Study on Analysis and Avoidance of Unstable Control for Flexible System Design

  • G. Q. ZhaiEmail author
  • R. Y. K. Zhang
  • F. W. Meng
  • Z. Y. Liu
  • S. Liu
  • X. R. Yan
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 582)


It is difficult to design the control law for flexible systems with multiple lightly damped modes. Particularly, when there exist parameter perturbations, for example, resonant frequency or damping ratio etc., the stability of the system cannot be guaranteed. Conventionally, the control design of the flexible system is only stabilization design, without considering the performance requirement of the system. For the H control, even the famous H loop shaping method proposed by McFarlaned, cannot improve further the performance of the system. Instead, the resulting controller is unstable, with is not easy to tune on in practice. In the proposed, the system bandwidth is chosen as the performance index for the H optimal control. The robustness of the system is further improved by considering the performance of the system. Furthermore, the controller is stable, i.e., the H strong stabilization problem is resolved. With this design, the control accuracy and the speed of response is improved, and also the controller can be tuned on easily. The proposed work is important for the application of flexible structures in the real world.


Flexible system H control Optimal design Weighting function Satellite attitude control 



Manuscript received April 7, 2018. This work was supported in part by the Doctoral Foundation of Liaoning Province (No. 20170520333), the Fundamental Research Funds for the Central Universities (No. N182304010), the Doctoral Foundation of Hebei Province (No. F2019501012).


  1. 1.
    Chen, L., Yan, Y., Mu, C., Sun, C.Y.: Characteristic model-based discrete-time sliding mode control for spacecraft with variable tilt of flexible structures.IEEE/CAA J. Automat. Sin. 3(1), 42 (2016)Google Scholar
  2. 2.
    Zhao, C., Guo, H.W., Deng, Z.Q., et al.: Structure design and performance evaluation of variable configuration truss-type satellite platform. J. Harbin Inst. Technol. 50(1), 11 (2018)Google Scholar
  3. 3.
    Tan, T.L.: State transition control of satellite attitude. Control Theor. Appl. 34(5), 655 (2017)MathSciNetGoogle Scholar
  4. 4.
    Wu, Y.L., Li, J.J., Zeng, H.B., et al.: Robust H-infinity control design for spacecrafts with large flexible netted antennas. Control Theor. Appl. 30(3), 365 (2013)Google Scholar
  5. 5.
    Balini, H., Scherer, C.W., Witte, J.: Performance enhancement for AMB systems using unstable H controller crossovers. IEEE Trans. Control Syst. Technol. 19(6), 1479 (2011)Google Scholar
  6. 6.
    Cherubini, G., Chung, C.C., Messner, W.C., et al.: Control methods in data-storage systems. IEEE Trans. Control Syst. Technol. 20(2), 296 (2012)CrossRefGoogle Scholar
  7. 7.
    Lu, Y.S.: Internal model control of lightly damped systems subject to periodic exogenous signals. IEEE Trans. Control Syst. Technol. 8(3), 699 (2010)CrossRefGoogle Scholar
  8. 8.
    Sun, C.Y., He, W., Hong, J.: Neural network control of a flexible robotic manipulator using the lumped spring-mass model. IEEE Trans. Syst. Man Cybern. Syst. 47(8), 1863 (2017)CrossRefGoogle Scholar
  9. 9.
    Yang, Y.C., He, W., Li, X.J.: Reinforcement learning control of a single-link flexible robotic manipulator. IET Control Theor. Appl. 11(9), 1426 (2017)Google Scholar
  10. 10.
    Yang, J., Shao, R., Li, B., et al.: Iterative learning observer based robust output feedback tracking control for flexible manipulator. J. Harbin Eng. Univ. 39(2), 1 (2018)zbMATHGoogle Scholar
  11. 11.
    Liu, F.C., Gao, J.F., Jia, X.J.: Adaptive network control of flexible-joint space manipulator in task space under gravity effect. J. Astronaut. 36(12), 1391 (2015)Google Scholar
  12. 12.
    McFarlane, D., Glover, K.: Robust controller design using normalized coprime factor plant descriptions. Lecture Notes in Control and Information Sciences. Springer, New York, 138 (1989)Google Scholar
  13. 13.
    Meng, F.W., Lv, X.Y., Liu, Y.Q., et al.: Hydrothermal preparation and microstructure analysis of silver tin oxide contact materials. Control Decis. 33(2), 371 (2018)Google Scholar
  14. 14.
    Meng, F.W., He, Z., Wang, G.X., et al.: Control design of flexible systems and H-infinity loop-shaping method. Control Theor. Appl. 30(8), 1014 (2013)Google Scholar
  15. 15.
    Nie, J., Conway, R., Horowitz, R.: Optimal H control for linear periodically time-varying systems in hard disk drives. IEEE/ASME Trans. Mechatron. 18(1), 212 (2013)CrossRefGoogle Scholar
  16. 16.
    He, Z., Meng, F.W., Liu, W., et al.: Robustness of H loop shaping design. Acta Automatica Sin. 36(6), 890 (2010)MathSciNetCrossRefGoogle Scholar
  17. 17.
    He, Z., Jiang, X.M., Meng, F.W., et al.: μ-synthesis in H loop-shaping design. Control Theor. Appl. 29(3), 347 (2012)Google Scholar
  18. 18.
    Franklin, G.F., Powell, J.D., Emami-Naeini, A.: Feedback Control of Dynamic Systems (Fourth Edition). Pearson Education, Beijing (2003)zbMATHGoogle Scholar
  19. 19.
    Meng, F.W., Pang, A.P., Dong, X., et al.: H optimal performance design of an unstable plant under Bode integral constraint. Complexity (Bio-Inspired Learning and Adaptation for Optimization and Control of Complex Systems) (2018)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • G. Q. Zhai
    • 1
    Email author
  • R. Y. K. Zhang
    • 1
  • F. W. Meng
    • 1
  • Z. Y. Liu
    • 1
  • S. Liu
    • 1
  • X. R. Yan
    • 1
  1. 1.School of Control EngineeringNortheastern University at QinhuangdaoQinhuangdaoChina

Personalised recommendations