Online Hybrid Model Predictive Controller Design for Cruise Control of Automobiles

In the proposed study, a Hybrid Model Predictive Controller is introduced for cruise control of an automobile model. The presented model consists of the engine, the gearbox, and the transmission dynamics, where the aerodynamics force and elastic friction between the tires and road are taken into account. Through Piecewise Linearization of nonlinearities in the system; (torque)-(throttle)-(angular velocity) of engine and (aerodynamic drag force)-(automobile velocity), a comprehensive piecewise linear model for the system is obtained. Then combined with the switch and shift between engaged gears in gearbox, the Piecewise Affine (PWA) model for the vehicle dynamics is acquired. As far as the control design is concerned, the cruise control problem for tracking a desired speed fashion is addressed by a MPC-based controller design. The proposed control approach is based on the online model predictive control, applied on the obtained PWA dynamics. The highlighted novelties of the presented research work are summarized as: first a more complete model is examined due to the consideration of a realistic model for engine. This improvement makes the polyhedron regions of the PWA system dependent to both state variable (i.e., velocity) and input signals (i.e., throttle and engaged gear) which brings the complexity to the design of control procedure. Second, due to the switch in the dynamics and dependence of our PWA model to discrete input (gear shift), the desperate need to solve the optimization problem through mixed integer programming, which needs high computation effort specially for our system, seems inevitable. We triumph over this challenge through introducing “possible gear shift scenario” sets. Hence, by constraining the optimization problem to the introduced logical sets, the problem still remains convex optimization type and the computation volume is reduced. In addition, we hired branch and bound method which allowed us to have large problems to be solved in a tractable amount of time and computation resources. At last, some simulations are presented to exhibit the performance of the proposed method.