Designing a robust controller for a system with timevarying delays poses a major challenge. In this paper, we propose a method based on mixed sensitivity H∞ for the control of linear time invariant（LTI） systems wit...Designing a robust controller for a system with timevarying delays poses a major challenge. In this paper, we propose a method based on mixed sensitivity H∞ for the control of linear time invariant（LTI） systems with varying time delays. The time delay is assumed bounded and the upper bound is known. In the technique we propose, the delay affecting the plant to be controlled is treated as an unmodeled uncertainty（in form of multiplicative uncertainty）. That uncertainty is approximated and then an H∞based controller, for the plant represented by the multiplicative uncertainty and the nominal model, is calculated. The obtained H∞controller is used to control the LTI systems with varying time delays. Simulation examples are given to illustrate the effectiveness of the proposed method.展开更多
The state space representations of fractional order linear time-invariant(LTI) systems are introduced, and their solution formulas are deduced by means of Laplace transform. The stability condition of fractional order...The state space representations of fractional order linear time-invariant(LTI) systems are introduced, and their solution formulas are deduced by means of Laplace transform. The stability condition of fractional order LTI systems is given, and its proof is deduced by means of using linear non-singularity transform and the derivative property of Mittag-Leffler function. The controllability condition of fractional order LTI systems is given, and its proof is deduced by means of using its characteristic polynomial and the Cayley-Hamilton theorem. The observability condition of fractional order LTI systems is given, and its proof is deduced by means of their solution formulas. Finally an example is given to prove the correctness of the stability, controllability, and observability conditions mentioned above.s are deduced by means of Laplace transform. Their stability, controllability and observability conditions are given as well as their proofs.展开更多
This work deals with the robust D-stability test of linear time-invariant(LTI) general fractional order control systems in a closed loop where the system and/or the controller may be of fractional order. The concept o...This work deals with the robust D-stability test of linear time-invariant(LTI) general fractional order control systems in a closed loop where the system and/or the controller may be of fractional order. The concept of general implies that the characteristic equation of the LTI closed loop control system may be of both commensurate and non-commensurate orders, both the coefficients and the orders of the characteristic equation may be nonlinear functions of uncertain parameters, and the coefficients may be complex numbers. Some new specific areas for the roots of the characteristic equation are found so that they reduce the computational burden of testing the robust D-stability. Based on the value set of the characteristic equation, a necessary and sufficient condition for testing the robust D-stability of these systems is derived. Moreover, in the case that the coefficients are linear functions of the uncertain parameters and the orders do not have any uncertainties, the condition is adjusted for further computational burden reduction. Various numerical examples are given to illustrate the merits of the achieved theorems.展开更多
针对含有随机噪声的模型未知线性时不变(LTI,linear time invariant)系统模型建立过程复杂且控制律难以得到的问题,提出一种基于数据驱动的预测控制方法;基于系统行为学理论和平衡子系统辨识方法,仅利用测量得到的系统数据构建被控系统...针对含有随机噪声的模型未知线性时不变(LTI,linear time invariant)系统模型建立过程复杂且控制律难以得到的问题,提出一种基于数据驱动的预测控制方法;基于系统行为学理论和平衡子系统辨识方法,仅利用测量得到的系统数据构建被控系统的非参数模型,将其和预测控制理论相结合设计出基于数据驱动的预测控制器,对于系统测量数据中存在的有界加性高斯噪声,通过引入数据的松弛变量和L2正则项来降低噪声扰动的影响,采用滚动时域优化策略计算最优控制序列并将其作用于被控系统,实现了系统对设定值的轨迹跟踪;将所提控制策略应用于四容水箱系统,仿真结果表明所提方法能实现四容水箱系统的液位跟踪控制,且与同样基于数据驱动的子空间预测控制方案相比,所提方法具有更好的动态性能,且该策略在抗噪声扰动方面有明显优势,具有更强的鲁棒性。展开更多
文摘Designing a robust controller for a system with timevarying delays poses a major challenge. In this paper, we propose a method based on mixed sensitivity H∞ for the control of linear time invariant（LTI） systems with varying time delays. The time delay is assumed bounded and the upper bound is known. In the technique we propose, the delay affecting the plant to be controlled is treated as an unmodeled uncertainty（in form of multiplicative uncertainty）. That uncertainty is approximated and then an H∞based controller, for the plant represented by the multiplicative uncertainty and the nominal model, is calculated. The obtained H∞controller is used to control the LTI systems with varying time delays. Simulation examples are given to illustrate the effectiveness of the proposed method.
基金stability, coSponsored by the National High Technology Research and Development Program of China (Grant No.2003AA517020), the National Natural Science Foundation of China (Grant No.50206012), and Developing Fund of Shanghai Science Committee (Grant No.011607033).
文摘The state space representations of fractional order linear time-invariant(LTI) systems are introduced, and their solution formulas are deduced by means of Laplace transform. The stability condition of fractional order LTI systems is given, and its proof is deduced by means of using linear non-singularity transform and the derivative property of Mittag-Leffler function. The controllability condition of fractional order LTI systems is given, and its proof is deduced by means of using its characteristic polynomial and the Cayley-Hamilton theorem. The observability condition of fractional order LTI systems is given, and its proof is deduced by means of their solution formulas. Finally an example is given to prove the correctness of the stability, controllability, and observability conditions mentioned above.s are deduced by means of Laplace transform. Their stability, controllability and observability conditions are given as well as their proofs.
文摘This work deals with the robust D-stability test of linear time-invariant(LTI) general fractional order control systems in a closed loop where the system and/or the controller may be of fractional order. The concept of general implies that the characteristic equation of the LTI closed loop control system may be of both commensurate and non-commensurate orders, both the coefficients and the orders of the characteristic equation may be nonlinear functions of uncertain parameters, and the coefficients may be complex numbers. Some new specific areas for the roots of the characteristic equation are found so that they reduce the computational burden of testing the robust D-stability. Based on the value set of the characteristic equation, a necessary and sufficient condition for testing the robust D-stability of these systems is derived. Moreover, in the case that the coefficients are linear functions of the uncertain parameters and the orders do not have any uncertainties, the condition is adjusted for further computational burden reduction. Various numerical examples are given to illustrate the merits of the achieved theorems.
文摘针对含有随机噪声的模型未知线性时不变(LTI,linear time invariant)系统模型建立过程复杂且控制律难以得到的问题,提出一种基于数据驱动的预测控制方法;基于系统行为学理论和平衡子系统辨识方法,仅利用测量得到的系统数据构建被控系统的非参数模型,将其和预测控制理论相结合设计出基于数据驱动的预测控制器,对于系统测量数据中存在的有界加性高斯噪声,通过引入数据的松弛变量和L2正则项来降低噪声扰动的影响,采用滚动时域优化策略计算最优控制序列并将其作用于被控系统,实现了系统对设定值的轨迹跟踪;将所提控制策略应用于四容水箱系统,仿真结果表明所提方法能实现四容水箱系统的液位跟踪控制,且与同样基于数据驱动的子空间预测控制方案相比,所提方法具有更好的动态性能,且该策略在抗噪声扰动方面有明显优势,具有更强的鲁棒性。
