对于非线性随机系统,以均值、方差等低阶统计特征作为研究目标往往难以满足实际的控制要求,需要考虑更高阶的统计特征。概率密度函数(Probability density function, PDF)包含了完全统计特征,因此PDF控制能够实现各阶矩的有效控制。针...对于非线性随机系统,以均值、方差等低阶统计特征作为研究目标往往难以满足实际的控制要求,需要考虑更高阶的统计特征。概率密度函数(Probability density function, PDF)包含了完全统计特征,因此PDF控制能够实现各阶矩的有效控制。针对受高斯白噪声激励的非线性随机系统,将福克-普朗克-柯尔莫哥洛夫(Fokker-PlanckKolmogrov, FPK)方程作为研究工具,提出一种基于多高斯闭合法(MGC)的PDF控制方法。首先,根据目标PDF的形状构造一个由多个高斯型PDF相叠加的PDF;然后,构造一个优化问题,使得该PDF逼近目标PDF;进一步,通过求解FPK方程得到被控系统的状态方程;最后,结合原始状态方程求得控制函数,实现对目标PDF的追踪控制。针对不同类型目标PDF进行的仿真结果表明了所提出方法的可行性和有效性。展开更多
The Pseudo-Derivative Feedback (PDF) algorithm is introduced into design of electro-hydraulic speed servos. With limited extra complexity in implementation of controller's electronic circuits, the PDF control enab...The Pseudo-Derivative Feedback (PDF) algorithm is introduced into design of electro-hydraulic speed servos. With limited extra complexity in implementation of controller's electronic circuits, the PDF control enables the electro-hydraulic speed servo to respond to a step command without steady-state error, and also to follow successfully a sinusoidal command at the frequency higher than that the system resulted from traditional design can reach. The numerical example-based comparison in dynamic and static behavior shows also the PDF system is superior to the traditional system in terms of both the capability of handling loads applied to the system and the robustness to ignore variation and uncertainty of the parameters of the hydraulic valve-actuator unit in operation.展开更多
文摘间歇过程的优化控制依赖于过程精确的数学模型,数据驱动的建模方法是目前间歇过程模型研究中的热点问题。突破传统数据驱动建模方法中采用均方差(mean squared error,MSE)作为准则函数的思想,提出一种新颖的间歇过程数据驱动建模方法,引入了概率密度函数(probability density function,PDF)控制的概念,构造间歇过程模型误差控制系统,将模型的可调参数作为控制系统的输入,模型误差PDF的形状作为控制系统的输出,从而把开环模型参数辨识问题转化为模型误差PDF形状的闭环控制问题。通过可调参数控制模型误差PDF的空间分布状态,不仅能够保障模型精度,还可控制模型误差的空间分布状态,从而消除模型中的有色噪声。仿真实验表明,基于模型误差PDF形状的间歇过程数据驱动模型具有较好的建模精度、鲁棒性和泛化能力,为间歇过程的数据驱动建模提供了一条新途径。
文摘对于非线性随机系统,以均值、方差等低阶统计特征作为研究目标往往难以满足实际的控制要求,需要考虑更高阶的统计特征。概率密度函数(Probability density function, PDF)包含了完全统计特征,因此PDF控制能够实现各阶矩的有效控制。针对受高斯白噪声激励的非线性随机系统,将福克-普朗克-柯尔莫哥洛夫(Fokker-PlanckKolmogrov, FPK)方程作为研究工具,提出一种基于多高斯闭合法(MGC)的PDF控制方法。首先,根据目标PDF的形状构造一个由多个高斯型PDF相叠加的PDF;然后,构造一个优化问题,使得该PDF逼近目标PDF;进一步,通过求解FPK方程得到被控系统的状态方程;最后,结合原始状态方程求得控制函数,实现对目标PDF的追踪控制。针对不同类型目标PDF进行的仿真结果表明了所提出方法的可行性和有效性。
基金This work is supported by National Natural Science Foundation of china under grant 59475075.
文摘The Pseudo-Derivative Feedback (PDF) algorithm is introduced into design of electro-hydraulic speed servos. With limited extra complexity in implementation of controller's electronic circuits, the PDF control enables the electro-hydraulic speed servo to respond to a step command without steady-state error, and also to follow successfully a sinusoidal command at the frequency higher than that the system resulted from traditional design can reach. The numerical example-based comparison in dynamic and static behavior shows also the PDF system is superior to the traditional system in terms of both the capability of handling loads applied to the system and the robustness to ignore variation and uncertainty of the parameters of the hydraulic valve-actuator unit in operation.
