Delta算子的网络控制系统量化反馈控制器设计
|
摘要
通过构建李雅普诺夫函数,以LMI形式给出了Delta算子描述的网络控制系统渐近稳定的充分条件,通过求解LMI可以得出量化反馈H_∞控制器参数.数值算例分析表明,快速采样时,基于Delta算子设计的网络控制系统量化反馈控制器不但保证了控制系统稳定,而且其控制器参数趋近于连续系统设计的量化反馈控制器参数,而传统Z变换设计的量化反馈控制器参数无法保证系统稳定.
By constructing Lyapunov function, the sufficient conditions for the asymptotic stability of the network control system described by the Delta operator are given in the form of LMI, and the parameters of the quantized feedback H_∞ infinity controller can be obtained by solving the LMI. The numerical example analysis shows that the quantitative feedback controller designed by the Delta operator method based on the fast sampling method not only ensures the stability of the control system, but also its controller parameters are close to the parameters of the quantized feedback controller designed by the continuous system method, and the parameters of the quantization feedback controller designed by the traditional Z transform square method will be used. It is impossible to ensure the stability of the system.
By constructing Lyapunov function, the sufficient conditions for the asymptotic stability of the network control system described by the Delta operator are given in the form of LMI, and the parameters of the quantized feedback H_∞ infinity controller can be obtained by solving the LMI. The numerical example analysis shows that the quantitative feedback controller designed by the Delta operator method based on the fast sampling method not only ensures the stability of the control system, but also its controller parameters are close to the parameters of the quantized feedback controller designed by the continuous system method, and the parameters of the quantization feedback controller designed by the traditional Z transform square method will be used. It is impossible to ensure the stability of the system.
引文
[1] CHEN H,GAO J,SHI T,et al.H∞ control for networked control systems with time delay,data packet dropout and disorder[J].Neurocomputing,2016,179(C):211-218.
[2] LIU D,LIU Y,ALSAADI F E.A new framework for output feedback controller design for a class of discrete-time stochastic nonlinear system with quantization and missing measurement[J].International Journal of General Systems,2016,45(5):1-15.
[3] WANG P P,CHE W W.Quantized H∞ filter design for networked control systems with random nonlinearity and sensor saturation[J].Neurocomputing,2016,193:14-19.
[4] LI Z M,CHANG X H,DU X K,et al.H∞ control of discrete-time uncertain linear systems with quantized feedback[J].Neurocomputing,2016,174(PB):790-794.
[5] HU Z,DENG F,ZHAO X,et al.Quantized H∞ control for stochastic systems with packet losses[C]// 36th Chinese Control Conference (CCC).Dalian:IEEE,2017:1838-1843.
[6] 周颖,郑凤,何磊.具有时变时延和丢包的网络控制系统H∞控制[J].计算机技术与发展,2017,27(5):164-169.
[7] 宋娟.具有时变时延的网络控制系统的量化控制[J].航天控制,2017(5):15-18.
[8] WANG P,CHE W.Quantized H∞ control for networked control systems with random packet losses[C]// 27th Chinese Control and Decision Conference.Qingdao:IEEE,2015:6557-6562.
[9] HONGJIU Y,LI L,JUNKAN H,et al.Robust H∞ control for discrete-time networks with state and input quantizations based on delta operator[C]// 27th Chinese Control Conference.Kunming:IEEE,2008:663-667.
[10] QIU J,LU K,DU X,et al.Robust H∞ control for uncertain delta system with time delays and non-linear perturbations based on delta operators approach[J].International Journal of Modelling Identification & Control,2010,11(3/4):150-163.
[11] 彭仁崇,林瑞全,杨富文,等.不确定Delta算子时滞系统鲁棒H∞控制器设计[J].集美大学学报(自然科学版),2008,13(2):157-161.
[12] FU M,XIE L.The sector bound approach to quantized feedback control[J].IEEE Transactions on Automatic Control,2005,50(11):1698-1711.
[13] 俞立.鲁棒控制:线性矩阵不等式处理方法[M].北京:清华大学出版社,2002.
[14] 刘英英,杨光红.量化的连续时间网络控制系统的H∞控制[J].东北大学学报(自然科学版),2010,31(4):457-460.
[15] SHI P,SHUE S P.Robust H∞ control for linear discrete-time systems with norm-bounded nonlinear uncertainties[J].IEEE Transactions on Automatic Control,1999,44(1):108-111.
[2] LIU D,LIU Y,ALSAADI F E.A new framework for output feedback controller design for a class of discrete-time stochastic nonlinear system with quantization and missing measurement[J].International Journal of General Systems,2016,45(5):1-15.
[3] WANG P P,CHE W W.Quantized H∞ filter design for networked control systems with random nonlinearity and sensor saturation[J].Neurocomputing,2016,193:14-19.
[4] LI Z M,CHANG X H,DU X K,et al.H∞ control of discrete-time uncertain linear systems with quantized feedback[J].Neurocomputing,2016,174(PB):790-794.
[5] HU Z,DENG F,ZHAO X,et al.Quantized H∞ control for stochastic systems with packet losses[C]// 36th Chinese Control Conference (CCC).Dalian:IEEE,2017:1838-1843.
[6] 周颖,郑凤,何磊.具有时变时延和丢包的网络控制系统H∞控制[J].计算机技术与发展,2017,27(5):164-169.
[7] 宋娟.具有时变时延的网络控制系统的量化控制[J].航天控制,2017(5):15-18.
[8] WANG P,CHE W.Quantized H∞ control for networked control systems with random packet losses[C]// 27th Chinese Control and Decision Conference.Qingdao:IEEE,2015:6557-6562.
[9] HONGJIU Y,LI L,JUNKAN H,et al.Robust H∞ control for discrete-time networks with state and input quantizations based on delta operator[C]// 27th Chinese Control Conference.Kunming:IEEE,2008:663-667.
[10] QIU J,LU K,DU X,et al.Robust H∞ control for uncertain delta system with time delays and non-linear perturbations based on delta operators approach[J].International Journal of Modelling Identification & Control,2010,11(3/4):150-163.
[11] 彭仁崇,林瑞全,杨富文,等.不确定Delta算子时滞系统鲁棒H∞控制器设计[J].集美大学学报(自然科学版),2008,13(2):157-161.
[12] FU M,XIE L.The sector bound approach to quantized feedback control[J].IEEE Transactions on Automatic Control,2005,50(11):1698-1711.
[13] 俞立.鲁棒控制:线性矩阵不等式处理方法[M].北京:清华大学出版社,2002.
[14] 刘英英,杨光红.量化的连续时间网络控制系统的H∞控制[J].东北大学学报(自然科学版),2010,31(4):457-460.
[15] SHI P,SHUE S P.Robust H∞ control for linear discrete-time systems with norm-bounded nonlinear uncertainties[J].IEEE Transactions on Automatic Control,1999,44(1):108-111.