Stabilization of the position of a circular membrane

✍ Scribed by E.K. Lavrovskii; A.M. Formal'skii

• Book ID: 104142551
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 514 KB
• Volume: 61
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(97)00056-7

✦ Synopsis

A uniform circular me:mbrane, the edges of which are damped to a large, absolutely rigid ring, is considered. In its tmdeformed state, the membrane lies in the same plane as the ring. One-dimensional displacements of the ring and membrane in a direction perpendicular to that plane are investigated. The problem of stabilizing the state of the system by means of an external control force operating in that direction on the ring is studied. Stabilizing control is realized by linear feedback with respect to the displacement and velocity of the ring, and the integral of the displacement and deformations of the membrane. Allowance is made for a delay in the control loop. The stability of the control process is considered, and the regions of asymptotic stability of the desired position of equih'brium of the membrane in the space of the feedback coefficients are found.