How to chose the step size for time constant identification

Hi,

I identified a BLDC motor using a series of steps with different PWM. The gain and delay was easy to find, but I am struggling with the time constant: the larger steps have larger time constants. So here is my question:

How do I determine the appropriate step size for a system identification process ? In particular the time constant identification.

Thank you for your help !

Answer 1

[Animesh]

Hello Antoine,

Here are some steps to help you determine an appropriate step size for time constant identification:

1. Start with smaller step sizes: Begin the system identification process with smaller step sizes. Smaller steps allow for better resolution and capture more details of the system's response. However, keep in mind that very small steps may not fully excite the system dynamics, leading to inaccurate time constant estimation.
2. Gradually increase step size: Increase the step size incrementally while monitoring the system's response. As the step size increases, the system's response will become more apparent, and you can observe the time constant more clearly. However, be cautious not to choose a step size that causes excessive overshoot or instability in the system.
3. Observe the response: Analyse the system's response to each step size. Look for a smooth and consistent behaviour that allows you to estimate the time constant accurately. If the response is too fast, it may indicate a step size that is too large. Conversely, if the response is too slow, it may indicate a step size that is too small.
4. Iterate and refine: Based on your observations, adjust the step size accordingly and repeat the system identification process. Gradually narrow down the step size range until you find the optimal value that provides a reliable estimation of the time constant.

Remember that the appropriate step size may vary depending on the specific characteristics of your BLDC motor and the desired accuracy of the time constant estimation. It is recommended to experiment with different step sizes and validate the results against known values or reference models if available.

Additionally, consider using established system identification techniques such as least squares fitting or system identification software tools, as they can provide more advanced methods for accurately estimating the time constant and other parameters of the BLDC motor.

Thanks,

Animesh Jha