Polynomial approach to non-linear predictive generalised minimum variance control
Polynomial approach to non-linear predictive generalised minimum variance control
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DOI：
10.1049/iet-cta.2009.0043
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发表时间：
2010-03
影响因子：
2.6
通讯作者：
M. Grimble;P. Majecki
中科院分区：
文献类型：
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作者：
M. Grimble;P. Majecki
针对非线性离散时间多变量系统，提出了一种相对简单的非线性预测广义最小方差控制方法。系统由一个不假定结构的稳定的非线性子系统和一个可能不稳定的线性子系统的组合来表示，并以多项式矩阵的形式建模。要最小化的多步预测控制成本指标包括加权误差和控制信号成本项。NPGMV控制律包含一个关于代价函数权重选择的假设，以确保稳定的非线性闭环系统的存在。控制律的一个有价值的特征是，在被控对象是线性的渐近情况下，控制器退化为众所周知的广义预测控制(GPC)控制器的多项式矩阵形式。在极限情况下，当被控对象为非线性且代价函数为单步时，控制器变为等于所谓的非线性广义最小方差控制器的多项式矩阵形式。该控制器可以以与史密斯预估器的非线性形式相关的形式来实现，但与该补偿器不同的是，对于开环不稳定过程，可以获得镇定控制律。
A relatively simple approach to non-linear predictive generalised minimum variance (NPGMV) control is introduced for non-linear discrete-time multivariable systems. The system is represented by a combination of a stable non-linear subsystem where no structure is assumed and a linear subsystem that may be unstable and modelled in polynomial matrix form. The multi-step predictive control cost index to be minimised involves both weighted error and control signal costing terms. The NPGMV control law involves an assumption on the choice of cost-function weights to ensure the existence of a stable non-linear closed-loop operator. A valuable feature of the control law is that in the asymptotic case, where the plant is linear, the controller reduces to a polynomial matrix version of the well known generalised predictive control (GPC) controller. In the limiting case when the plant is non-linear and the cost-function is single step the controller becomes equal to the polynomial matrix version of the so-called non-linear generalised minimum variance controller. The controller can be implemented in a form related to a non-linear version of the Smith predictor but unlike this compensator a stabilising control law can be obtained for open-loop unstable processes.