Abstract

This paper compares three control strategies to stabilize a two-wheeled inverted pendulum (TWIP). The study of TWIP or balancing robot has been extensive because of its unstable and multivariable nature with highly non-linear dynamics. The mathematical model was derived using Lagrangian approach and was linearized around the equilibrium point where was considered that the pitch angle tends to zero. The study used a classic PID control, a Linear-Quadratic Regulator (LQR) and a Slide Mode Control (SMC). The SMC part of state-space representation of the system and the slide surface was designed from the poles obtained from LQR, therefore design an Optimal SMC. All the close-loop controllers are in discrete-time; therefore, they were implemented in a digital way. The results were obtained by simulation using Matlab. The stabilization results were compared in terms of disturbances rejection capability and the integral square error (ISE) is used to measure their performance.