Vibration control of a class of mechatronic systems using Negative Imaginary theory

Abstract

This paper proposes a new controller design methodology for a class of mechatronics systems that satisfy stable and minimum-phase Negative Imaginary (NI) property. The proposed methodology relies on the classical Internal Model Control (IMC) principle. The closed-loop stability of the proposed scheme depends only on the DC loop gain, which is theoretically established by the internal stability result of NI theory. In this scheme, the design problem of the IMC parameter (known as the Youla parameter) has been cast as a Negative Imaginary (NI) controller synthesis problem. We propose an LMI-based IMC design approach, which can be readily solved using the commercially available SDP solver packages. A frequency-domain design approach is also presented, which depends on the solution of a simple constrained least-square problem. An in-depth simulation case study on the vibration attenuation problem of a lightweight cantilever beam is executed to demonstrate the usefulness and potential application of the proposed NI-based IMC scheme.