Shape Control of a Flexible Mirror Using an Electron Gun

Abstract

Mirrors made of PVDF film are being considered for lightweight transportation and deployment in space. An array of electrodes can be used to distribute charges over the PVDF film for active shaping of the mirrors. This paper presents the derivation of a matrix that enables calculation of the shape of the two-dimensional mirror for any given electron distribution. Finite element simulation shows good agreement with a theoretical example. Furthermore, if a desired shape is given, the required voltage distribution can be computed using the singular value decomposition. Experiments were done in a vacuum vessel, where an electron gun was used to actuate a PVDF bimorph to a desired shape. Dynamic shape control is attainable at low frequencies. At higher frequencies, still significantly below structural resonance, actuation lag and parasitic DC offset can be significant problems that require future research to solve.

Deflection model for corner-supported plates with segmented in-plane actuators

“…Continuing theoretical research includes the development of an efficient inverse model and control algorithms to provide voltage distributions that effect desired shapes. This will build on previous analysis for edge-supported laminates in [21]. Finally, other issues to consider include the optimization of number and placement of actuator segments, as well as robust identification methods for the model parameters.…”

“…Then, given coefficients in (44) with w max = 382 µm, the least squares solution to the inverse problem is solved using the singular value decomposition [21]. Figure 5a illustrates the predicted deflection using 2048 expansion terms.…”

“…To facilitate computation, we can reduce the indices m and n into one index using several methods, such as sorting by natural frequency [21]. With single index j, the expansion has the form…”

“…Employing basis functions admissible for simple edge supports in (20) leads to the model developed in [21]. In this simplified case, an explicit expression for (41) is constructed in terms of the expansion…”

Shape and vibration control of active laminated plates for RF and optical applications

“…Because this research assumes the orthotropic properties of the PVDF film in developing the model it is expected that the results will be more accurate and realistic thereby increasing the practicality of implementation. Recently research has been conducted for the quasi-static shape control of the laminate [14,15,16]. The primary aim of this research is to include the dynamic case thus controlling the vibration and shape of the laminated plate.…”