When a double-degree-of-freedom dynamical system with hard boundaries subjects to periodic excitations and random impulsive disturbances, the oscillator will collide with the boundaries and exhibit complex chaotic behavior. In this paper, an intelligent framework with the Soft Actor-Critic reinforcement learning algorithm is proposed to achieve both vibration control and base motion tracking. In addition, the dynamic control effect of the double-degree-of-freedom system on a moving base with hard boundary is also studied in a wide frequency range. By constructing a composite reward function that incorporates relative displacement and control force, high-precision trajectory tracking and vibration suppression in dynamic system are achieved. The results demonstrate that the algorithm can achieve effective vibration control in a wide frequency range from 0.01 Hz to 1 Hz. A comparison with the PID control method further exhibits the stability and generalizability of this approach in complex environments.