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摘要: 设计了一种针对不确定机械系统的鲁棒控制器.首先分析了质量矩阵的奇异性及上边界性质,展示了质量矩阵可能会因为模型的过度简化而变为半正定.而且,进一步研究了质量矩阵上边界的一致性.在质量矩阵正定及上边界的假设条件下,提出了一种新型鲁棒控制器以抑制机械系统中的不确定性效果.从理论上证明了设计的鲁棒控制器的一致有界性及最终一致有界性.最终趋近边界球的尺寸大小可由设计者决定.最后展示了仿真结果并作了讨论.Abstract: We design a new robust controller for uncertain mechanical systems. The inertia matrix's singularity and upper bound property are first analyzed. It is shown that the inertia matrix may be positive semi-definite due to over-simplified model. Furthermore, the inertia matrix's being uniformly bounded above is also limited. A robust controller is proposed to suppress the effect of uncertainty in mechanical systems with the assumption of uniform positive definiteness and upper bound of the inertia matrix. We theoretically prove that the robust control renders uniform boundedness and uniform ultimate boundedness. The size of the ultimate boundedness ball can be made arbitrarily small by the designer. Simulation results are presented and discussed.
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Key words:
- Inertia matrix /
- mechanical system /
- robust control /
- uncertainty
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[1] Slotine J J E, Li W P. Applied Nonlinear Control. New Jersey: Prentice Hall, 1991 [2] Li X P, Chang B C, Banda S S. Robust control system design using H∞ optimization theory. Journal of Guidance, Control and Dynamics, 1992, 2: 1975-1980 [3] Shen T L, Tamura K. Robust H∞ control of uncertain nonlinear system via state feedback. IEEE Transactions on Automatic Control, 1995, 40(4): 766-768 [4] Packard A, Doyle J, Balas G. Linear multivariable robust control with a μ perspective. ASME Transactions on Systems, Measurement and Control, 1993, 115(2B): 426-438 [5] Chapellat H, Dahleh M, Bhattacharyya S P. On robust stability of interval control systems. IEEE Transactions on Automatic Control, 1991, 36(1): 59-67 [6] Bartlett A C, Tesi A, Vicino A. Vertices and segments of interval plants are not sufficient for step response analysis. System and Control Letters, 1992, 19(5): 365-370 [7] Chen Y H, Leitmann G. Robustness of uncertain systems in the absence of matching assumptions. International Journal of Control, 1987, 45(5): 1527-1542 [8] Schoenwald D A, Ozgunner I. Robust stabilization of nonlinear systems with parametric uncertainty. IEEE Transactions on Automatic Control, 1994, 39(8): 1751-1755 [9] Nwokah O, Jayasuriya S, Chait Y. Parametric robust control by quantitative feedback theory. Proceedings of American Control Conference, 1991, 15: 944-952 [10] Bossert D E. Design of robust quantitative feedback theory controllers for pitch attitude hold systems. Journal of Guidance, Control and Dynamics, 1994, 17(1): 217-219 [11] McKerrow P J. Introduction to Robotics. Sydney: Addison-Wesley, 1991. 388-390 [12] Craig J J. Introduction to Robotics: Mechanics and Control (2nd edition ). Sydney: Addison Wiley, 1989. 201-210 [13] Chen Y H, Kuo C Y. Fundamental properties of rigid serial manipulators for control design. Proceedings of the American Control Conference, 1999, 5: 3003-3007 [14] Corless M J, Leitmann G. Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems. IEEE Transactions on Automatic Control, 1981, 26(5): 1139-1144
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