• Rasmus Christiansen
  • Jesper Hede Christensen
4. term, Control and Automation, Master (Master Programme)
This thesis describes the process of design-
ing a nonlinear control scheme for swing-
ing up and stabilising an inverted pendu-
lum on a cart.
A model of the cart and pendulum dynam-
ics has been derived using Lagrangian me-
chanics. The actuator dynamics are mod-
elled by a first order transfer function. The
combined model has been implemented
in Simulink and verified. An Extended
Kalman Filter has been developed to esti-
mate the full state vector.
A two-step control strategy has been de-
veloped, which consists of swing-up con-
trollers and stabilising controllers. A catch
trigger algorithm manages the transition
between the controllers. Swinging up the
pendulum concerns controlling the energy
of the system such that the pendulum
reaches its heteroclinic orbits.
The stabilising controllers keep the cart
close to a position reference while keeping
the pendulum upright at its unstable equi-
librium. Six controllers; three swing-up
and three stabilising, have been designed,
implemented and compared.
Results indicate minimal difference be-
tween the stabilising controllers when con-
sidering their ability to keep the pendulum
upright and the cart at a desired position.
LanguageEnglish
Publication date8 Jun 2017
ID: 259414984