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Research Papers

Temperature Control of a Cutting Process Using Fractional Order Proportional-Integral-Derivative Controller

[+] Author and Article Information
Mahsan Tavakoli-Kakhki

e-mail: mah_tavakoli@ee.sharif.edu

Mohammad Haeri1

e-mail: haeri@sina.sharif.edu Advanced Control System Laboratory, Electrical Engineering Department,  Sharif University of Technology, Tehran 1458889694, Iran

1

Corresponding author.

J. Dyn. Sys., Meas., Control 133(5), 051014 (Aug 24, 2011) (10 pages) doi:10.1115/1.4004059 History: Received October 30, 2010; Revised March 05, 2011; Accepted March 14, 2011; Published August 24, 2011; Online August 24, 2011

In this paper, the fractionalized differentiating method is implemented to reduce commensurate fractional order models complexity. The prominent properties of this method are its simplicity and guarantee of preserving the stability of a specific class of fractional order models in their reduced counterparts. The presented reduction method is employed in simplifying complicated fractional order controllers to a fractional order PID (FOPID) controller and proposing tuning rules for its parameters adjustment. Finally, the efficiency of the FOPID tuning rule obtained based on the proposed reduction method is shown in the temperature control of a cutting process.

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Figures

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Figure 3

Bode diagrams of C1(s) (bold solid), and the reduced models C1D(s) (dotted), C1DP(s) (dashed), C1DSP(s) (dashed dotted), and C1DRI(s) (solid)

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Figure 4

Step response and control signal of the closed loop system obtained by implementing the controllers C(s) (bold solid), CrD(s) (dotted), CrDP(s) (dashed), CrDSP(s) (dashed dotted), and CrDRI(s) (solid) (a, c) wide scope and (b, d) zoomed plot

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Figure 5

Reference tracking and load disturbance rejection by FOPID controller 42

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Figure 6

Representation of a cutting process by turning. The four parts of the system are (A): tool insert, (B): tool holder, (C): workpiece, (D): chips [29].

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Figure 7

Three heat sources in a cutting process

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Figure 8

(a) A sample insert tool and insert holder [29]; (b) schematic of the identification experiment [9]

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Figure 9

Closed loop control system for temperature control of a cutting process

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Figure 10

Appropriate step response and slow load disturbance rejection by FOPID controller 46

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Figure 11

Appropriate load disturbance rejection and oscillatory reference tracking by FOPID controller 49

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Figure 1

Stability and instability regions of a commensurate fractional order system with (a) commensurate order 0<α<1 and (b) commensurate order 1≤α<2

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Figure 2

Configuration of a closed loop control system

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