Eigenvalue Assignment of a Nonlinear Electromagnetic System by the Receptance Method: Theory and Experiment

This paper presents experimental and numerical active vibration control of a nonlinear system for eigenvalue assignment and active damping, using receptance method. A nonlinear electromagnetic setup consist of two identical coils, two magnets and a cantilever beam has been built for this purpose. By varying the electrical current and distance between the two coils, nonlinear cubic stiffness with various strengths obtained. Active damping control performed experimentally in order to validate the performance of control method on the designed nonlinear setup. For eigenvalue assignment, first, receptance of the open loop system is experimentally measured by varying electrical currents and the coil distance to define the effect of parameter variations on the system’s FRF. Next step involved developing an iterative Sherman-Morrison formula to obtain the feedback control gains for the eigenvalue assignment. This step was challenging due to the amplitude dependence and also instability and jump phenomena that exist in the nonlinear FRFs. Increasing excitation level causes strong nonlinear effects in closed loop receptance, as shown by simulation. In the end, a stability analysis is conducted and discussed to prevent instability during the eigenvalue assignment process. Considered method effectively assigned poles and ensured the stability of the system under different conditions.