Samenvatting

The Inverted Pendulum is one of the classical control problems of an inherently unstable system.
The idea is that the pendulum, fixed on a cart, stays upright in its vertical position while the cart
is moving, or disturbances are applied. The system is used to demonstrate the capability of the
target hardware and software platform developed by BECKHOFF. With the platform, it is possible
to run controllers in real-time while connecting to Input/Output signals from the real world.
The Inverted Pendulum setup is built based on a machine mainly used in transportation, called
XTS, eXtended Transport System. Due to a limitation of the setup, the pendulum starts from an
upright position, making a unique setup. Compared to other work that has already been done in
the past, their pendulums start from a downward position. The Inverted Pendulum setup was not
working at BECKHOFF. A controller, written in PLC languages, must be implemented to keep the
pendulum in its vertical position.
In order to obtain a controller for the system, first, a mathematical model of the system is analyzed,
then a physical machine is investigated. How does the machine work? How can it be controlled?
Besides this, an encoder, which reads an angle of the pendulum, is analyzed. When the inputs
and outputs are clearly understood, a correct model corresponding to the system has been built
and simulated in MATLAB/Simulink. A PID Tuner from Simulink is used to tune PID controller
parameters to achieve a robust design with the desired response time.
It turned out that the traditional PID-Controller was not suitable enough for
the system. In specific, the steady state error never becomes 0, and the
control signal grows unboundedly. Instead of using the PID-Controller, a
pole placement technique has been used. A new controller has been
made and simulated. The simulation gives a good result. Based on the
new controller and the Simulink model, a PLC program has been
implemented.