## Controlling Parametric Resonance: Induction and Stabilization of Unstable Motions

Publication: Research - peer-review › Book chapter – Annual report year: 2012

### Standard

**Controlling Parametric Resonance : Induction and Stabilization of Unstable Motions.** / Galeazzi, Roberto; Pettersen, Kristin Ytterstad.

Publication: Research - peer-review › Book chapter – Annual report year: 2012

### Harvard

*Parametric Resonance in Dynamical Systems.*vol. 4, Springer, pp. 305-327. DOI: 10.1007/978-1-4614-1043-0_15

### APA

*Parametric Resonance in Dynamical Systems*(Vol. 4, Chapter 15, pp. 305-327). Springer. DOI: 10.1007/978-1-4614-1043-0_15

### CBE

### MLA

*Parametric Resonance in Dynamical Systems.*Chapter 15, Springer. 2012. 305-327. Available: 10.1007/978-1-4614-1043-0_15

### Vancouver

### Author

### Bibtex

}

### RIS

TY - CHAP

T1 - Controlling Parametric Resonance

T2 - Induction and Stabilization of Unstable Motions

AU - Galeazzi,Roberto

AU - Pettersen,Kristin Ytterstad

PY - 2012

Y1 - 2012

N2 - Parametric resonance is a resonant phenomenon which takes place in systems characterized by periodic variations of some parameters. While seen as a threatening condition, whose onset can drive a system into instability, this chapter advocates that parametric resonance may become an advantage if the system undergoing it could transform the large amplitude motion into, for example, energy. Therefore the development of control strategies to induce parametric resonance into a system can be as valuable as those which aim at stabilizing the resonant oscillations. By means of a mechanical equivalent the authors review the conditions for the onset of parametric resonance, and propose a nonlinear control strategy in order to both induce the resonant oscillations and to stabilize the unstable motion. Lagrange’s theory is used to derive the dynamics of the system and input–output feedback linearization is applied to demonstrate the feasibility of the control method.

AB - Parametric resonance is a resonant phenomenon which takes place in systems characterized by periodic variations of some parameters. While seen as a threatening condition, whose onset can drive a system into instability, this chapter advocates that parametric resonance may become an advantage if the system undergoing it could transform the large amplitude motion into, for example, energy. Therefore the development of control strategies to induce parametric resonance into a system can be as valuable as those which aim at stabilizing the resonant oscillations. By means of a mechanical equivalent the authors review the conditions for the onset of parametric resonance, and propose a nonlinear control strategy in order to both induce the resonant oscillations and to stabilize the unstable motion. Lagrange’s theory is used to derive the dynamics of the system and input–output feedback linearization is applied to demonstrate the feasibility of the control method.

U2 - 10.1007/978-1-4614-1043-0_15

DO - 10.1007/978-1-4614-1043-0_15

M3 - Book chapter

SN - 978-1-4614-1042-3

VL - 4

SP - 305

EP - 327

BT - Parametric Resonance in Dynamical Systems

PB - Springer

ER -