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# understanding the system modeling

## understanding the system modeling

(OP)
Hello,

This is sundaram, I'm working on a speed control of belt driven drum project and I'm new to control system concepts.

I'm trying to find the transfer function of the system so that I can model it in simulink and tune the PID and look in to other aspects of the system.

The blocks and variable i'm outputting is in the attached Image (picture 2)

http://files.engineering.com/getfile.aspx?folder=a...

The speed loop control (PID) is in the control block and it has a microcontroller in it (where I tuned the system partially).
Now the variable I'm out putting on to the scope is the internal speed var which gets calculated at a rate of 18KHz .
From the over shoots and rise time I could calculate damping ratio and natural frequency in rad/sec
and substitute in the standard 2nd order system transfer function.

But the 2nd order transfer function which I got above includes the PID control which is in the microcontroller.
But to the best of my knowledge it should not be included and it should be separated,then only I can use it in MATLAB.
From the diagram (picture 3) H(s) is the transfer function I have, D(s) is the PID loop and G(s) is the plant model.

http://files.engineering.com/getfile.aspx?folder=7...

Can anyone help me, I'm I right in my approach ?, if so how can I separate both transfer function
is this the way to do it..?
Now I have H(s)=D(s)*G(S) ( from picture 3)
And I know the PID gains => I know the 2nd order transfer function of the PID controller ie, D(s)
to get the G(s) I need to divide the H(s) with D(s)
G(s)=[H(s)/D(s)]

Is it right or am i missing something?

### RE: understanding the system modeling

You don't know H(s), since G(s) is unknown. H(s) cannot be determined by fitting a transfer function to the step response data because you aren't accounting for the feedback in the system. You aren't clear about how you are producing the step response data, so I'm assuming it is a step in r that is producing the response in y, since that is a common method. However, the overall closed-loop transfer function for your diagram in Picture 3 from r to y is not H(s)=D(s)G(s), it's D(s)G(s)/[1+D(s)G(s)], i.e., H(s)/[1+H(s)]. If you find a transfer function that fits the step response, it is the step response of that closed-loop transfer function, not H(s) alone.

Search the internet for "closed-loop system identification", as that's what you're trying to do. There are many available resources.

xnuke
"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand, Atlas Shrugged.
Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

### RE: understanding the system modeling

(OP)
Thank you sir for your inputs;
I'm understanding what ur trying to explain, you are right R is step input and y is the output
from picture 4 which I have the transfer function F(S) and need to get G(S)by understanding the concept of "closed-loop system identification" for me to model in Simulink and I know the D(s) as it is the PID loop I use..

I'm I right..?

http://files.engineering.com/getfile.aspx?folder=3...

### RE: understanding the system modeling

You are correct. You can get a model of the transfer function F(s) from the step response from r to y, however, closed-loop system identification techniques will be required for you to get a model for G(s).

xnuke
"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand, Atlas Shrugged.
Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

### RE: understanding the system modeling

(OP)
Hello Sir, I have done some googleing and found the below papers

1) http://www.ualberta.ca/~slshah/public_share/IDfrom...
2) http://arrow.dit.ie/cgi/viewcontent.cgi?article=11...
3) http://www.mii.lt/informatica/pdf/INFO282.pdf

I feel the paper 1 and 2 have some relevance with what I'm trying to look for

Pl suggest are this ok or you have some thing more simple and I can understand as I'm very new to this field.

### RE: understanding the system modeling

Can you tell us something about the power amplifier and the motor you will be driving. Is the amplifier a voltage amplifier and the motor a brush DC motor.

### RE: understanding the system modeling

(OP)
The motor I'm using is a BLDC with drive, I dont use any amp but, IGBTs to generate 3-phases..

### RE: understanding the system modeling

(OP)
I have one more thought, can I make the I and D gains of my PID control to zero and make Kp = 1, now by looking at the out put Y(s) with respect to r(s) with this can I get the transfer function of F(s) shown in the below figure
http://files.engineering.com/getfile.aspx?folder=3...

and as D(s) in the above system to unity or say 1 the F(s) has only G(s) and so the Y(s)/r(s) =G(s).

Sorry if it sounds as a bad idea, but I'm trying to make systems D(s) insignificant so the I can find G(s)... My goal is to get G(s)...

Thanks..!

### RE: understanding the system modeling

You say the motor you are using is "Brushless DC with Drive." Does the drive supply voltage or current to the motor. I assume that the drive commutates the motor.

### RE: understanding the system modeling

(OP)
yes, we control the current and the drive commutates

### RE: understanding the system modeling

Then the drive motor combination looks like an integrator with gain. The drive creates amps/ volts, the motor creates torque/amp, the torque creates angular acceleration of
acc = Torque/Inertia and the acceleration integrates to velocity.

### RE: understanding the system modeling

Or the basic transfer function is K/s.

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