Determining first order process parameter
Determining first order process parameter
You got the Impulse-reaction of the motor with an brake (to get a higher inertia - the braking effect is near zero). It was the green marked line at http://www.loaditup.de/345634.html
At this sheet I was astonished, that the curve of the impulse response didnt have a typical exponential behaviour.
As from the step experiment, I got the information, that the process amplification is about 4 and the time constant Tau was about 1s. You can see it at the upper curve of
Then I build a model under Scicos from the Motor controller and the motor with load and then I understand the result of the response impulse behaviour:
The current of the motor produces an "electrical torque". To get the net effective torque - which acellerates the inertia - you must subtract the "load torque" from the electrical torque. (Sometimes you will understand it better if you use the word friction instead torque).
The load torque consists ot three different types:
1. Type: Speed dependend torque. This type produces a linear (or more complex) speed dependend load torque. At speed = 0, the torque is zero.
This type is not the explanation for the impulse response. If the load torque is dominated by this type, the speed decreasing may not be almost linear - it must be exponential.
2. Type: Speed independent torque with torque at zero speed:
You got theis type e.g. with a fixed wheel with a spooled wire and a fixed mass. The result is a speed independent torque.
If the load is dominated by this type then the impulse response is the following: After the impulse, the motor has a certain speed. Now the electrical current is zero. We suppose, that the constant load torque is working in a way, that the motor begins to speed down. At any time the motor stops and is accellerated in the opposite direction - friven by the constant load torque of the wheel with mass. But because the "back electrc motoric force" (which is speed dependent) works against the accelleration and so the motor reaches a certain speed in the other direction a at the impulse. The motor reaches the speed limit, when the BEMF-force has the same amount as the load torque of the wheel/mass.
Because of the speed dependent BEMF, this change of the speed immediatelly after the impulse and the stationary speed in opposite direction has an exponential character.
But this load cant explain the measured impulse response. Because the motor decreases to speed 0 and stops.
3. Type: Speed independent torque with zero torque at zero speed. You get this load torque for example at a ideal disk brake. At zero speed, no torque is produced. It the disk of the brake has a speed > 0, a constant torque against the motor is produced.
This type of load torque is responsible for the shown impulse response. After the impulse, the decreasing speed behaviour is the same as at type 2. The important difference is, that at zero speed, the BEMF force of the motor reaches zero and the load torque of the disk brake reaches zero. The motor stops. (Only at type 2 the the fixed mass at the wire produces further torque and the motor speeds up in the oposite direction.)
I hope you understand what I tried to explain. As in the meantime written by you at sci.engr.control , the impulse response is the first part of a exponential curve with the stationary speed <> zero.
If you understand the principle - it would not be mantadory to send you the Scicos files. It you dont understand it after a longer time - please let me know and I send you the Scicos modell and the explanation of it.
After understanding I made a further impulse experiment: At first I gave an impulse for 120ms. then I reduced the current not to zero, but rather to a value that the motor speeds down. This fix current after the impuls was at always new experiments decreased until I got the limit that the motor stops and didnt rotate stationary. So I compensated the constant load torque.
And now look at the curve of the impuls result with the torque compensation:
And now you can see as at the step experiment:
1. Tau is about 1s
2. with h(t) = impulse response
k = amplification of the
first oder system G(s) = k/(1+s*T)
k = integral (from 0 to infinite) of h(t) dt
And if I use this for evaluation of the impulse response, I get K = 4 !!!
So Tau and K is in this case the same as got by the step experiment.