Variable Structure Control for a Simplified Linear Model of a Wheelchair

In this manuscript, a variable structure control strategy is proposed for a simplified linear model which represents a wheelchair commanded by blowing and suction. This model has a proportional and a proportional-integral controller, which were previously included to guarantee stability on the wheelchair. In the simplified model, variations on the parameters of the motors are assumed as polytopic uncertainties, which are considered for the description of the system in state space. Firstly, for a plant $\{A(\alpha), B(\alpha), C\}$ an output feedback matrix $G$ and a constant output tandem matrix $F$ were obtained such that the system $\{A((x)-B(\alpha)GC, B((x), FC\}$ is strictly positive real. Then, the variable structure control law is designed for the system. The simulation results show the fast convergence of the state variables, even considering the uncertainties.