Stabilizing Set and Phase Margin Computation for Resonant Controllers

Author(s)

Magossi, Rafael F. Q. ; Oliveira, Vilma A. ; Machado, Ricardo Q. ; Bhattacharyya, Shankar P. ; IEEE

• Document type: Journal article
• Source: 2019 IEEE 58TH CONFERENCE ON DECISION AND CONTROL (CDC); v. N/A, p. 6-pg., 2019-01-01.

Abstract

In this work, we present the computation of the complete stabilizing set for a general three-terms resonant controller which includes the proportional-resonant (PR) controller commonly used in grid-connected voltage source inverter solutions. The stabilizing set is based on the generalization of the Hermite-Biehler theorem which provides the concept of signature for polynomials. Using the signature concept, the stabilizing set can be computed by linear programming methods. Phase margin and gain crossover frequency specifications are commonly used in the design of PR controllers. Therefore, we also present a procedure to find the controller which provides the prescribed phase margin and gain crossover frequency, as well a prediction for the corresponding gain margin. In order to illustrate the design, numerical examples are presented. (AU)

• FAPESP's process: 16/21120-2 - Tuning an adaptive PID controller obtained via linear optimization with constraints and pointwise Thévenin equivalent
• Grantee: Rafael Fernando Quirino Magossi
• Support Opportunities: Scholarships in Brazil - Master
• FAPESP's process: 17/21577-5 - Use of stabilizers sets as linear constraints to obtain the gains of a PID controller obtained via quadratic optimization
• Grantee: Rafael Fernando Quirino Magossi
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• FAPESP's process: 14/50851-0 - INCT 2014: National Institute of Science and Technology for Cooperative Autonomous Systems Applied in Security and Environment
• Grantee: Marco Henrique Terra
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 16/25017-1 - Measurement-Based Control and Its Applications
• Grantee: Vilma Alves de Oliveira
• Support Opportunities: Regular Research Grants