对角CARIMA模型多变量广义预测近似解耦控制

Approximate decoupling multivariable generalized predictive control of diagonal CARIMA model

针对多变量系统中存在的强耦合,提出基于对角CARIMA模型的多变量广义预测控制近似解耦算法.根据对角CARIMA模型中的A和C矩阵为对角形式的特点,将多输入多输出系统分解为多个多输入单输出系统进行预测和控制,一定程度上降低了变量之间的耦合性.根据模型预测值与参考轨迹之间的偏差实时调整目标函数中跟踪误差的加权系数,达到进一步降低各个回路之间耦合的目的.加权系数调整的基本原则是,每个输出跟踪误差的加权系数是由其他输出在同时刻偏离参考轨迹的加权误差平方和构成.当某个输出偏离目标值时,其他输出的跟踪误差权值相对增大,以避免输出之间的相互扰动,达到近似解耦的目的.利用单变量GPC、多变量MGPC、基于设定值观测器解耦的MGPC以及提出的近似解耦方法,分别对温室温度和相对湿度控制系统进行仿真实验.仿真结果显示,近似解耦算法控制平稳,输出变量之间的相互扰动显著降低.

An approximate decoupling multivariable generalized predictive control of diagonal controlled autoregressive integrated moving average （CARIMA） model was proposed for strong coupling existing in multivariable system. According to the feature of a diagonal CARIMA model whose matrices C and A were chosen to be diagonal, the prediction and control problem of a multi-input and multi-output （MIMO） process was transformed into generating a set of optimal prediction and control for a series of multi-input single-output processes, which weakened the coupling of outputs in some measure. The weight coefficients of tracking error in cost function were real-time adjusted according to the difference of the model prediction value and the reference trajectory to further reduce the coupling among outputs. The basic idea of weight coefficients adjusting is that the weight coefficient of each output tracing error is composed of weighing error square sum of deviation of other output at same sampling time point. When one output deviating from its trajectory, the weight coefficients of tracking error of other outputs will be increased correspondingly to eliminate the possible disturbance caused by that output deviating and gain approximate decoupling. The comparison experiments were made on a greenhouse temperature and relative humidity control system using single variable GPC, multivariable GPC, decoupling MGPC with reference observation, and the approximate decoupling MGPC of diagonal CARIMA model developed respectively. Simulation results show that approximate decoupling method has a smooth and steady control and can remarkably reduce the disturbance among outputs.