Passivation Theory and its Application to Automotive Systems

In this report, we consider a passivation method that uses an input-output transformation matrix. This matrix generalizes the commonly used methods of series, feedback and parallel (or feedforward) interconnections to passivate a system. Through an appropriate design of this matrix, positive passivity levels can be guaranteed for the system. The passivation parameters can be selected by solving an optimization problem such as minimizing the tracking error. As an application of our passivation method, we consider systems with input-output time delay. In automotive systems, time-delays cannot be avoided due to software implementations of the control algorithms. We show that our passivation method can be used to compensate for the time-delay in the controller and improve the closed-loop system performance. To validate our results, we provide simulation results in CarSim and Simulink.