Fractional Calculus is usually applied to control systems by means of the well-known PIλDμ scheme, which adopts integral and derivative components of non-integer orders λ and µ. An alternative approach is to add equally distributed fractional-order terms to the PID scheme instead of replacing the integer-order terms (Distributed Order PID, DOPID). This work analyzes the properties of the DOPID scheme with five terms, that is the PII1/2DD1/2 (the half-integral and the halfderivative components are added to the classical PID). The frequency domain responses of the PID, PIλDμ and PII1/2DD1/2 controllers are compared, then stability features of the PII1/2DD1/2 controller are discussed. A Bode plot-based tuning method for the PII1/2DD1/2 controller is proposed and then applied to the position control of a mechatronic axis. The closed-loop behaviours of PID and PII1/2DD1/2 are compared by simulation and by experimental tests. The results show that the PII1/2DD1/2 scheme with the proposed tuning criterium allows remarkable reduction in the position error with respect to the PID, with a similar control effort and maximum torque. For the considered mechatronic axis and trapezoidal speed law, the reduction in maximum tracking error is −71% and the reduction in mean tracking error is −77%, in correspondence to a limited increase in maximum torque (+5%) and in control effort (+4%).

Fractional-Order PII1/2DD1/2 Control of a Mechatronic Axis: Influence of the Discrete-Time Approximation of the Half-Order Derivative and Integral.

Bruzzone, Luca;Nodehi, Shahabedin
2022-01-01

Abstract

Fractional Calculus is usually applied to control systems by means of the well-known PIλDμ scheme, which adopts integral and derivative components of non-integer orders λ and µ. An alternative approach is to add equally distributed fractional-order terms to the PID scheme instead of replacing the integer-order terms (Distributed Order PID, DOPID). This work analyzes the properties of the DOPID scheme with five terms, that is the PII1/2DD1/2 (the half-integral and the halfderivative components are added to the classical PID). The frequency domain responses of the PID, PIλDμ and PII1/2DD1/2 controllers are compared, then stability features of the PII1/2DD1/2 controller are discussed. A Bode plot-based tuning method for the PII1/2DD1/2 controller is proposed and then applied to the position control of a mechatronic axis. The closed-loop behaviours of PID and PII1/2DD1/2 are compared by simulation and by experimental tests. The results show that the PII1/2DD1/2 scheme with the proposed tuning criterium allows remarkable reduction in the position error with respect to the PID, with a similar control effort and maximum torque. For the considered mechatronic axis and trapezoidal speed law, the reduction in maximum tracking error is −71% and the reduction in mean tracking error is −77%, in correspondence to a limited increase in maximum torque (+5%) and in control effort (+4%).
2022
978-3-031-04869-2
File in questo prodotto:
File Dimensione Formato  
Fractional-Order_PII12DD12_Control_Theoretical_Asp.pdf

accesso aperto

Descrizione: Contributo in atti di convegno
Tipologia: Documento in versione editoriale
Dimensione 2.65 MB
Formato Adobe PDF
2.65 MB Adobe PDF Visualizza/Apri

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/11567/1092434
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? ND
social impact