The inverted pendulum robot on wheels is a classic plant of control systems, non-linear and unstable in open loop. In this work, modeling is carried out using fundamental physical laws of the constituent parts of the robot: the pendulum, the wheel and the activation motors. The aggregation of the equations of these parts leads to a fourth-order model that expresses the dynamic properties of the system. The adopted control strategy was of the model pole reallocation in state space. Since this is a linear technique, there was a need to linearize the model around the desired operating point for the system. The fourth-order linear model proved to be controllable, but unobservable, so that it was necessary to exclude one of the variables from the model, leading to a third-order controllable and observable structure. The controller and observer design were successful, and computational results of the controlled system performance were obtained. The work also presents the description, design and implementation of the real plant, to be used in the implementation of the control strategy in future works.
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