The vibration testing system of a large structure spacecraft presents inaccurate precision tracking and high oscillations in the neighborhood of its vibrational modes, particularly at higher frequencies. In the presence of varying modal parameters of a spacecraft such as the mode frequency and corresponding damping ratio, the performance of the controlled system degrades. Robust high precision tracking control of such systems with varying modal parameters is rarely addressed in the literature. A new closed-loop system architecture is proposed in this paper, based on a feedforwardfeedback tracking control strategy involving an H controller. Simulation results show that the new architecture allows precise tracking of a sine sweep acceleration reference signal avoiding vibrations when sweeping through modes. Furthermore, it appears to be highly robust against varying parameters, model uncertainties, as well as the presence of sensor noise. The proposed controller also limits the control effort to avoid the actuator saturation. A minimal order controller is derived which makes it tractable for further industrial implementation.