Jacobian SISO Models

In order to make the robot to stand it is needed that we know the dynamics from the knee servos to the IMU and from the hip servos to the IMU. These dynamics are being identified based on transfer functions. Even though looking at the behaviour of the structure it is possible to see that what we want is a small order transfer function, the truth is we are dealing with a real signal. This signal has noise and it even measures vibration caused by the high flexibility of the legs of the robot.

Because of these facts the aproach mentioned in previous posts that suggests identifying with greater order models and then simplifying them is used. In the zip file SISO.zip there are pictures of the models identified (original and simplified), and a .txt file saying the orders of the best models (original ones only).

Just a reminder, identification of the transfer functions is done using ArX where the three parameters na, nb and nk represent the order of the denominator, numerator and number of delays, repectively.

Now we procede in assembling these SISO models into a MIMO model that represents the full robot, and from that MIMO model the controler will be synthesized.

I leave you with an example of what you will find in the zip file.