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Due to its superior power-to-weight ratio, a hydrostatic dynamometer is an ideal candidate for transient engine or powertrain testing. It can load or motor the engine to follow any desired speed and acceleration profiles for real-world applications. Given its high bandwidth, the hydrostatic dynamometer can be further used to emulate the dynamics of hybrid powertrains and, therefore, investigate the interactions between the engine and the hybrid power source in real time. This will greatly expedite the research of various hybrid powertrain architectures and control methodologies, without actually building the complete physical system. This paper presents the design, modeling, tracking control, and experimental investigation of a transient hydrostatic dynamometer. A ninth-order physics-based dynamic model for the dynamometer is formulated and then identified and validated with experimental data. To control the dynamometer to emulate the real-world engine speed/torque profiles, two different nonlinear control strategies are investigated and implemented. First, a nonlinear model-based inversion plus PID control is designed to achieve precise tracking. Then, a state feedback control via feedback linearization is designed and implemented. Experimental results demonstrate precise tracking performance with less than 5% tracking error for both transient and steady-state operations.