Modal analysis of active flexible multibody systems containing PID controllers with non-collocated sensors and actuators

•Coupled mechanical and control system equations are expressed in second-order form.•n-Space eigensolvers can be used without damping and steady-state error elimination.•2n eigensolvers can be used with damping.•New 3n eigensolver method allows for both damping and steady-state error elimination.

A method for performing modal analysis of undamped active flexible multibody systems with collocated sensors and actuators in a finite element environment was recently developed by the authors. In this paper, the theory is further expanded to include systems with non-collocated sensors and actuators, damping and steady-state error elimination. The closed-loop eigenvalue problem for active flexible multibody systems with multiple-input multiple-output proportional-integral-derivative (PID) feedback type controllers and multiple degrees of freedom finite element models is solved.