Multivariable Inverted Decoupling Active Disturbance Rejection Control and Its Application to a Distillation Column Process
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摘要: 化工生产是一类典型的多变量过程对象，该类对象具有时变性、耦合性、时滞性等特点，传统的单变量控制方法很难在此类系统中取得良好的控制效果.针对时变性，本文在假设对象模型未知的前提下，利用阶跃响应数据，研究了基于最小二乘的一阶、二阶时滞系统辨识方法.针对多变量系统存在耦合性的特点，采用逆解耦方法实现对象的解耦.再对解耦后的时滞子系统设计了自抗扰控制器.仿真实验中，以精馏塔的Wood-Berry模型和Ogunnaike-Ray模型为例，验证了算法的有效性.Abstract: Chemical industry is a class of typical multivariable process plants, and has the characteristics of time-varying, coupling, and time delay. It is difficult to achieve good control effect in such systems by using traditional single variable control methods. In this paper, aiming at time-varying behavior, it is assumed that the model of the plant is unknown. By using step response data, an identification method for first-order and second-order delay systems is studied based on least squares method. For the coupling of multivariable systems, the inverted decoupling method is used to decouple the plant. And then an active disturbance rejection controller is designed for the decoupled delay subsystem. In the simulation experiment, the effectiveness of the algorithm is verified by the Wood-Berry model and the Ogunnaike-Ray model of the distillation column.1) 本文责任编委 王伟
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图 2 三种方法跟踪轨迹以及抗扰性能
Fig. 2 Tracking and disturbance rejection performance of three methods
图 4 采用NSR=10 %下辨识数据控制效果
Fig. 4 Control efiect by using identiflcation data of NSR=10 %
图 5 三种方法跟踪轨迹以及抗扰性能
Fig. 5 Tracking and disturbance rejection performance of three methods
图 7 采用NSR=10 %下辨识数据控制效果
Fig. 7 Control efiect by using identiflcation data of NSR=10 %
表 1 Wood-Berry模型辨识结果的均方误差
Table 1 Mean square error of the Wood-Berry model
G11 G12 G21 G22 NSR=1% 1.93×10-4 6.37×10-5 2.98×10-5 4.69×10-5 NSR=10% 4.88×10-5 6.32×10-4 6.62×10-4 2.10×10-3 
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表 2 三种算法IAE指标对比
Table 2 Comparison of IAE for three methods
IAE1 IAE2 Sum 3-ADRC 6.01 15.15 21.16 ID-ADRC 5.25 21.09 26.34 ID-TDADRC 2.59 8.77 11.36
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表 3 采用辨识数据控制下的IAE指标
Table 3 IAE by using identiflcation data
IAE1 IAE2 Sum NSR=1% 2.62 8.78 11.40 NSR=10% 2.73 8.77 11.50
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表 4 三种算法IAE指标对比
Table 4 Comparison of IAE for three methods
G11 G12 G13 G21 G22 G23 G31 G32 G33 NSR=1% 1.62×10-7 5.19×10-7 7.08×10-12 3.63×10-6 1.94×10-6 1.07×10-10 5.60×10-4 4.69×10-5 1.38×10-6 NSR=10% 2.36×10-8 1.35×10-6 1.95×10-10 1.61×10-6 3.45×10-6 3.12×10-10 2.70×10-3 2.00×10-3 2.38×10-4
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表 5 三种算法IAE指标对比
Table 5 Comparison of IAE for three methods
IAE1 IAE2 IAE3 Sum 3-ADRC 15.22 23.41 19.23 57.86 ID-ADRC 17.75 10.65 35.16 63.56 ID-TDADRC 4.59 5.41 8.86 18.86
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表 6 采用辨识数据控制下的IAE指标
Table 6 IAE by using identiflcation data
IAE1 IAE2 IAE3 Sum NSR=1% 4.61 5.50 17.85 27.96 NSR=10% 4.63 5.55 38.15 48.33
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