Application of fractional calculus in iterative sliding mode synchronization control

• Autorzy: Zhang Xin , Wen-Ru Lu , Zhang Liang , Xu Wen-Bo

Identyfikatory

DOI

10.24425/aee.2020.133915

• Języki publikacji: EN

Abstrakty

EN

In order to control joints of manipulators with high precision, a position tracking control strategy combining fractional calculus with iterative learning control and sliding mode control is proposed for the control of a single joint of manipulators. Considering the coupling between joints of manipulators, a fractional-order iterative sliding mode crosscoupling control strategy is proposed and the theoretical proof of its progressive stability is given. The paper takes a two-joint manipulator as the research object to verify the control strategy of a single-joint manipulator. The results show that the control strategy proposed in this paper makes the two-joint mechanical arm chatter less and the tracking more accurate. The synchronous control of the manipulator is verified by a three-joint manipulator. The results show that the angular displacement adjustment times of the threejoint manipulator are 0.11 s, 0.31 s and 0.24 s, respectively. 3.25 s > 5 s, 3.15 s of a PD cross-coupling control strategy; 2.85 s, 2.32 s, 4.22 s of a PD iterative cross-coupling control strategy; 0.14 s, 0.33 s, 0.28 s of a fractional-order sliding mode cross-coupling control strategy. The root mean square error of the position error of the designed control strategy is 6.47 × 10−6 rad, 3.69 × 10−4 rad, 6.91 × 10−3 rad, respectively. The root mean square error of the synchronization error is 3.96×10−4 rad, 1.36×10−3 rad, 7.81×10−3 rad, superior to the other three control strategies. The results illustrate the effectiveness of the proposed control method.

Słowa kluczowe

EN

cross-coupling control; fractional calculus; iterative learning control; PD control; robot arm; sliding mode control

• Wydawca: Polish Academy of Sciences, Committee on Electrical Engineering
• Czasopismo: Archives of Electrical Engineering
• Rocznik: 2020
• Tom: Vol. 69, nr 3
• Strony: 499--519
• Opis fizyczny: Bibliogr. 22 poz., rys., tab., wz.

Twórcy

autor

Zhang Xin

• School of Automation & Electrical Engineering of Lanzhou Jiaotong University Lanzhou, 730070, China
• Gansu Provincial Engineering Research Center for Artificial Intelligence and Graphics and Image Processing, China

autor

Wen-Ru Lu

• School of Automation & Electrical Engineering of Lanzhou Jiaotong University Lanzhou, 730070, China

autor

Zhang Liang

• School of Automation & Electrical Engineering of Lanzhou Jiaotong University Lanzhou, 730070, China

autor

Xu Wen-Bo

• School of Automation & Electrical Engineering of Lanzhou Jiaotong University Lanzhou, 730070, China

Bibliografia

• [1] Shi X.P., Liu S.R., A survey of trajectory tracking control for robot manipulators, Control Engineering of China, vol. 18, no. 1, pp. 116–122 (2011).
• [2] Liu J.K., Design of robot control system and MATLAB simulation, Tsinghua University press (2008).
• [3] Hu S.B., Sliding mode control of nonlinear multi joint robot system, National Defense Industry Press (2015).
• [4] Chen Q., Luo P., Adaptive sliding mode control for electromechanical servo system with saturation compensation based on extended state observer, Journal of Systems Science and Mathematical Sciences, vol. 36, no. 10, pp. 1535–1547 (2016).
• [5] Li W.L., Shi X.H., Ke J., Engine torque pulsation simulation under idling speed based on sliding mode and iterative learning control, Journal of Vibration Measurement and Diagnosis, vol. 36, no. 2, pp. 359–365 (2016).
• [6] Yan L.Y., Ye P.Q., Zhang H., Disturbance rejection for linear motor based on multi-periodic learning variable structure control, Electric Machines and Control, vol. 21, no. 1, pp. 8–13 (2017).
• [7] Zhang Z., Ye D., Sun Z.W., Sliding mode fault tolerant attitude control for satellite based on iterative learning observer, Journal of National University of Defense Technology, vol. 40, no. 1, pp. 17–23 (2018).
• [8] Matusiak M., Ostalczyk P., Problems in solving fractional differential equations in a microcontroller implementation of an FOPID controller, Archives of Electrical Engineering, vol. 68, no. 3, pp. 565–577 (2019).
• [9] Yin C., Cheng Y., Zhong S.M., Fractional-order sliding mode-extremum seeking control design with fractional-order PI sliding surface, Control Conference, IEEE, pp. 539–544 (2015).
• [10] Zhang K.J., Peng G.H., Dou J.J., Robustness of PD∂ type iterative learning control for fractional-order linear time-delay systems, Science Technology and Engineering, vol. 453, no. 20, pp. 135–139 (2018).
• [11] Song S.M., Deng L.W., Chen X.L., Application characteristics of fractional calculus in sliding mode control, Journal of Chinese Inertial Technology, vol. 22, no. 4, pp. 439–444 (2014).
• [12] Koren Y., Cross-coupled biaxial computer controls for manufacturing systems, Journal of Dynamic Systems Measurement and Control, vol. 102, no. 4, pp. 265–272 (1980).
• [13] Xu W., Hou J., Yang W., Wang C., A double-iterative learning and cross-coupling control design for high-precision motion control, Archives of Electrical Engineering, vol. 68, no. 2, pp. 427–442 (2019).
• [14] Chu T.T., Research on robotic high precision tracking based on multiaxial coupling synchronized control, Harbin Institute of Technology (2015).
• [15] Zhong G., Shao Z., Deng H., Precise position synchronous control for multi-axis servo systems, IEEE Transactions on Industrial Electronics, vol. 64, no. 5, pp. 3707–3717 (2017).
• [16] Delavari H., Baleanu D., Sadati J., Stability analysis of caputo fractional-order nonlinear systems revisited, Nonlinear Dynamics, vol. 67, no. 4, pp. 2433–2439 (2012).
• [17] Dadras S., Momeni H.R., Fractional terminal sliding mode control design for a class of dynamical systems with uncertainty, Communications in Nonlinear Science and Numerical Simulation (S1007-5704), vol. 17, no. 1, pp. 367–377 (2012).
• [18] Devika K.B., Thomas S., Power rate exponential reaching law for enhanced performance of sliding mode control, International Journal of Control, Automation and System, vol. 15, no. 6, pp. 2636–2645 (2017).
• [19] Umarov S., Introduction to fractional and pseudo-differential equations with singular symbols, Springer International Publishing (2015).
• [20] Benito F.M., Rolando R., Anthony T., Carlos F., Application of fractional calculus to oil industry, Intech (2017).
• [21] Li Y., Chen Y.Q., Podlubny I., Technical communique: mittag-leffler stability of fractional order nonlinear dynamic systems, Automatica (S0005-1098), vol. 45, no. 8, pp. 1965–1969 (2009).
• [22] Tepljakov A., Petlenkov E., Belikov J., FOMCON: fractional-order modeling and control toolbox for MATLAB, International Conference Mixed Design of Integrated Circuits and Systems – Mixdes, IEEE, pp. 684–689 (2011).

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).