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中文摘要：
为了提高对主动约束阻尼梁的减振效率和稳定性，依据能量法和有限元法建立压电约束阻尼梁的动力学模型，应用Ritz法缩减了系统模型，根据模型特点采用加速度二级反馈减振控制，并对控制系统Lyapunov方程的稳定性进行了证明，基于此提出一种分段线性二次规划（Piecewise linear quadratic programming, PLQR）自适应减振控制方法。通过对多种控制方式和不同初始频率时简支梁振动特性的分析，表明控制增益和补偿频率的选取直接影响减振控制的稳定性和收敛速度；PLQR自适应控制相对于线性二次规划（Linear quadratic programming, LQR）和恒增益恒频率调控对系统振动衰减最快；与被动约束阻尼减振相比，在固有频率附近电压和中点振幅的自适应变换最显著，具有更好的减振效果。
英文摘要：
In order to improve the efficiency and stability of the active constralned layered damping beam, the dynamic model of a constralned damping piezoelectric beam is established based on the energy method and the finite element method. The reduced system model is achieved by use of the Ritz method. According to the characteristics of the model, an acceleration feedback is applied to suppress the vibration in a second order pattern and the Lyapunov equation of control system is proved to be stable. Based on these, a kind of piecewise linear quadratic programming （PLQR） adaptive control method is put forward. By analyzing transient response and frequency response of simply supported beam and the control voltage in different control ways and with various initial frequencies, it is shown that the control galn and compensation frequency directly influence the stability and convergence speed of the vibration control. PLQR adaptive control can attenuate the system vibration faster than the linear quadratic programming （LQR） and the control of constant galn and frequency. Compared with passive constralned damping treatment, the adaptive transformation of the midpoint amplitude and control voltage is most obvious near the natural frequency and makes damping effect better.
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