Multi-parametric model predictive control for variable valve timing

Volumetric efficiency (VE) in a four-stroke internal combustion (IC) engine has been an important issue in the automotive industry because it determines IC engine performance. VE is determined by the volume of air in the intake manifold, the valve sizes, the valve locations, and cam profile characteristics. Variable valve timing (VVT) control is a technique used to optimize VE by continuously varying valve timing. Among VVT control strategies, a variable valve phasing (VVP) controller that varies exhaust camshaft phasing is designed using multi-parametric model predictive control(mpMPC). Model predictive control (MPC) has been regarded as a powerful control method for anticipating future events and fulfilling constraints on the state and input by online optimization. However, the corresponding computational complexity of online optimization is a major drawback of MPC; therefore, mpMPC has been suggested to alleviate the computational burden by parametrizing the state vector. mpMPC computes an optimal input to the plant by solving a multi-parametric quadratic program (mp-QP). A VVP mechanism model and a PID controller, as well as an mpMPC controller, are presented in this paper. The proposed controller demonstrates superiority over the PID controller in terms of its tracking performance and bandwidth.