How to tune two PID controllers that is series connected for Furuta pendulum

Hi

I am trying to tune two tune two PID controlers series for the Furuta pendulum or rotatry inverted pendulum any suggestions ?

Is it possible to do automatic?

[Mathieu NOE]

I assume the inner loop is velocity and the outer position (?)

simply start with the inner loop first and when done , tune the second PID

[CyberRobotics]

The inner loop is angle of pendulum the outer loop is angle of the rod

[Mathieu NOE]

ok, tx for correcting me . I just discover what a Furuta pendulum is indeed .

so I assume the two loops have a lot of coupling so my approach of sperately tuning the inner then outer loop may be not doable.

seems this is not a new topic and there is a lot of publication on the control of such device

Furuta pendulum - Wikipedia

[Sam Chak]

Hi @CyberRobotics, could you indicate where the two PID control laws are incorporated in the differential equations of the Furuta Pendulum? This will help verify whether the Simulink model is constructed correctly in accordance with the linearized differential equations (as implied by the State-space block), as well as identify the inputs to the PID controllers.

Info on Wikipedia presents the simplified differential equations (which remain nonlinear) as follows. The control torques and are not cascaded; therefore, they should differ from those in your Simulink model.

[Sam Chak]

@CyberRobotics: The inner loop is angle of pendulum the outer loop is angle of the rod.

However, the Furuta Pendulum is a fourth-order system, as the double-dot notation and imply the state variables , , and . You likely intended to convey that the inner loop describes the rotational motion of the pendulum, while the outer loop describes the rotational motion of the rod.

[CyberRobotics]

yes the inner loop is the describes the rotataional motion of the pendulum and the outer loop describes the rotational motion of the rod

[Sam Chak]

Okay, begin tuning the two PID controllers now.

[CyberRobotics]

How to do it with pid tuner app

[Sam Chak]

I am unable to provide guidance without the requested information.

However, as a starting point, you can certainly follow @Mathieu NOE's advice to begin by tuning the PID controller in the inner loop. Once that is completed, you may proceed to tune the 2nd PID controller in the outer loop, assuming that you believe your single-input state-space model is correct, which differs from the two-input model presented on the Wikipedia page for the Furuta Pendulum.