State Space Control of 3 DOF Dual Inverted Pendulum

State space is a method of modeling complex dynamic systems as a set of first order differential equations. Control design in the state space is convenient for handling multiple inputs and outputs and allows the designer to manually shift the dynamic characteristics of the system in order to achieve stability. In this project, state space is used to model the dual inverted pendulum and design a controller that will balance it in the upright position.

The dual pendulum in this project is an electro-mechanical system with three degrees of motion. The physical bodies that make up the pendulum are the cart and the two arms. The cart sits on a linear track which can move on a single, horizontal axis. The first pendulum arm is connected at one end to the cart by a pivot joint whose axis of rotation is normal to the horizontal plane. The second pendulum arm is connected to the opposite end of the first arm by another pivot joint; the two arms rotate in parallel planes. The input force of the system is supplied by a DC motor connected to the cart with a belt transmission. The linear motion of the cart and the rotational motions of the two pendulum arms make up the three degrees of freedom of the system.

The natural, unforced state of the system is defined by an arbitrary location (x) of the cart and the two pendulum arms hanging downward, subjected to the force of gravity and the reaction forces at their joints. The purpose of this project is to design a controller to balance the two pendulum arms in the upright position (one on top of the other) and have the cart come to rest near the center of its range of motion.

For more information about this project you can download my masters thesis at bryankappa.com/resume.html.

Category:

Science & Technology

Tags:

• nonlinear
• multivariable
• state
• space
• control
• inverted
• pendulum
• balance
• mechatronics
• mechanical
• engineering
• portland
• university

[rosalindasampley]

thanks for a lot of information i will try this features.

[huhq1]

i have one question how can u identify the parameters of the system when u were doing the modeling

[huhq1]

MIMO linear state space control...well done

[gr3y]

@TheBeefBaron I'm guessing Matlab.

[TheBeefBaron]

That's really cool. What software did you use to model and control the system?

[menzoic]

this is the exact opposite of what I was looking for, but still cool

[xXK2KILLERXx]

cool

[IamTheMaxXx]

well done! try with fuzzy logic too!

[pikachuthesquirtle]

looks pretty cool