On guaranteeing passivity and performance with a human controller

While designing controllers that guarantee the passivity of a closed loop system has a long history, much less attention has been paid to the situation when the control actions are performed by a human. We consider as an example a human who is driving a car. The behavior of human controllers as drivers has been modeled in the literature as a linear time invariant system cascaded with a time delay. We show that such a human model is not passive. In order to guarantee passivity of a closed loop system with a human controller, we use a passivation method. Through an appropriate design of the passivation parameters, positive passivity indices can be guaranteed for the closed loop system. The passivation parameters can be selected by solving an optimization problem such as minimizing the tracking error. To validate our theory, we provide simulation results in CarSim and Simulink.