The use of a lower sampling rate for designing a discrete-time state feedback-based controller fails to capture information of fast states in a two-time-scale system, while the use of a higher sampling rate increases ...The use of a lower sampling rate for designing a discrete-time state feedback-based controller fails to capture information of fast states in a two-time-scale system, while the use of a higher sampling rate increases the amount of computation considerably. Thus,the use of single-rate sampling for systems with slow and fast states has evident limitations. In this paper, multirate state feedback(MRSF) control for a linear time-invariant two-time-scale system is proposed. Here, multirate sampling refers to the sampling of slow and fast states at different sampling rates. Firstly, a block-triangular form of the original continuous two-time-scale system is constructed. Then, it is discretized with a smaller sampling period and feedback control is designed for the fast subsystem. Later, the system is block-diagonalized and equivalently represented into a system with a higher sampling period. Subsequently, feedback control is designed for the slow subsystem and overall MRSF control is derived. It is proved that the derived MRSF control stabilizes the full-order system. Being the transformed states of the original system, slow and fast states need to be estimated for the MRSF control realization.Hence, a sequential two-stage observer is formulated to estimate these states. Finally, the applicability of the design method is demonstrated with a numerical example and simulation results are compared with the single-rate sampling method. It is found that the proposed MRSF control and observer designs reduce computations without compromising closed-loop performance.展开更多
为应对当今供应链库存管理面临的牛鞭效应、两时间尺度特性和不确定性干扰等挑战,开发了一种基于径向基函数神经网络(radial basis function neural network,RBFNN)的两时间尺度供应链H_(∞)最优控制器。利用奇异摄动理论将原两时间尺...为应对当今供应链库存管理面临的牛鞭效应、两时间尺度特性和不确定性干扰等挑战,开发了一种基于径向基函数神经网络(radial basis function neural network,RBFNN)的两时间尺度供应链H_(∞)最优控制器。利用奇异摄动理论将原两时间尺度供应链模型分解为2个具有不同时间尺度的独立子系统;创新性地使用RBFNN在线近似补偿子系统的不确定项,进而采用H_(∞)控制来抑制RBFNN近似误差带来的不确定性。在理论层面上分析证明了所提方法的稳定性。通过一个电视机生产流程仿真案例,验证了所提方法相比2种其他两时间尺度问题解决方法,具有更高的跟踪控制精度和应用可行性。展开更多
基金supported by National Natural Science Foundation of China (No. 61750110524)National Key R&D Program of China (No. 2017YFE0128500)。
文摘The use of a lower sampling rate for designing a discrete-time state feedback-based controller fails to capture information of fast states in a two-time-scale system, while the use of a higher sampling rate increases the amount of computation considerably. Thus,the use of single-rate sampling for systems with slow and fast states has evident limitations. In this paper, multirate state feedback(MRSF) control for a linear time-invariant two-time-scale system is proposed. Here, multirate sampling refers to the sampling of slow and fast states at different sampling rates. Firstly, a block-triangular form of the original continuous two-time-scale system is constructed. Then, it is discretized with a smaller sampling period and feedback control is designed for the fast subsystem. Later, the system is block-diagonalized and equivalently represented into a system with a higher sampling period. Subsequently, feedback control is designed for the slow subsystem and overall MRSF control is derived. It is proved that the derived MRSF control stabilizes the full-order system. Being the transformed states of the original system, slow and fast states need to be estimated for the MRSF control realization.Hence, a sequential two-stage observer is formulated to estimate these states. Finally, the applicability of the design method is demonstrated with a numerical example and simulation results are compared with the single-rate sampling method. It is found that the proposed MRSF control and observer designs reduce computations without compromising closed-loop performance.
文摘为应对当今供应链库存管理面临的牛鞭效应、两时间尺度特性和不确定性干扰等挑战,开发了一种基于径向基函数神经网络(radial basis function neural network,RBFNN)的两时间尺度供应链H_(∞)最优控制器。利用奇异摄动理论将原两时间尺度供应链模型分解为2个具有不同时间尺度的独立子系统;创新性地使用RBFNN在线近似补偿子系统的不确定项,进而采用H_(∞)控制来抑制RBFNN近似误差带来的不确定性。在理论层面上分析证明了所提方法的稳定性。通过一个电视机生产流程仿真案例,验证了所提方法相比2种其他两时间尺度问题解决方法,具有更高的跟踪控制精度和应用可行性。
