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Research Papers

Cluster Analysis and Switching Algorithm of Multi-Objective Optimal Control Design

[+] Author and Article Information
Zhi-Chang Qin

Department of Mechanics,
Tianjin University,
Tianjin 300072, China
e-mail: qinzhichang123@126.com

Jian-Qiao Sun

Fellow ASME
School of Engineering,
University of California,
Merced, CA 95343
e-mail: jqsun@ucmerced.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 7, 2016; final manuscript received August 12, 2016; published online September 30, 2016. Assoc. Editor: Lei Zuo.

J. Vib. Acoust 139(1), 011002 (Sep 30, 2016) (7 pages) Paper No: VIB-16-1110; doi: 10.1115/1.4034626 History: Received March 07, 2016; Revised August 12, 2016

The multi-objective optimal control design usually generates hundreds or thousands of Pareto optimal solutions. How to assist a user to select an appropriate controller to implement is a postprocessing issue. In this paper, we develop a method of cluster analysis of the Pareto optimal designs to discover the similarity of the optimal controllers. After we identify the clusters of optimal controllers, we develop a switching strategy to select controls from different clusters to improve the performance. Numerical and experimental results show that the switching control algorithm is quite promising.

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References

Figures

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Fig. 1

The block diagram of switching control

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Fig. 2

The relationship between number of clusters with the validity function for the system (11). The optimal number of clusters is Kopt = 3 when fv = 0.9204 is maximum.

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Fig. 3

Three clusters of the Pareto front marked by different symbols

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Fig. 4

The tracking error of the switching control. Magenta dash line represents case (a) in Table 1; red dot dash line represents case (b); black dot line represents case (c); and the blue real line represents the performance with the switching control.

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Fig. 5

The identification index (ID) Is(t) of the active PID control and the switching index π(t)

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Fig. 6

The relationship between number of clusters with the validity function for the system (19). The optimal number of clusters is Kopt = 7 when fv = 2.1646 is maximum.

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Fig. 7

Seven clusters of the Pareto front marked by different symbols

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Fig. 8

Simulated tracking response of the sliding mode control with the switching strategy in Sec. 3

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Fig. 9

Simulation results of the sliding surface and control force of the sliding mode control with the switching strategy in Sec. 3

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Fig. 10

Simulation results of the ID Is(t) of the sliding mode control and the switching index π(t)

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Fig. 11

The rotary flexible joint experimental setup made by Quanser

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Fig. 12

Experimental tracking response of the sliding mode control with the switching strategy in Sec. 3

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Fig. 13

Experimental results of the sliding surface and control force of the sliding mode control with the switching strategy in Sec. 3

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Fig. 14

Experiment results of the ID Is(t) of the sliding mode control and the switching index π(t)

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