Ball and Beam model Simscape Multibody

Hello :)

I'm doing a project for my studies, and I need to do a Simscape Multibody model of ball and beam which is supported in the middle. I am using R2016a version of MATLAB. I did make a model, which looked like it had good physicall behaviour, but when I tried to add PID controller nothing changed (ball is still falling). Does anyone know what I'm missing or doing wrong?

I've tried to model a system based on following equations:

,

,

,

where: θ- beam deviation angle, I-moment of inertia of beam, - moment of inertia of ball, U- torque (input), x- distance of the ball center from the middle of the beam (output), m- mass of the ball, h- height of the beam, F- friction force, r- radius of the ball.

I attach screenshots of my work and .slx file of the project.

Any help would be appreciated :)

Answer 1

[Steve Miller]

Hi Wojciach,

There are a few problems with see_saw.slx. The most important one is that it appears you are trying to apply the force from the ball to the beam. That is not necessary - Simscape Multibody calculates the force that the ball applies to the beam for you.

The other problem has to do with your controller. There are many strategies which I am sure you can find in a Google search. You will probably need a control strategy that includes the angle of the beam.

I have attached a version that deals with both of the issues cited above. It is not the only way to solve the problem.

--Steve

[Alireza]

Hi Steve,

Why does it only works for initial position of ball less than 0.01 m?

I get this error when I try to change the initial position of the ball; x > 0.01 m. But when I changed the the revolute joint input from motion to torque, the error solved, but I need motion as input, how can I solve it?

Caused by: Derivative of state 'untitled.Revolute_Joint1.Rz.w' in block 'untitled/Revolute Joint1' at time 0.0105 is not finite. The simulation will be stopped. There may be a singularity in the solution. If not, try reducing the step size (either by reducing the fixed step size or by tightening the error tolerances)