In this paper, we present a novel technique to design fixed structure controllers, for both continuous-time and discrete-time systems, through an H∞ mixed sensitivity approach. We first define the feasible controller parameter set, which is the set of the controller parameters that guarantee robust stability of the closed-loop system and the achievement of the nominal performance requirements. Then, thanks to Putinar positivstellensatz, we compute a convex relaxation of the original feasible controller parameter set and we formulate the original H∞ controller design problem as the non-emptiness test of a set defined by sum-of-squares polynomials. Two numerical simulations and one experimental example show the effectiveness of the proposed approach.

A Unified Framework for the H∞ Mixed-Sensitivity Design of Fixed Structure Controllers through Putinar Positivstellensatz / Razza, Valentino; Salam, Abdul. - In: MACHINES. - ISSN 2075-1702. - ELETTRONICO. - 9:8(2021), p. 176. [10.3390/machines9080176]

A Unified Framework for the H∞ Mixed-Sensitivity Design of Fixed Structure Controllers through Putinar Positivstellensatz

Razza, Valentino;Salam, Abdul
2021

Abstract

In this paper, we present a novel technique to design fixed structure controllers, for both continuous-time and discrete-time systems, through an H∞ mixed sensitivity approach. We first define the feasible controller parameter set, which is the set of the controller parameters that guarantee robust stability of the closed-loop system and the achievement of the nominal performance requirements. Then, thanks to Putinar positivstellensatz, we compute a convex relaxation of the original feasible controller parameter set and we formulate the original H∞ controller design problem as the non-emptiness test of a set defined by sum-of-squares polynomials. Two numerical simulations and one experimental example show the effectiveness of the proposed approach.
File in questo prodotto:
File Dimensione Formato  
machines-09-00176.pdf

accesso aperto

Tipologia: 2a Post-print versione editoriale / Version of Record
Licenza: Creative commons
Dimensione 940.5 kB
Formato Adobe PDF
940.5 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2918394