Adaptive sliding mode control using monitoring functions. (English) Zbl 1414.93056
Clempner, Julio B. (ed.) et al., New perspectives and applications of modern control theory. In honor of Alexander S. Poznyak. Cham: Springer. 269-285 (2018).
Summary: In this chapter, we propose an adaptive sliding mode control approach based on monitoring functions, to deal with disturbances of unknown bounds. An uncertain linear system is considered as well as a quite general class of non-smooth disturbances. Global tracking is demonstrated using only output feedback. The proposed adaptation method is able to make the control gain less conservative, but large enough when the disturbance grows and allows it to decrease if the latter vanishes, leading to reduced chattering effects. Simulations are presented to show the potential of the new adaptation scheme in this adverse scenario of possibly growing, temporarily large, or vanishing disturbances.
For the entire collection see [Zbl 1393.93003].
For the entire collection see [Zbl 1393.93003].
MSC:
| 93B12 | Variable structure systems |
| 93C40 | Adaptive control/observation systems |
| 93B07 | Observability |
| 93C41 | Control/observation systems with incomplete information |
| 93C05 | Linear systems in control theory |
| 93B52 | Feedback control |
References:
| [1] | Bartolini, G., Levant, A., Plestan, F., Taleb, M., Punta, E.: Adaptation of sliding modes. IMA J Math. Control Inf. 30(3), 285-300 (2013) · Zbl 1273.93035 · doi:10.1093/imamci/dns019 |
| [2] | Cunha, J.P.V.S., Hsu, L., Costa, R.R., Lizarralde, F.: Output-feedback model-reference sliding mode control of uncertain multivariable systems. IEEE Trans. Autom. Control 48(12), 2245-2250 (2003) · Zbl 1364.93121 · doi:10.1109/TAC.2003.820156 |
| [3] | Cunha, J.P.V.S., Costa, R.R., Hsu, L.: Design of first-order approximation filters for sliding-mode control of uncertain systems. IEEE Trans. Ind. Electron. 55(11), 4037-4046 (2008) · doi:10.1109/TIE.2008.2005142 |
| [4] | Edwards, C., Shtessel, Y.B.: Adaptive continuous higher order sliding mode control. Automatica 65, 183-190 (2016) · Zbl 1328.93066 · doi:10.1016/j.automatica.2015.11.038 |
| [5] | Estrada, A., Plestan, F., Allouche, B.: An adaptive version of a second order sliding mode output feedback controller. In: 2013 European Control Conference (ECC), pp. 3228-3233. IEEE, Zurich, Switzerland (2013) |
| [6] | Filippov, A.F.: Differential equations with discontinuous right-hand side. Am. Math. Soc. Transl. 42(2), 199-231 (1964) · Zbl 0148.33002 |
| [7] | Hsu, L., Araújo, A.D., Costa, R.R.: Analysis and design of I/O based variable structure adaptive control. IEEE Trans. Autom. Control 39(1), 4-21 (1994) · Zbl 0805.93006 · doi:10.1109/9.273335 |
| [8] | Hsu, L., Lizarralde, F., Araújo, A.D.: New results on output-feedback variable structure model-reference adaptive control: design and stability analysis. IEEE Trans. Autom. Control 42(3), 386-393 (1997) · Zbl 0876.93057 · doi:10.1109/9.557582 |
| [9] | Hsu, L., Costa, R.R., Cunha, J.P.V.S.: Model-reference output-feedback sliding mode controller for a class of multivariable nonlinear systems. Asian J. Control 5(4), 543-556 (2003) · doi:10.1111/j.1934-6093.2003.tb00171.x |
| [10] | Hsu, L., Oliveira, T.R., Cunha, J.P.V.S.: Extremum seeking control via monitoring function and time-scaling for plants of arbitrary relative degree. In: Proceedings \(13^{th}\) International Workshop on Variable Structure System, Nantes, pp. 1-6 (2014) |
| [11] | Ioannou, P.A., Sun, J.: Robust Adaptive Control. Prentice-Hall, Upper Saddle River (1996) · Zbl 0839.93002 |
| [12] | Khalil, H.K.: Nonlinear Systems, 2nd edn. Prentice-Hall, Upper Saddle River (1996) · Zbl 0892.93002 |
| [13] | Moreno, J.A., Negrete, D.Y., Torres-González, V., Fridman, L.: Adaptive continuous twisting algorithm. Int. J. Control. 89(9), 1798-1806 (2016) · Zbl 1352.93063 · doi:10.1080/00207179.2015.1116713 |
| [14] | Oliveira, T.R., Peixoto, A.J., Nunes, E.V.L., Hsu, L.: Control of uncertain nonlinear systems with arbitrary relative degree and unknown control direction using sliding modes. Int. J. Adapt. Control. Signal Process 21(8/9), 692-707 (2007) · Zbl 1128.93022 · doi:10.1002/acs.978 |
| [15] | Oliveira, T.R., Leite, A.C., Peixoto, A.J., Hsu, L.: Overcoming limitations of uncalibrated robotics visual servoing by means of sliding mode control and switching monitoring scheme. Asian J. Control 16(3), 752-764 (2014) · Zbl 1302.93063 · doi:10.1002/asjc.899 |
| [16] | Oliveira, T.R., Cunha J.P.V.S., Hsu, L.: Adaptive sliding mode control for disturbances with unknown bounds. In: Proceedings 14th International Workshop on Variable Structure Systems, Nanjing, Jiangsu, China, pp. 59-64 (2016) |
| [17] | Plestan, F., Shtessel, Y., Brégeault, V., Poznyak, A.: New methodologies for adaptive sliding mode control. Int. J. Control 83(9), 1907-1919 (2010) · Zbl 1213.93031 · doi:10.1080/00207179.2010.501385 |
| [18] | Utkin, V.I.: Sliding Modes and Their Application in Variable Structure Systems. MIR Publishers, Moscow (1978) · Zbl 0398.93003 |
| [19] | Utkin, V.I., Poznyak, A.S.: Adaptive sliding mode control with application to super-twist algorithm: equivalent control method. Automatica 49(1), 39-47 (2013) · Zbl 1257.93022 · doi:10.1016/j.automatica.2012.09.008 |
| [20] | Yan, L., Hsu, L., Xiuxia, S.: A variable structure MRAC with expected transient and steady-state performance. Automatica 42(5), 805-813 (2006) · Zbl 1137.93015 · doi:10.1016/j.automatica.2006.01.007 |
| [21] | Yan, L., Hsu, L., Costa, R.R., Lizarralde, F.: A variable structure model reference robust control without a prior knowledge of high frequency gain sign. Automatica 44(4), 1036-1044 (2008) · Zbl 1283.93068 |
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