Gain-Scheduled Controller Design by Linear Programming with Application to a Double-Axis Positioning System
Gain-Scheduled Controller Design by Linear Programming with Application to a Double-Axis Positioning System
复制标题
线性规划增益调度控制器设计及其在双轴定位系统中的应用
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
R. Longchamp
中科院分区：
文献类型：
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作者：
M. Kunze;A. Karimi;R. Longchamp
提出了一种线性编程方法来调整固定阶线性参数化增益调度控制器，以实现稳定的 SISO 线性参数变化 (LPV) 设备。该方法基于奈奎斯特图中开环传递函数的整形，并限制鲁棒性裕度和交叉频率的较低近似值。考虑两个优化问题：鲁棒性优化和性能优化。该方法直接根据不同工作点的一组频域模型或 LPV 模型计算增益调度控制器，无需插值。在闭环性能方面，这种方法带来了非常好的结果。然而，闭环稳定性仅在本地以及调度参数缓慢变化时得到保证。应针对调度参数的快速变化进行稳定性分析。在高精度双轴定位系统中的应用说明了该方法的有效性。
A linear programming approach is proposed to tune fixed-order linearly parameterized gain-scheduled controllers for stable SISO Linear Parameter Varying (LPV) plants. The method is based on the shaping of the open-loop transfer functions in the Nyquist diagram with constraints on the robustness margins and on the lower approximation of the crossover frequency. Two optimization problems are considered: optimization for robustness and optimization for performance. This method directly computes a gain-scheduled controller from a set of frequency-domain models in different operating points or from an LPV model and no interpolation is needed. In terms of closed-loop performance, this approach leads to extremely good results. However, closedloop stability is ensured only locally and for slow variations of the scheduling parameters. A stability analysis should be performed for fast variations of the scheduling parameters. An application to a high-precision double-axis positioning system illustrates the effectiveness of the proposed approach.