### Author Topic: bandwidth of two wheel inverted pendulum  (Read 664 times)

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#### kover_ferenc

• Beginner
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##### bandwidth of two wheel inverted pendulum
« on: May 14, 2014, 06:13:46 AM »
Hello guys, i tried to ask the following Topic in the category Electronics, but no answer was received.
I am trying now here, i hope someone can help:

I am working on a 2wheel inverted pendulum project, ive already built the mathematical model with the quite accurate parameters. I would like to use gyro and accelerometer for tilt measurement (estimation), i already chosed the sensors, but i have to choose also the lowpass filter capacitor at the outputs, and for that i have to know the bandwidth of the pendulum.

My (could be silly) question is:
1: How can i calculate the bandwidth of my invpendulum by the use of the robot parameters? Or any other way?

Also i have another question block:
I want to simulate the behavior of the accelerometer in simulink. For that i already tried to set up the three-axis accelerometer block, but in three settings i am not sure:
2a: Natural frequency, what should i put there? because in the datasheet of the sensor i did not find this (i am using ADXL103)
2b: here i want to cite first the document i used for mathematical model:
http://www.pages.drexel.edu/~dml46/Tutorials/BalancingBot/files/NXTway-GS%20Model-Based_Design.pdf
- Shall i use for the "Ab" input the acceleration vector dd/dt [xb,yb,zb] or the vector dd/dt [xm,ym,zm]?
- is it OK if i use for the "omega"input the d/dt [0, psi, fi]?

Thank you very much for your help in advance.
Waiting for the replies.
Regards, Feri

Now i want to choose

#### ootbrobo

• Jr. Member
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##### Re: bandwidth of two wheel inverted pendulum
« Reply #1 on: June 19, 2014, 11:22:22 PM »
Okay,

So that document is pretty involved so I honestly just skimmed it.  The setup in the doc seemed to be referring to the use of encoders and a gyro not an accelerometer.  So I assume you are using the Accel for your pendulum gravity vector, and the gyro for the rate?

As for using a physical filter at the output of the accelerometer, I would suggest going with a digital filter instead, such as an IIR.  This ought to be a more powerful and robust solution.  Keep in mind you may need to compensate for a lack of an FPU though depending on the processor you are using.

The natural frequency of the sensor?  I don't think that is what you are looking for.  If you need a natural frequency at all it ought to be of the pendulum.

The problem I think you may run into here is that an accelerometer + gyro combinaton here does not give you sufficient information without some assumptions, or references.  Point being the accelerometer picks up three distinct vectors 1) gravity 2)centrpital accel due to pendulum angular rate 3) linear acceleration of the robot as a whole.  You can derive #2's contribution from the gyro, but you do not have direct feedback for the forward motion of the entire robot.  I would recommend adding encoders to get position/ rate data from the wheels in reference to the pendulum mast.

#### Billy

• Robot Overlord
• Posts: 132
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##### Re: bandwidth of two wheel inverted pendulum
« Reply #2 on: July 14, 2014, 11:09:12 PM »
As for using a physical filter at the output of the accelerometer, I would suggest going with a digital filter instead, such as an IIR.

He/she needs an anti-aliasing filter. That is always physical. The IIR or FIR can be used for tuning.

Everything else you said was spot-on!
Late to conversation. My apologies.
« Last Edit: July 14, 2014, 11:11:03 PM by Billy »

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