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  • Placement optimization of piezoelectric sensors in a clamped-free plate like solar panel on a LSS space Structure

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    Dr. Ijar M. Da Fonseca, Instituto Nacional de Pesquisas Espaciais (INPE), Brazil


    Prof. Peter M. Bainum, Howard University, United States



    Piezoelectric materials have the property to convert mechanical energy associated with elastic deformation to electrical energy and vice-versa. That kind of material can work as sensors and actuators on space structure aiming the elastic vibration damping. In designing spacecraft attitude and control subsystems (ACS) it may be required the study and analysis of the elastic vibration effects in the attitude motion depending on the mission pointing requirements. If piezoelectric sensors and/or actuators are chosen then the correct placement of the sensors and/or actuator on the elastic part of the structure is mandatory to guarantee a good performance of the ACS. The procedure to obtain the best placement for those devices is optimization. This paper deals with the placement optimization of PZT sensors on a solar panel for a Large Space Structure (LSS) in a low earth orbit (LEO) under the effect of the gravity-gradient torque. The LSS mathematical model is obtained by the Lagrangian formulation for generalized coordinates combined with Lagrangian formulation for quasi-coordinates. The assumed mode method is used to represent the elastic displacement so as to allow the whole equation of motion to be described by ordinary differential equations. The sensor placement optimization is carried out by using the NEWSUMT-A (New Sequential Unconstrained Minimization Technique) optimization software package combined with MATLAB computational environment, used for the attitude and elastic vibration control. The sequential programming is the optimization method implemented in that optimization software. A function relating the elastic deformation with the output energy associated with the PZT sensor is defined to determine the optimal placement of the sensor. A modified LQR technique is used to implement the whole system attitude and vibration control in which the state waiting matrix includes the sensor outputs. That state matrix is in general arbitrary but satisfying the positive semidefiniteness requirements. In this work it is still arbitrary but a new requirement is imposed on it by including the sensor outputs.
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    Manuscript document