Optimal Tracking Control Method for Discrete-time Linear Multivariable Systems With Decoupling Performance
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摘要: 在传统线性二次跟踪控制方法的基础上, 针对一类具有强耦合特性的离散时间线性多变量系统, 提出了一种具有解耦性能的最优跟踪控制方法. 首先为实现解耦, 将耦合项作为可测干扰, 基于零和博弈思想提出了一种新的性能指标; 然后针对该性能指标, 利用极小值原理设计最优跟踪控制器, 通过适当加权矩阵的选择, 同步实现解耦和跟踪; 最后进行仿真实验, 仿真结果表明了该方法的有效性以及在最优性能等方面的优越性.Abstract: In this paper, for a class of discrete-time multivariable linear systems with strong coupling property, based on the traditional linear quadratic tracking control method, an optimal tracking controller with decoupling performance is proposed. First, in order to achieve decoupling, the coupling term is viewed as the measurable disturbance, and then a novel performance index which is inspired by the two-player Zero-Sum game problem is introduced. Based on the novel performance index, the optimal tracking controller is derived by using the minimum principle. Then, it is proved that by choosing appropriate weighting matrices, the proposed method can simultaneously decouple the closed-loop system in dynamic and make the tracking error converge asymptotically. Finally, simulations are conducted, whose results demonstrate the effectiveness of the proposed method and its superiority in optimal performance comparing with the traditional controller.
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Key words:
- Decoupling /
- tracking control /
- discrete-time linear systems /
- multivariable systems
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图 7 第1组参数下, 2种策略的最优性能比较
Fig. 7 Comparison of the performance under the first set of parameters
图 8 第2组参数下, 2种策略的最优性能比较
Fig. 8 Comparison of the performance under the second set of parameters
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