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Research Papers

Model Following Adaptive Sliding Mode Tracking Control Based on a Disturbance Observer for the Mechanical Systems

[+] Author and Article Information
Kun-Yung Chen

Department of Mechanical Engineering,
Air Force Institute of Technology,
No. 198, Jieshou W. Road,
Gangshan District,
Kaohsiung 820, Taiwan
e-mail: u9615906@nkfust.edu.tw

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 7, 2017; final manuscript received October 1, 2017; published online December 19, 2017. Assoc. Editor: Hashem Ashrafiuon.

J. Dyn. Sys., Meas., Control 140(5), 051012 (Dec 19, 2017) (15 pages) Paper No: DS-17-1242; doi: 10.1115/1.4038165 History: Received May 07, 2017; Revised October 01, 2017

A model following adaptive sliding mode tracking control (MFASMTC) with the adjustable control gain based on a disturbance observer (DOB) for the mechanical system is proposed in this paper. The control gains of the proposed controller are automatically adjusted to compensate the unknown time-varying disturbances by the DOB. First, the unknown variables and uncertainties are lumped as the disturbance terms and the system dynamic model consist of the nominal matrix and disturbances vector. The desired model and sliding mode controller (SMC) are integrated by using the Lyapunov function candidate to obtain the general model following sliding mode tracking control (MFSMTC) with the fixed control gain. To stabilize and compensate the unknown time-varying disturbances for the control system, a DOB is combined with the MFSMTC to obtain the MFASMTC to automatically adjust the control gains. The mass-spring-damper system and two-link manipulator robot system are both used as examples system to demonstrate the proposed control scheme, respectively. The comparisons between MFSMTC with the fixed control gain and MFASMTC with the adjustable control gain based on a DOB are performed in this paper. From the simulation results, the proposed MFASMTC with the adjustable control gain based on a DOB demonstrates the stable and robust control performance for the unknown uncertainties and external disturbances. The proposed control method also can be applied to the other mechanical systems with the desired model to find the desired model following adaptive sliding mode tracking control.

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Figures

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Fig. 1

Mass-spring-damper system

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Fig. 2

Block diagram of the MFASMTC based on a DOB for the mass-spring-damper system

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Fig. 3

A two-link manipulator robot system

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Fig. 4

Block diagram of the MFASMTC based on a DOB for the two-link manipulator robot system

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Fig. 5

Responses comparisons of the MFSMTC by using the fixed control gains ϕ=10 and ϕ=35: (a) displacement x1 versus time, (b) velocity x2 versus time, (c) control input u versus time, and (d) sliding surface function s versus time

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Fig. 6

Responses comparisons of the MFSMTC among the fixed control gains ϕ=10,ϕ=35 and real control gain ϕ∗: (a) comparisons between ϕ=10 and ϕ∗ and (b) comparisons between ϕ=35 and ϕ∗

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Fig. 7

Responses comparison of the MFASMTC based on a DOB for cases 1 and 2: (a) x1 versus time, (b) x2 versus time, (c) u versus time, (d) s versus time, (e) comparisons between ϕ̂ and ϕ* with case 1, and (f) comparisons between ϕ̂ and ϕ* with case 2

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Fig. 8

Responses comparison of the MFASMTC based on a DOB for cases 3 and 4: (a) x1 versus time, (b) x2 versus time, (c) u versus time, (d) s versus time, (e) comparisons between ϕ̂ and ϕ* with case 3, and (f) comparisons between ϕ̂ and ϕ* with case 4

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Fig. 9

Comparisons between MFSMTC and MFASMTC based on a DOB: (a) x1 versus time, (b) x2 versus time, (c) u versus time, (d) s versus time, (e) comparisons among ϕ*,ϕ̂ and ϕ, and (f) external impulse force fe versus time

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Fig. 10

Responses comparison for the arm 1 of the two-link manipulator robot system: (a) q1 versus time, (b) q˙1 versus time, (c) u1 versus time, and (d) s1 versus time

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Fig. 11

Comparisons between the real and estimated control gains ϕ1* and ϕ̂1

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Fig. 12

Responses comparison for the arm 2 of the two-link manipulator robot system: (a) q2 versus time, (b) q˙2 versus time, (c) u2 versus time, and (d) s2 versus time

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Fig. 13

Comparisons between the real and estimated control gains ϕ2* and ϕ̂2

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