Abstract
This paper solves the problem of exact computation of the phase and gain margins of multivariable control systems. These stability margins are studied using the concept of the Davis–Wielandt shell of complex matrices. Calculation of the phase and gain margins requires solving a quadratically constrained quadratic program (QCQP) and a parametrized quadratically constrained problem, respectively, which are known to be difficult in general. The semidefinite relaxation (SDR) technique is often used as a computationally efficient approximation technique to solve QCQPs. It turns out that the QCQPs formulated from the phase and gain margin problems in this paper fall under the class of quadratic optimization problem, for which the SDR is exact. This is so in the sense that optimal values of the QCQP and its SDR are equal, and an optimal solution for the original QCQP problem can be obtained from an optimal solution of its SDR. Thus, we are able to propose computationally efficient algorithms to compute the phase and gain margins with an arbitrarily high precision. Numerical examples are given to illustrate the effectiveness of the proposed algorithms.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.