Control of the elastodynamic vibrations of a ¯exible slider±crank mechanism using m- synthesis Mansour A. Karkoub* College of Engineering and Petroleum, Mechanical and Industrial Engineering Department, Kuwait University, Kuwait Received 4 December 1998; received in revised form 14 September 1999; accepted 10 October 1999 Abstract Suppression of the elastodynamic vibrations of a slider±crank mechanism with a very ¯exible connecting rod is addressed in this paper. A model for the mechanism is derived using Euler±Lagrange equations and the assumed modes method. The control action uses two feedback signals: the crank angle and the connecting rod coupler midpoint de¯ection. The actuator is located at the crank ground joint. This arrangement of actuators and sensors has been proven to be very eective. Two control schemes are proposed for the control of the ¯exible slider±crank mechanism. One scheme is a simple PD control scheme with feedback linearization. The second scheme is based on the m-synthesis control technique. Both the m-synthesis control scheme and the PD control scheme yielded good results. However, in terms of robustness, the results achieved via the m-synthesis control design are better than those achieved with the PD control scheme. 7 2000 Elsevier Science Ltd. All rights reserved. 1. Introduction Four-bar mechanisms are widely used in machinery such as photocopiers card feeders, engines, pumps, etc. One of the many contemporary design objectives of 0957-4158/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S0957-4158(99)00083-5 Mechatronics 10 (2000) 649±668 * Tel.: +965-481-1188 x5884; fax: +965-484-7131. E-mail address: mansourk@kuc01.kuniv.edu.kw (M.A. Karkoub).