Integrated topology optimization and optimal control for vibration suppression in structural design

This paper presents a topology design methodology for structures with active vibration control. The methodology takes into account the structural effect of the control forces and includes the modal control design. Location points for the actuation forces are chosen a priori. Structural topology optimization is used for distributing material on a fixed domain, using continuum finite element discretization for the static and free vibration analyses. Optimal control for transient response in modal space is used to derive the control force. The cost function for the optimization combines the strain energy and the control energy. Results of the numerical simulations validates the proposed methodology.

[1]  Noboru Kikuchi,et al.  Integrated optimal structural and vibration control design , 1996 .

[2]  Z. Kang,et al.  Topology optimization of space vehicle structures considering attitude control effort , 2009 .

[3]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[4]  Ole Sigmund,et al.  Optimization of piezoelectric bimorph actuators with active damping for static and dynamic loads , 2009 .

[5]  Jun Sergio Ono Fonseca,et al.  Simultaneous Piezoelectric Actuator and Sensor Placement Optimization and Control Design of Manipulators with Flexible Links Using SDRE Method , 2010 .

[6]  D. Naidu,et al.  Optimal Control Systems , 2018 .

[7]  Ole Sigmund,et al.  A 99 line topology optimization code written in Matlab , 2001 .

[8]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[9]  R. Haftka,et al.  Elements of Structural Optimization , 1984 .

[10]  K. Bathe.  Finite Element Procedures , 1995 .

[11]  Noboru Kikuchi,et al.  Optimal design of controlled structures , 1996 .

[12]  M. Bendsøe,et al.  Material interpolation schemes in topology optimization , 1999 .

[13]  Dong Sun,et al.  A PZT actuator control of a single-link flexible manipulator based on linear velocity feedback and actuator placement , 2004 .

[14]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[15]  S. Narayanan,et al.  Active vibration control of beams with optimal placement of piezoelectric sensor/actuator pairs , 2008 .

[16]  J. Fonseca,et al.  Complexity control in the topology optimization of continuum structures , 2003 .

[17]  N. Kikuchi,et al.  Solutions to shape and topology eigenvalue optimization problems using a homogenization method , 1992 .

[18]  Yaowen Yang,et al.  Integrated optimal design of vibration control system for smart beams using genetic algorithms , 2005 .

[19]  N. L. Pedersen.  Maximization of eigenvalues using topology optimization , 2000 .