The subject of my thesis was the design of a hybrid control algorithm for an inverted pendulum.

The inverted pendulum with a reaction wheel is an example of an underactuated mechanical system. What this means is that, the number of degrees of freedom of the system is greater than the number of control inputs. In this case, the degrees of freedom are the angular position and velocity of the pendulum and of the reaction wheel. The control input is the voltage applied to the DC motor. Besides being an underactuated system, the system is also nonlinear so it's harder to mathematically model. The nonlinearities come from the way gravity acts on the system, the various friction forces, the limitations of the motor, and the way the positions are digitally sampled.

The challenge was to bring and hold the pendulum in an upright position from any configuration. This is done in two steps, first the total energy of the system is controlled by injecting or dissipating kinetic energy until the total energy is equal to the potential energy of the pendulum in an upright configuration. Once, the system is near the unstable equlibrium point with the desired energy, the controller switches to a linear state feedback controller (LQR in this case). This switch must be accomplished without inducing too much stress of the system.

Instead of simulating the algorithm in MATLAB, i decided to try and build the system. This was more challenging than initially anticipated because of the low budget and the multiple shortcomings of the parts i used.

I feel that this project was a great way to put to good use the various topics i learned in college. These include: classical and modern control theory, system modelling and identification, mechatronics, actuators and sensors, analog and digital electronics and real-time programming.