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首页> 外文期刊>Journal of Sound and Vibration >OPTIMAL SENSOR/ACTUATOR PLACEMENT FOR ACTIVE VIBRATION CONTROL USING EXPLICIT SOLUTION OF ALGEBRAIC RICCATI EQUATION
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OPTIMAL SENSOR/ACTUATOR PLACEMENT FOR ACTIVE VIBRATION CONTROL USING EXPLICIT SOLUTION OF ALGEBRAIC RICCATI EQUATION

机译：代数ricicati方程的显式求解用于主动振动控制的最佳传感器/执行器位置

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摘要

This paper deals with an optimal placement problem of sensors and actuators for active vibration control of flexible structures. For undamped structures with collocated rate sensors and actuators, two solutions of generalized algebraic Riccati equations (generalized control algebraic Riccati equation, GCARE; generalized filtering algebraic Riccati equation, GFARE) are obtained explicitly. Employing these explicit solutions, we can obtain a stabilizing H_(∞) controller based on the normalized coprime factorization approach without solving any algebraic Riccati equations numerically. Generally, in a optimal sensor/actuator placement problem with a model-based control law (LQG or H_(∞)), the feedback controller needs to be obtained for all candidates of the optimal placement (which may be derived with some numerical optimization techniques) by solving algebraic Riccati equations numerically. Therefore, the amount of computation required to determine the optimal sensor/actuator placement and the controller increases rapidly for large-scale structures which have many pairs of sensor/actuators. The H_(∞) controller in this paper can be obtained just by addition and multiplication of several matrices. Furthermore, a closed-loop property on H_(∞) norm is automatically bounded for all candidates of the optimal placement. Hence, we can formulate the optimal sensor/actuator placement problem to optimize other closed-loop properties (norm of the closed-loop system) with less computational requirement than the model-based method mentioned above. The gradient of the H_(2) norm of the closed-loop system, which is necessary for a descent-based optimization technique, is derived. Using this sensitivity formula, we obtain the optimal placements of two pairs of sensors and actuators which minimize the H_(2) norm of the closed-loop system for a simply supported beam by the quasi-Newton method. The simulation results show the effectiveness of the proposed design method.
机译：本文探讨了用于柔性结构主动振动控制的传感器和执行器的最佳放置问题。对于具有并置速率传感器和执行器的无阻尼结构，明确获得了广义代数Riccati方程（广义控制代数Riccati方程，GCARE;广义滤波代数Riccati方程，GFARE）的两个解。利用这些显式解，我们可以基于归一化的互质分解方法获得稳定的H_（∞）控制器，而无需数值求解任何代数Riccati方程。通常，在具有基于模型的控制律（LQG或H_（∞））的最佳传感器/执行器放置问题中，需要为最佳放置的所有候选对象获取反馈控制器（可以使用一些数值优化技术来得出该反馈控制器） ）通过数值求解代数Riccati方程。因此，对于具有许多对传感器/执行器的大型结构，确定最佳传感器/执行器位置和控制器所需的计算量迅速增加。本文中的H_（∞）控制器仅需通过几个矩阵的加法和乘法即可获得。此外，H_（∞）范数上的闭环性质会自动约束到最佳位置的所有候选者。因此，我们可以制定最佳传感器/执行器放置问题，以比上述基于模型的方法更少的计算需求来优化其他闭环特性（闭环系统的范数）。得出了基于下降的优化技术所必需的闭环系统H_（2）范数的梯度。使用此灵敏度公式，我们通过准牛顿法获得了两对传感器和执行器的最佳位置，该位置使简单支撑梁的闭环系统的H_（2）范数最小。仿真结果表明了该设计方法的有效性。

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