Two wheels lego mindstorms balancing control based on discrete time delta representation

Two wheel balancing robot referred as inverted pendulum is analyzed and implemented using Lego Mindstorms kit. The mathematical model was derived based on inverted pendulum equations with real parameters values appropriate to the real robot. The linearized state space mathematical model was converted into δ-domain counterpart due to the advantages of discrete time δ-operator in the context of finite word length representation. The most important factors which have a decisive importance are the sampling period and the numerical integration technique. LQR controller is proposed in order to stabilize the self-balancing two-wheeled robot. This control strategy optimally balances the error and control effort based on a cost function. Implementation of the constrained LQ on a real inexpensive hardware with very fast dynamic justifies this control approach and δ-domain discretization method which is numerically more stable.