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Research Papers

Stability and Performance Analysis of Time-Delayed Actuator Control Systems

[+] Author and Article Information
Bing Ai

Department of Computer Science,
University of Texas at Austin,
Austin, TX 78712
e-mail: bingai@cs.utexas.edu

Luis Sentis

Department of Mechanical Engineering,
University of Texas at Austin,
Austin, TX 78705
e-mail: lsentis@austin.utexas.edu

Nicholas Paine

Department of Mechanical Engineering,
University of Texas at Austin,
Austin, TX 78705
e-mail: npaine@utexas.edu

Song Han

Department of Computer Science and Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: song@engr.uconn.edu

Aloysius Mok

Department of Computer Science,
University of Texas at Austin,
Austin, TX 78712
e-mail: mok@cs.utexas.edu

Chien-Liang Fok

Department of Mechanical Engineering,
University of Texas at Austin,
Austin, TX 78705
e-mail: liangfok@utexas.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 8, 2015; final manuscript received December 14, 2015; published online March 10, 2016. Assoc. Editor: M. Porfiri.

J. Dyn. Sys., Meas., Control 138(5), 051005 (Mar 10, 2016) (20 pages) Paper No: DS-15-1164; doi: 10.1115/1.4032461 History: Received April 08, 2015; Revised December 14, 2015

Time delay is a common phenomenon in robotic systems due to computational requirements and communication properties between or within high-level and low-level controllers as well as the physical constraints of the actuator and sensor. It is widely believed that delays are harmful for robotic systems in terms of stability and performance; however, we propose a different view that the time delay of the system may in some cases benefit system stability and performance. Therefore, in this paper, we discuss the influences of the displacement-feedback delay (single delay) and both displacement and velocity feedback delays (double delays) on robotic actuator systems by using the cluster treatment of characteristic roots (CTCR) methodology. Hence, we can ascertain the exact stability interval for single-delay systems and the rigorous stability region for double-delay systems. The influences of controller gains and the filtering frequency on the stability of the system are discussed. Based on the stability information coupled with the dominant root distribution, we propose one nonconventional rule which suggests increasing time delay to certain time windows to obtain the optimal system performance. The computation results are also verified on an actuator testbed.

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Figures

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Fig. 1

Hypothetical robot control architecture

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Fig. 2

Possible root distribution of retarded LTI-TDS

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Fig. 3

RT of retarded LTI-TDS

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Fig. 6

Maximum tolerable latency of the system with filtering frequency of 1 Hz

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Fig. 7

Maximum tolerable latency of the system with filtering frequency of 25 Hz

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Fig. 8

Maximum tolerable latency of the system with filtering frequency of 50 Hz

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Fig. 9

Maximum tolerable latency of the system with filtering frequency of 150 Hz

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Fig. 10

Optimal tolerable latency of the system with different filtering frequencies

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Fig. 11

Maximum tolerable latency of the system with different filtering frequencies

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Fig. 5

UT actuator testbed with displacement delay

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Fig. 4

Actuator model with external force and actuator force: (a) schematic and (b) model

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Fig. 12

Optimal dominant root of the system

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Fig. 21

Stability map and the NU roots for the two-delay system with (KD,Kυ,fυ)=(14,553,2610,50)

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Fig. 22

Stability maps for the system with different filtering frequencies with controller gains (KD,Kυ)=(14,553,2610)

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Fig. 23

Stability maps for the system with different filtering frequencies with controller gains (KD,Kυ)=(130,979,10,331)

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Fig. 24

Stability maps for the system with different filtering frequencies with controller gains (KD,Kυ)=(363,833,18,051)

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Fig. 25

Stability maps for the system with different filtering frequencies with controller gains (KD,Kυ)=(1,455,332,37,353)

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Fig. 26

Area of MSA of the system for varying filtering frequency with different control gain combinations

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Fig. 27

Relationship between the optimal dominant root and filtering frequency

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Fig. 28

Dominant root and step responses of the system with (KD,Kυ,fυ)=(130,979,10,331,50)

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Fig. 29

UT actuator testbed. A motor drives a ball screw via a belt reduction. A sensor measures the linear displacement of the actuator.

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Fig. 13

Optimal dominant root of the system using different filtering frequencies

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Fig. 14

Optimal delay of the system using different filtering frequencies

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Fig. 15

Step response of the system using different latencies with (KD,Kυ,fυ)=(14,553,2610,50)

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Fig. 19

Three-dimensional graphic solution for the two-delay system with (KD,Kυ,fυ)=(14,553,2610,50)

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Fig. 20

The kernel and its root tendencies of the two-delay system with (KD,Kυ,fυ)=(14,553,2610,50)

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Fig. 16

Step response of the system using different latencies with (KD,Kυ,fυ)=(14,553,2610,121)

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Fig. 17

Root distribution of the system using different latencies with (KD,Kυ,fυ)=(14,553,2610,121)

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Fig. 18

UT actuator testbed with displacement and velocity delays

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Fig. 30

Stability of the system under different displacement-feedback delays with  (KD,Kυ,fυ)=(1,290,000,22,000,100)

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Fig. 31

Step responses of the system under different displacement-feedback delays with (KD,Kυ,fυ)=(1,290,000,22,000,100)

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Fig. 32

Stability of the system under different displacement and velocity feedback delays with (KD,Kυ,fυ)=(130,979,10,331,50)

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Fig. 33

Stability of the system under different displacement and velocity feedback delays with (KD,Kυ,fυ)=(363,833,18,051,50)

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Fig. 34

Step responses of the system under different latency combinations with fυ=50  Hz

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