Vibrations is a common problem in mechanical structures, particulary in flexible parts, for instance aircraft wings or robot arms. This can be avoided if the flexibility is reduced by making such parts strong or heavy enough. For many applications, e.g. in aircrafts and spacecrafts (satellites), it is desirable to keep the weight as low as possible, which makes such solutions less suitable. Instead one would like to have a device which can perform active damping of the vibrations without any substantial increase of the mass. In the case when such a device is embedded in the material of the structure it is often referred to as a smart material or a smart structure.

One way to design smart structures is to use piezoelectric elements that are attached to the material. Piezoelectric elements exhibit a significant deformation when an electric field is applied, and they produce an electric field when deformed. Therefore they can be used both as actuators and sensors in a smart structure. When used as an actuator the input signal is the voltage over the piezoelectric element, which will tend to deform and thereby cause a strain in the material it is attached to, and when used as a sensor the output signal is the voltage caused by the deformation, which in its turn is caused by the strain in the material.

In this project we study different control strategies for smart structures, i.e., how the input signals should be chosen to achieve good performance, not only to dampen vibrations, but also to prevent wave propagation along a structure. The latter include the design of a "mechanical wave diode" which is based on feedforward control. Other utilizations of smart structures are also considered, e.g. stabilization and wave forming. Here we investigate how to choose the input signal to the piezoelectric elements in order to generate pulses with prescribed shape. The work is both theoretical and practical in the sense that theoretical results will be tested and validated both in simulations and in experiments.

Another topic that has been investigated is efficient separation of overlapping waves in the presence of unknown disturbances.

The project is a co-operation with Solid Mechanics, Department of Materials Science, Uppsala University.

Participants from Systems and Control: Hans Norlander, Peter Nauclér, Torsten Söderström.

[1] Peter Karlsson, Hans Norlander, Anders Jansson and Torsten Söderström. Modeling and Control of a Viscoelastic Piezolaminated Beam, Preprint of Reglermöte, Gothenburg, Sweden, May 26-27, 2004.

[2] Peter Nauclér, Hans Norlander, Anders Jansson and Torsten Söderström. Modeling and Control of a Viscoelastic Piezolaminated Beam, Proc. of 16th IFAC World Congress on Automatic Control, Prague, Czech Republic, 2005.

[3] Peter Nauclér, Modeling and Control of Vibration in Mechanical Structures. Department of Information Technology, Licentiate thesis 2005-005, October 2005.

[4] Peter Nauclér, Bengt Lundberg and Torsten Söderström. A Mechanical Wave Diode: Using Feedforward Control for One-way Transmission of Elastic Extensional Waves, IEEE Transactions on Control Systems Technology, 15(4):715-724, July 2007.

[5] Peter Nauclér and Torsten Söderström. Polynomial Feedforward Design Techniques for a Mechanical Wave Diode System, Technical report 2007-025, Department of Information Technology, Uppsala University, 2007.

[6] Peter Nauclér and Torsten Söderström. Separation of One-dimensional Waves - a Stochastic Systems Approach, Proc. of 41st Asilomar Conference on Signals, Systems and Computers, Pacific Grove, USA, November 4-7, 2007.

[7] Peter Nauclér and Torsten Söderström. Separation of Waves Governed by the One-dimensional Wave Equation - a Stochastic Systems Approach. Mechanical Systems and Signal Processing, vol 23, no 3, pp 823-844, April 2009.

[8] Peter Nauclér and Torsten Söderström. On the Tradeoff Between Feedback Properties and Disturbance Attenuation for a Cantilever Beam System, Preprint of Reglermöte, Luleå, Sweden, June 3-5, 2008.

[9] Peter Nauclér and Torsten Söderström. Polynomial Feedforward Design Techniques for a Mechanical System with Marginally Stable Inverse, Proc. of 17th IFAC World Congress, Seoul, Korea, July 6-11, 2008.

[10] Peter Nauclér. Estimation and Control of Resonant Systems with Stochastic Disturbances, Ph.D. Thesis, Department of Information Technology, Uppsala University, Uppsala, Sweden, 2008.

[11] Hans Norlander, Active Damping of a Viscoelastic beam: A Case Study, National Conference on Control (Reglermöte 2010), Lund, Sweden, June 8-9, 2010.