LAUSR

We report a procedure to design fixed-structure strictly negative imaginary (SNI) controllers for collocated, highly resonant systems based on frequency response data. We formulate the problem in a two-input two-output (TITO) framework that includes robustness and stability constraints. The controller synthesis is cast as a convex optimization problem using convex approximation techniques. The measured frequency response of a two-degree-of-freedom (2-DOF) microelectromechanical system (MEMS) nanopositioner is used to compute the frequency response of the controller by minimizing the difference between the actual and desired closed-loop responses in an $H_{2}$ sense. By including the negative imaginary (NI) stability criterion as a constraint in the optimization algorithm, closed-loop stability is guaranteed. Performance of the synthesized controllers is verified in time and frequency domains through closed-loop experiments with the MEMS nanopositioner.