Convex Synthesis of SNI Controllers Based on Frequency-Domain Data: MEMS Nanopositioner Example
Nastaran Nikooienejad, S. O. Reza Moheimani
Abstract
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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{2}$ </tex-math></inline-formula> 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.