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Unformatted text preview: Department of Mechanical Engineering University of Minnesota ME8281 Advanced Control Systems Spring 2012 Prof. Perry Li Assignment #1. Assigned: Feburary 3, 2012 (Friday) Due: February 15, 2012 (Wednesday) 1. (Modeling Hydraulic Hybrid Vehicle) The hydraulic hybrid vehicle architecture being devel- oped at the Center for Compact and Efficient Fluid Power is shown in Fig. 1. It consists of an engine in series with pump/motor B connected to the carrier of a planetary differential gear set. The two half-shafts of the differential are connected to pump/motor E and the wheel respectively. The pump/motors B and E are connected hydraulically to a hydraulic accumulator. For simplicity, we consider only the left wheel drive unit. Also, assume that all the gear reductions have unity ratios. Shafts 1 of both differentials are connected to the left and right pump Es, and the carrier of both differentials are connected to the main mechanical shaft. The dynamics are given by: J veh L 2 =- T L (1) J LE L 1 =- T L + u L (2) J mech c = 2 T L + [ u E + u B ] (3) where J veh , J LE and J mech are the inertias of the vehicle/wheel, pump E and the engine/pump B respectively; L 2 , L 1 and c are the speeds of the vehicle/wheel, pump E and the en- gine/pump B. T L is the half shaft torques and half of the carrier torque at the differential....
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