Dry Clutch Control for Automotive Applications

"5 Optimal Standing-start (p. 71--72)

5.1 Principle

The solution of the optimal control problem through the use of a quadratic programming formulation has raised the activation time limitation imposed by the solution of the TPBVP over long intervals, allowing calculation of a complete optimal standing-start trajectory. This kind of solution could be used for the control of a AMT or a clutch-by-wire system where the clutch has to be controlled by the gearbox control unit from the very beginning of the engagement. In the previous chapter the solution of the optimal control problem has been obtained under the hypothesis of a constant engine torque.

This condition, perfectly reasonable for a short activation time over the last part of the engagement, is very hard if not downright impossible to assure when considering a whole standing-start operation. The possibility of having an engine torque evolution described by an homogeneous linear system could partially solve this di?culty but does not allow for a change of the driver’s wish during the engagement.

Taking into account these changes not only increases the driving comfort but is essential for security since the driver has to be always able to intervene in the vehicle behavior in order to react to a rapid change in his environment. To meet the opposing needs of taking into account the driver’s input and having some simple hypothesis on future input allowing for an optimal planning, the trajectory is not computed once and for all at the beginning of the engagement and then simply tracked by feedback, but periodically updated to follow the changes in the driver’s input and the actual behavior of the vehicle.

5.2 Exact Dynamic Replanning

5.2.1 Model Predictive Control

The model-based predictive control (MPC) is a control strategy that, in its most general formulation, consists in solving an optimal control problem in QP formulation for a simpli?ed and/or liberalized system over a ?nite time horizon of Nh samples and issuing the ?rst Nc control samples before using the newly measured or estimated system state x0 as the starting point for a new optimization. Compared to the previous control schemes the MPC strategy shows two main advantages, the ?rst being that a change in the driver’s input can be readily taken into account in the next optimization. The second advantage is that trajectory stabilization does not need to be assured by an external feedback loop since each new optimal trajectory has as a starting point the measured or estimated system state x0 that directly takes into account the actual system behavior."