from a triangle wave running through your circuit you should do a Fourier transform of the triangle equation to identify the frequencies and phases present in your waveform. Multiply the Taylor series values for your waveform times the Fourier transform of your circuit and then execute a reverse Fourier transform to obtain the anticipated time based waveform. (Remember that by multiplying the Fourier functions you will actually be doing a convolution in the time domain.)

Thanks for the information, so if the input signal is sinusoidal,does the output will be also sinusoidal but shifted by angle equivalent to the circuit's time constant ?

Yes the output will be sinusoidal but the delay will be related to but not be precisely your time constant. Let me think a minute. If you have just one pole in the circuit, then the 3dB down point will be at the frequency corresponding to your time constant. At the 3dB frequency you will have a 45° shift which is then 1/8 of the time constant of your filter. Now if you have multiple poles, it all depends on their relationship to each other.