| Title:
|
Parametric control to quasi-linear systems based on dynamic compensator and multi-objective optimization (English) |
| Author:
|
Gu, Da-Ke |
| Author:
|
Zhang, Da-Wei |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
56 |
| Issue:
|
3 |
| Year:
|
2020 |
| Pages:
|
516-542 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper considers a parametric approach for quasi-linear systems by using dynamic compensator and multi-objective optimization. Based on the solutions of generalized Sylvester equations, we establish the more general parametric forms of dynamic compensator and the left and right closed-loop eigenvector matrices, and give two groups of arbitrary parameters. By using the parametric approach, the closed-loop system is converted into a linear constant one with a desired eigenstructure. Meanwhile, it also proposes a novel method to realize multi-objective design and optimization. Multiple performance objectives, containing overall eigenvalue sensitivity, $H_2$ norm, $H_\infty$ norm and low compensation gain, are formulated by arbitrary parameters, then robustness and low compensation gain criteria are expressed by a comprehensive objective function which contains each performance index weighted. By utilizing degrees of freedom (DOFs) in arbitrary parameters, we can optimize the comprehensive objective function such that an optimized dynamic compensator is found to satisfy the robustness and low compensation gain criteria. Finally, an example of attitude control of combined spacecrafts is presented which proves the effectiveness and feasibility of the parametric approach. (English) |
| Keyword:
|
quasi-linear systems |
| Keyword:
|
parametric control |
| Keyword:
|
dynamic compensator |
| Keyword:
|
multi-objective design and optimization |
| Keyword:
|
utilize DOFs in parameter matrices |
| MSC:
|
93B51 |
| MSC:
|
93B52 |
| MSC:
|
93B60 |
| idZBL:
|
Zbl 07250735 |
| idMR:
|
MR4131741 |
| DOI:
|
10.14736/kyb-2020-3-0516 |
| . |
| Date available:
|
2020-09-02T09:24:35Z |
| Last updated:
|
2021-02-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148312 |
| . |
| Reference:
|
[1] Chang, J.: Dynamic compensator-based second-order sliding mode controller design for mechanical systems..IET Control Theory A 7 (2013), 13, 1675-1682. MR 3115112, 10.1049/iet-cta.2012.1027 |
| Reference:
|
[2] Chen, C. K., Lai, T. W., Yan, J. J., Liao, T. L.: Synchronization of two chaotic systems: Dynamic compensator approach..Chaos Soliton. Fract. 39 (2009), 15, 1055-1063. MR 2512914, 10.1016/j.chaos.2007.04.004 |
| Reference:
|
[3] Santos, J. F. S. Dos, Pellanda, P. C., Simões, A. M.: Robust pole placement under structural constraints..Syst. Control Lett. 116 (2018), 8-14. MR 3804535, 10.1016/j.sysconle.2018.03.008 |
| Reference:
|
[4] G.-R, Duan: Generalized Sylvester Equations - Unified Parametric Solutions..CRC Press Taylor and Francis Group, Boca Raton 2014. MR 3380768 |
| Reference:
|
[5] Duan, G.-R.: Parametric control of quasi-linear systems by output feedback..In: Proc. 14th International Conference on Control, Automation and Systems, IEEE Press, Gyeonggi-do 2014, pp. 928-934. 10.1109/iccas.2014.6987917 |
| Reference:
|
[6] Duan, G.-R., Yu, H.-H.: LMIs in Control Systems Analysis, Design and Applications..CRC Press Taylor and Francis Group, Boca Raton 2013. MR 3328859, 10.1201/b15060 |
| Reference:
|
[7] Gu, D.-K., Liu, G.-P., Duan, G.-R.: Parametric control to a type of quasi-linear second-order systems via output feedback..Int. J. Control 92 (2019), 2, 291-302. MR 3938071, 10.1080/00207179.2017.1350885 |
| Reference:
|
[8] Gu, D.-K., Zhang, D.-W., Duan, G.-R.: Parametric control to a type of quasi-linear high-order systems via output feedback..Eur. J. Control. 47 (2019), 44-52. MR 3948880, 10.1016/j.ejcon.2018.09.008 |
| Reference:
|
[9] Gu, D.-K., Zhang, D.-W., Duan, G.-R.: Parametric control to linear time-varying systems based on dynamic compensator and multi-objective optimization..Asian J. Control (2019). MR 4001112, 10.1002/asjc.2112 |
| Reference:
|
[10] Gu, D.-K., Zhang, D.-W.: Parametric control to second-order linear time-varying systems based on dynamic compensator and multi-objective optimization..App. Math. Comput. 365 (2020), 124681. MR 4001112, 10.1016/j.amc.2019.124681 |
| Reference:
|
[11] Hashem, I., Telen, D., Nimmegeers, P., Logist, F., Impe, J. V.: Multi-objective optimization of a plug flow reactor using a divide and conquer approach..IFAC-PapersOnLine 50 (2017), 1, 8722-8727. 10.1016/j.ifacol.2017.08.1712 |
| Reference:
|
[12] Jadachowski, L., Meurer, T., Kugi, A.: Backstepping observers for periodic quasi-linear parabolic PDEs..IFAC Proc. Vol. 47 (2014), 3, 7761-7766. 10.3182/20140824-6-za-1003.01246 |
| Reference:
|
[13] Klug, M., Castelan, E. B., Leite, V. J S.: A dynamic compensator for parameter varying systems subject to actuator limitations applied to a T-S fuzzy system..IFAC Proc. Vol. 44 (2011), 1, 14495-145000. 10.3182/20110828-6-it-1002.02175 |
| Reference:
|
[14] Knüppel, T., Woittennek, F.: Control design for quasi-linear hyperbolic systems with an application to the heavy rope..IEEE T. Automat. Control 60 (2015), 1, 5-18. MR 3299410, 10.1109/tac.2014.2336451 |
| Reference:
|
[15] Konigorski, U.: Pole placement by parametric output feedback..Syst. Control Lett. 61 (2012), 2, 292-297. MR 2878717, 10.1016/j.sysconle.2011.11.015 |
| Reference:
|
[16] Li, K., Nagasio, T., Kida, T.: Gain-scheduling control for extending space structures..Trans. Japan Soc. Mechani. Engineers Series C 70 (2004), 702, 1401-1408. 10.1299/kikaic.70.1401 |
| Reference:
|
[17] Lim, D., Yi, K., Jung, S., Jung, H., Ro, J.: Optimal design of an interior permanent magnet synchronous motor by using a new surrogate-assisted multi-objective optimization..IEEE T. Magn. 51 (2015), 11, 1-4. 10.1109/tmag.2015.2449872 |
| Reference:
|
[18] Liu, G.-P., Patton, R. J.: Eigenstructure Assignment for Control System Design..John Wiley and Sons, Hoboken 1998. |
| Reference:
|
[19] Manuel, P., Gonzalo, R., Victor, T.: Linear attraction in quasi-linear difference systems..J. Differ. Equ. Appl. 17 (2011), 5, 765-778. MR 2795524, 10.1080/10236190903260820 |
| Reference:
|
[20] Mehrotra, K., Mahapatra, P.: A jerk model to tracking highly maneuvering targets..IEEE T. Aero. Elec. Sys. 33 (1997), 4, 1094-1105. 10.1109/7.624345 |
| Reference:
|
[21] Mihai, M.: Optimal singular control for quasi-linear systems with small parameters..Proc. Appl. Math. Mech. 7 (2007), 4130033-4130034. 10.1002/pamm.200700782 |
| Reference:
|
[22] Patton, R. J., Liu, G.-P., Patel, Y.: Sensitivity properties of multirate feedback control systems, based on eigenstructure assignment..IEEE Trans. Automat. Control 40 (1995), 2, 337-342. MR 1312908, 10.1109/9.341806 |
| Reference:
|
[23] Rotondo, D., Nejjari, F., Puig, V.: Model reference switching quasi-LPV control of a four wheeled omnidirectional robot..IFAC Proc. Vol. 47 (2014), 3, 4062-4067. 10.3182/20140824-6-za-1003.00054 |
| Reference:
|
[24] Seo, J. H., Shim, H., Back, J.: Consensus of high-order linear systems using dynamic output feedback compensator: Low gain approach..Automatica 45 (2009), 11, 2659-2664. MR 2889327, 10.1016/j.automatica.2009.07.022 |
| Reference:
|
[25] She, S. X., Dong, S. J.: Varying accelerated motion and comfort..Phys. Engrg. 16 (2006), 35-37. (In Chinese) |
| Reference:
|
[26] Slotine, J.-J. E., Li, W.-P.: Applied Nonlinear Control..Pearson Education Company, Upper Saddle River 1991. Zbl 0753.93036 |
| Reference:
|
[27] Tang, Y. R., Xiao, X., Li, Y. M.: Nonlinear dynamic modeling and hybrid control design with dynamic compensator for a small-scale UAV quadrotor..Measurement 109 (2017), 51-64. 10.1016/j.measurement.2017.05.036 |
| Reference:
|
[28] Tsuzuki, T., Yamashita, Y.: Global asymptotic stabilization for a nonlinear system on a manifold via a dynamic compensator..IFAC Proc. Vol. 41 (2008), 2, 6178-6183. 10.3182/20080706-5-kr-1001.01043 |
| Reference:
|
[29] Yi, T., Huang, D., Fu, F., He, H., Li, T.: Multi-objective bacterial foraging optimization algorithm based on parallel cell entropy for aluminum electrolysis production process..IEEE Trans. Ind. Electron. 63 (2016), 4, 2488-2500. 10.1109/tie.2015.2510977 |
| Reference:
|
[30] Yuno, T., Ohtsuka, Y.: Rendering a prescribed subset invariant for polynomial systems by dynamic state-feedback compensator..IFAC-PapersOnLine 49 (2016), 18, 1042-1047. 10.1016/j.ifacol.2016.10.305 |
| Reference:
|
[31] Zhou, B., Duan, G.-R.: A new solution to the generalized Sylvester matrix equation $AV-EVF=BW$..Syst. Control Lett. 55 (2009), 3, 193-198. MR 2188507, 10.1016/j.sysconle.2005.07.002 |
| Reference:
|
[32] Zhou, D., Wang, J., Jiang, B., Guo, H., Ji, Y.: Multi-task multi-view learning based on cooperative multi-objective optimization..IEEE Access 6 (2018), 19465-19477. 10.1109/access.2017.2777888 |
| Reference:
|
[33] Zola, E., Barcelo-Arroyo, F., Kassler, A.: Multi-objective optimization of WLAN associations with improved handover costs..IEEE Commun. Lett. 18 (2014), 11, 2007-2010. 10.1109/lcomm.2014.2359456 |
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