Design of PID controllers with H∞ performance index and for selective harmonic mitigation

Author(s)

Rafael Fernando Quirino Magossi

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Escola de Engenharia de São Carlos (EESC/SBD)
• Defense date: 2019-01-28

Examining board members

Vilma Alves de Oliveira; Grace Silva Deaecto; Flávio Andrade Faria

• Advisor: Vilma Alves de Oliveira

Abstract

Proportional + integral + derivative (PID) controllers are widely used in the industry due to their structure containing integral and derivative actions and for having a fixed order. In the literature, there are several methods for PID tuning. In this work it is presented a way to obtain PID tuning using a non-iterative H∞ design. This tuning is done using the state-space representation in the controllable canonical form. However, because it is a fixed-order controller, plant variations can significantly interfere with the desired performance and need to be compensated. Thus, it is also proposed to adapt the PID parameters so as to keep the closed-loop transfer function as close as possible to the nominal used in the tuning. For this, the control structure is modeled as an over-determined linear system with linear constraints, derived from stabilizing sets based on the Hurwitz signature concept, and a quadratic optimization method is used to obtain the controller parameters. In order to circumvent the conservatism of the norm H∞, a method to mitigate only the effect of selected harmonics on the output of the system is also proposed, constraining the sensitivity function of the system which is represented by ellipses in the stabilizing gains locus of the PID. Simulations in Matlab, Simulink and PSIM softwares were used to validate the proposed models and methodologies. Experimental results demonstrated the effectiveness of the harmonic mitigation method in a boost DC–DC converter. (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