Inverted Pendulum Stability Regarding Bandwidth and Center of Mas

Sammanfattning: This bachelor thesis at the Royal Institute of Technology in Stockholm, Sweden, aims to clarify how the minimum bandwidth of a stabilised mobile inverted pendulum is affected by the position of its center of mass and the frequency of measuring the state variables. The scope is to apply basic theories in automation control and electronic systems when designing the system. The mechatronical system in the experimental trials is constructed with the main components consisting of bipolar stepper motors, stepper motor drivers (DRV8825), potentiometer and Arduino UNO. The mobile pendulum in question consists of a cart on a rail with a potentiomoter and a rod mounted to it. In the experimental trials in this paper, three different radial positions of the center of mass are analysed with regards to the bandwidth of relevant measurements. A variety of PID parameters, for both the angle and position regulation, are the essential basis on which these stability trials are performed. The results are limited to the resolution of the potentiometer outputs, the length of the rail and the stiffness of the rod. The result is presented by comparisons between data of the greatest angles which are stabilised and the corresponding maximal latency of the angle corrections. These data concludes to that the minimum required bandwidth to sustain stability decreases for an increasing length between the center of mass and the point of rotation.