Inverted Dual Pendulum

The controllability of the dual inverted pendulum is an- alyzed using LQR design concepts and an observer-based controller. I show that the system must be set up with pen- dulums of different lengths in order to maximize control. Moreover, I present a set of LQR parameters that main- tain reasonable cart displacement, rod displacement, and required external control force under a few common initial conditions. Following this train of thought, I show the sys- tem’s response to the most and least ideal sets of initial con- ditions and offer a physical intuition as to why the model is sound. Finally, I design an observer-based controller to show the estimated response in the presence of noise.