周期激励下广义离散Duffing系统的多稳态分析

具有硬边界的动基座双自由度动力学系统在受到基座周期性激励与随机冲击扰动时,振子与边界碰撞后的强非线性特性导致系统产生复杂的混沌行为.本文基于Soft Actor-Critic强化学习框架,构建了同时实现振动控制与基座运动跟随的智能算法,研究了宽频域范围内含有硬边界约束的动基座双自由度系统的动力学控制效果.通过构建包含相对位移、控制力的复合奖励函数,实现动力学系统精度较高的轨迹跟踪与振动抑制.结果表明,该算法可以实现频率范围跨2个数量级(0.01Hz到1Hz)的有效振动控制,并通过与PID控制方法的比较,展现了该方法在复杂环境中的稳定性与泛化性.

Multi-Stability Analysis of Generalized Discrete Duffing Systems under Periodic Excitation

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.