Robust Model Predictive Iterative Learning Control With Iteration-varying Reference Trajectory
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摘要: 迭代学习模型预测控制是针对间歇过程的先进控制方法.它能通过迭代高精度跟踪给定参考轨迹，并保证时域上的闭环稳定性.然而，现有的迭代学习模型预测控制算法大多基于线性/线性化系统，且没有考虑参考轨迹变化的情况.本文基于线性参变系统提出一种能有效跟踪变参考轨迹的鲁棒迭代学习模型预测控制算法.首先，采用线性参变模型准确涵盖原始非线性系统的动态特性.然后，将鲁棒H∞控制与传统迭代学习模型预测控制相结合，抑制变参考轨迹带来的跟踪误差波动，通过优化线性矩阵不等式约束下的目标函数求得控制输入.深入分析了鲁棒迭代学习模型预测控制的鲁棒稳定性和迭代收敛性.最后，通过对数值例子和连续搅拌反应釜系统的仿真验证了所提出算法的有效性.Abstract: Model predictive iterative learning control (MPILC) is a popular approach to control systems with repetitive nature like batch systems, as it is capable of tracking the plant reference trajectory with high accuracy and guaranteed closed-loop stability. However, the existing MPILCs are mostly based on linear/linearized system with no consideration of reference trajectory variation. In this paper, a robust MPILC (RMPILC) based on the linear parameter varying (LPV) model is derived to track the iteration-varying reference trajectory. The LPV model is chosen to represent the dynamic property of nonlinear systems accurately. Robust H∞ control is incorporated with MPILC to restrain the fluctuation of tracking errors, with control inputs solved by optimizing the objective function constrained by linear matrix inequalities. The robust stability and convergence condition of the system controlled by RMPILC are analyzed. The effectiveness of the proposed controller is verified through the simulations on a numerical example and a continuous stirred tank reactor (CSTR) system.1) 本文责任编委 魏庆来
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图 6 RMPILC控制下第5批次当$\varepsilon=5.8$、$\varepsilon=10$和$\varepsilon=15$时的跟踪曲线
Fig. 6 The tracking trajectories in the fifth batch when $\varepsilon=5.8, 10, 15$
图 7 RMPILC控制下$\varepsilon=5.8$、$\varepsilon=10$和$\varepsilon=15$时的不变集$\Omega_{\tilde{x}_k}$在原状态空间的象集
Fig. 7 The image set of $\Omega_{\tilde{x}_k}$ when $\varepsilon=5.8, 10, 15$
图 8 CSTR反应温度$T$参考轨迹
Fig. 8 The reference trajectories of CSTR reaction temperature $T$
图 9 RMPILC控制下反应温度$T$参考轨迹跟踪曲线
Fig. 9 The tracking trajectories for $T$ under RMPILC control
图 10 RMPILC控制下控制输入$T_c$轨迹
Fig. 10 The trajectories of control input $T_c$ under RMPILC
表 1 $F_k(t)$优化值
Table 1 Optimized feedback control law
批次($k$) $F_k(61)$ 2 [$-$46.7539 $-$24.0899 $-$5.0529 0.0000] 3 [$-$42.9654 $-$25.0475 $-$3.7597 0.0000] 4 [$-$57.4573 $-$29.2520 $-$5.4621 $-$0.0000] 5 [$-$16.9782 $-$7.8604 $-$1.2311 $-$0.0000] 6 [$-$37.0429 $-$26.9746 $-$3.0976 0.0000] 7 [$-$41.3123 $-$27.2625 $-$2.9534 $-$0.0000] 8 [$-$54.1913 $-$32.1226 $-$4.9777 0.0000] 
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表 2 $F_k(t)$优化值
Table 2 Optimized feedback control law
批次$k$ $F_k(200)$ 2 [-7.8076 -12.6079 -7.9428 -0.0000] 3 [-8.4202 -12.9000 -8.2264 -0.0000] 4 [-7.8744 -12.6839 -7.9521 -0.0000] 5 [-8.9258 -13.1178 -8.4572 -0.0000] 6 [-9.7286 -13.2893 -9.0092 0.0000] 7 [-6.9490 -11.3713 -7.6883 0.0000] 8 [-7.5195 -12.4532 -8.0074 -0.0000] 9 [-7.7803 -12.6691 -7.9535 -0.0000]
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