Modeling and Control of Vibration in Mechanical Structures

All mechanical systems exhibit vibrational response when exposed to exter-nal disturbances. In many engineering applications vibrations are undesir-able and may even have harmful effects. Therefore, control of mechanicalvibration is an important topic and extensive research has been going on inthe field over the years.In active control of vibration, the ability to actuate the system in a controlledmanner is incorporated into the structure. Sensors are used to measure thevibrations and secondary inputs to the system are used to actuate the flexiblebody in order to obtain some desired structural response.In this thesis, feedback and feedforward control of active structures are ad-dressed. The thesis is divided into four parts. The first part contains ageneral introduction to the subject of active vibration control and also pro-vides an outline of the thesis.The second part of the thesis treats modeling and feedback control of a beamsystem with strain sensors and piezoelectric actuators. Physical modelingand system identification techniques are utilized in order to obtain a loworder parametric model that is suitable for controller design.The third part introduces the concept of a mechanical wave diode, whichis based on feedforward control. A controller is derived on the basis ofequations that describe elastic waves in bars. The obtained controller isshown to have poor noise properties and is therefore modified and furtheranalyzed. The final part of the thesis treats the same type of wave diode system aspart three, but with more general feedforward filters. Especially, a controllerbased on Wiener filter theory is derived and shown to drastically improvethe performance of the mechanical wave diode. List of Publications The thesis is based on the following publications, which will be referred toin the following order:[I] PETER NAUCLÉR, HANS NORLANDER, ANDERS JANSSON ANDTORSTEN SÖDERSTRÖM, Modeling and Control of a ViscoelasticPiezolaminated Beam, Proc. 16th IFAC World Congress, Prague,Czech Republic, July 3-8, 2005. [II] PETER NAUCLÉR, BENGT LUNDBERG AND TORSTEN SÖDERSTRÖM,A Mechanical Wave Diode: Using Feedforward Control for One-WayTransmission of Elastic Extensional Waves, Submitted to IEEETransactions on Control Systems Technology, 2005. [III] PETER NAUCLÉR AND TORSTEN SÖDERSTRÖM, Polynomial Feed-forward Design Techniques for a Mechanical Wave Diode System,Submitted to Control Engineering Practice, 2005. A version of Paper I was also presented asPETER NAUCLÉR, HANS NORLANDER, ANDERS JANSSON ANDTORSTEN SÖDERSTRÖM, Modeling and Control of a ViscoelasticPiezolaminated Beam, Preprint of Reglermöte, Gothenburg, Sweden,May 26-27, 2004.