Optimal piecewise-linear control of dry clutch engagement

Based on a discrete-time second order state-space dynamic model of the powertrain system, a piecewise feedback control for the dry clutch engagement process is proposed. The engine speed and the clutch disk speed are assumed to be measurable and the control input is the normal engaging force applied to the disks. The controller is designed by minimizing a quadratic performance index subject to constraints on the normal force, normal force derivative, and engine speed. The resulting Model Predictive Controller (MPC) is shown to consist of a piecewise linear feedback control: the state space can be divided into several regions, such that in each region an off-line computed linear controller must be implemented. The explicit piecewise linear form of the MPC law is obtained by using a multiparametric programming solver and can be tuned so that fast engagement, small friction losses and smooth lock-up are achieved. The paper reports numerical results, carried out by a Simulink/MPC Toolbox simulation scheme and a realistic set of parameters, showing the good performance of the closed-loop system