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摘要: 针对具有多个运行点的非线性离散时间多变量强耦合系统, 提出一种最优切换解耦控制方法. 首先, 将非线性系统在多个运行点附近泰勒展开, 得到多个近似线性模型, 通过引入开关函数, 并利用矩阵分解方法建立控制器设计模型; 然后, 基于考虑耦合影响的复合型性能指标, 利用嵌入转换技术、极小值原理及二次规划技术, 推导出最优切换准则函数及最优切换解耦控制器, 并设计鲁棒补偿器以提升控制系统性能; 最后, 进行数值仿真实验, 实验结果验证了所提方法的有效性及优越性.Abstract: An optimal switching decoupling control method for nonlinear discrete-time multivariable systems with multiple operating points and strong coupling. First, the nonlinear system is approximated by several local linear models obtained via Taylor expansion around multiple operating points. A switching function is introduced, and a controller design model is established using matrix decomposition techniques. Then, based on a composite performance index that takes coupling effects into account, the optimal switching criterion and the optimal decoupled controller are derived using embedding transformation, the minimum principle, and quadratic programming. A robust compensator is further designed to enhance the performance of the control system. Finally, numerical simulations are conducted, and the results verify the effectiveness and superiority of the proposed method.
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图 1 具有鲁棒特性的最优切换解耦控制系统结构图
Fig. 1 Structure of the robust optimal switching decoupling control system
图 4 采用本文所提方法时系统的切换序列
Fig. 4 Switching sequence of the system using the proposed method
表 1 具有鲁棒特性的最优切换解耦控制算法
Table 1 The robust optimal switching decoupling control algorithm
算法1 具有鲁棒特性的最优切换解耦控制算法 步骤1. 根据先验知识, 确定线性化模型数量$M$并建立控制器设计模型; 步骤2. 选择系统初始状态$x_0 $, 终止时间$k_{\max}$; 步骤3. 根据式(42)计算最优切换函数$i_{k}^{*}$, 根据式(43)计算最优切换解耦控制律$u_{k}^{i^*}$; 步骤4. 根据式(44)获得最优模型状态$x_{k+1}^{i^*}$; 步骤5. 根据式(46)计算具有鲁棒特性的最优切换解耦控制律$u_k $; 步骤6. 返回步骤3直到$k>k_{\max}$. 
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