A unified Hamiltonian framework for H2 and H-infinity preview control algorithms with application to a variable valve timing engine.

Abstract

Preview control has been widely used to improve achievable control bandwidth, for systems with delay or nonminimum phase zeros, when the future desired output or exogenous disturbance is available. A framework for solving the <italic> H</italic>₂ and <italic>H</italic>_infinity preview control algorithm for both continuous and discrete time is developed. A Hamiltonian approach is used to derive the full information special problem that minimizes the infinity norm of the transfer function between the exogenous disturbance, <italic>w</italic>, and the performance output, <italic> z</italic>. The resulting solution consists of the standard <italic>H</italic>₂ or <italic>H</italic>_infinity full state feedback term as well as a preview term. In order to extend the preview results to a wider range of problems, the <italic>H</italic>_infinity preview output feedback controller is developed. The formulation consists of the development of several preview special problems that are used together with a separation argument to obtain the output feedback case. The dynamic output feedback controller consists of a feedback and a preview term. The feedback term is the same as the standard <italic> H</italic>_infinity output feedback control. The resulting preview control algorithms are applied to two automotive applications of a variable valve timing engine. In the first, a preview controller is used to softly seat the valve of the electro-magnetic valve actuator. A model of the valve actuator system is developed. The preview control algorithm is compared with the standard <italic>H</italic>_infinity feedback control. Experimental results show a significant improvement of the preview over the feedback only control. In the second application, a preview controller is used in the torque tracking of the variable valve timing engine output control. A four induction event delay is inserted in the control loop after a driver demand map to efficiently schedule the demanded torque and to allow the use of preview. A control oriented torque delivery model of a 2.0 Liter Zetec engine is derived, and a novel valve optimization approach is developed to the obtain the valve timing for best fuel conversion efficiency and NOx. The optimized valve timing is used to construct a feedforward lookup term that is used in conjunction with the <italic>H</italic>_infinity preview control. Simulations results show improved torque tracking of the <italic> H</italic>_infinity preview/feedback/feedforward control over the standard <italic>H</italic>_infinity feedback/feedforward approach.