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根据压电智能结构的特点,针对一类由悬臂梁、传感器和压电作动器构成的压电智能梁系统的振动主动控制进行了研究。利用压电方程建立了压电智能梁系统的状态空间模型,采用线性二次最优控制(LQR)对智能梁的振动进行了主动控制。对二次性能指标中的加权矩阵的选取方式进行了深入研究,提出了一种基于多种群遗传算法的加权矩阵选取方式。仿真和实验结果表明:多种群遗传算法比简单遗传算法具有更快的收敛速度,且遗传代数少,能够有效避免陷入局部最优解。基于多种群遗传算法的LQR振动主动控制算法对压电智能梁的振动主动控制具有可行性和稳定性,相对基于简单遗传算法的LQR振动主动控制算法达到稳定的时间短且具有更好的控制效果。
According to the characteristics of piezoelectric smart structure, a kind of active vibration control of piezoelectric smart beam system composed of cantilever beam, sensor and piezoelectric actuator is studied. The state space model of piezoelectric intelligent beam system is established by using piezoelectric equations. The vibration of intelligent beam is actively controlled by linear quadratic optimal control (LQR). The method of choosing the weighting matrix in the quadratic performance index is deeply studied, and a weighted matrix selection method based on multi-population genetic algorithm is proposed. Simulation and experimental results show that the multi-population genetic algorithm has faster convergence rate than the simple genetic algorithm and less genetic algebra, which can effectively avoid falling into the local optimal solution. The LQR vibration active control algorithm based on multi-population genetic algorithm is feasible and stable for the active vibration control of piezoelectric smart beam. Compared with the simple genetic algorithm based LQR vibration active control algorithm, the LQR vibration active control algorithm achieves a stable time and has better control effects .