【作者】 李鹏；

【导师】 杨洪玖；

【作者基本信息】 燕山大学 ， 控制理论与控制工程， 2019， 硕士

【摘要】 Delta算子离散化方法作为连续时间模型和离散时间模型的统一描述方法,已成为连接连续系统和离散系统的纽带。在快速采样条件下,Delta算子描述的离散模型趋近于相应的连续模型,可以有效地避免使用传统移位算子描述系统所带来的数值不稳定问题。执行器饱和现象普遍存在于实际的控制系统中。当执行器的输入量达到一定限制从而进入饱和状态时,进一步增加输入不能对执行器的输出产生任何影响。执行器饱和将使系统的动态性能降低,甚至导致闭环系统不稳定。频域方法是控制理论与工程领域的一种基本研究手段,许多控制问题都可归结为有限频域性能指标的分析与综合问题。因此,本论文在时域和有限频域内研究带有执行器饱和的Delta算子系统性能优化问题,分析有限频域约束下系统H_?性能。通过广义KYP引理将系统频域条件转化为时域线性矩阵不等式条件来设计系统控制器,使带有执行器饱和的Delta算子系统快速趋于稳定。本论文主要研究成果总结如下。首先,考虑带有执行器饱和的Delta算子系统的整体收敛速度问题。基于给定的Delta算子系统整体收敛速度显式定义,得到使得闭环系统整体收敛速度达到最优的控制器增益,并进一步给出该最优控制下整体收敛速度的求解方式。利用Delta算子系统整体收敛速度相关性质,求解执行器饱和Delta算子系统整体收敛速度与吸引域半径的函数关系表达式。通过整体收敛速度和吸引域的折衷优化,得到闭环系统保证一定收敛速度且吸引域最优的控制器设计方法。其次,考虑基于Delta算子方法的航天器姿态执行器饱和系统的模糊控制问题。对于线性化处理后的航天器姿态控制系统,通过Delta算子离散化采样处理,得到带有执行器饱和的航天器姿态Delta算子系统模型。设计T-S模糊规则,进一步得到满足闭环系统控制性能的综合模糊控制律。基于Delta域的Lyapunov方法,给出航天器姿态执行器饱和系统的全局渐进稳定性判据。并利用凸包方法,将模糊状态反馈控制器设计问题转化为线性矩阵不等式求解问题。然后,针对带有执行器饱和的网络化控制系统,研究其在高频约束下的稳定性。通过Delta算子方法,高频网络化控制系统被离散化为带有高频约束的Delta算子执行器饱和系统。基于扩展的积分二次约束框架,将带有时变时延和执行器饱和两个非线性项的闭环系统转化为双闭环反馈组态形式,并得到其在高频段稳定的频域不等式判据。利用广义KYP引理,带有执行器饱和的高频网络化控制系统频域不等式条件被转化为易于求解的线性矩阵不等式条件。最后,考虑带有干扰输入的低频网络化控制系统,设计基于分散式事件触发机制的H_?静态输出反馈控制器。采用分散式事件触发机制,使得在每个采样时刻只有满足触发条件的测量输出被发送到控制端,减少不必要的数据传输以节省网络资源。利用积分二次约束方法和广义KYP引理,得到闭环系统稳定同时满足期望低频H_?性能指标的线性矩阵不等式判据。设计启发式算法处理判据中的双线性矩阵不等式问题,最终得到满足条件的静态输出反馈控制器。更多还原

【Abstract】 As a unified description method of continuous and discrete time models,a delta operator is a link between continuous and discrete time systems.Under fast sampling conditions,discrete time models described by the delta operator tend to the corresponding continuous time models,which avoids numerical instability caused by the use of a shift operator to describe discrete time systems.Note that actuator saturation is ubiquitous in actual control systems.When a input of an actuator reaches a certain limit and enters a saturated state,further increase of the input does not have any effect on an output of the actuator.Actuator saturation degrades dynamic performance of systems and even causes instability for closed-loop systems.Frequency domain analysis is a basic research method in the field of control theory and engineering.Many control problems are attributed to the analysis and synthesis of finite frequency domain performance.Therefore,a performance optimization problem is investigated for delta operator systems with actuator saturation in time and finite frequency domains.Some interesting analysis results are further obtained for H_?performance under finite frequency domain constraints.Moreover,a generalized KYP lemma is used to transform frequency domain conditions into time domain linear matrix inequality conditions to design controllers,so that the delta operator systems with actuator saturation are stabilized quickly.The main research results are given as follows.Firstly,a overall convergence rate for a delta operator system with actuator saturation is considered.Based on an explicit definition of the overall convergence rate,a controller gain is obtained to make the overall convergence rate optimal for the closed-loop system,and a solution is further given under the optimal control.Based on some related properties of the overall convergence rate,a functional relationship is obtained between the overall convergence rate and the domain of attraction for the actuator saturated delta operator system.By a compromise optimization of the overall convergence rate and the domain of attraction,an optimal controller design method is shown for the closed-loop system with a certain overall convergence rate.Secondly,a fuzzy control problem is considered for a spacecraft attitude actuator saturation system based on a delta operator method.For the spacecraft attitude control system after a linearization,a delta operator model with actuator saturation is obtained by a discrete sampling processing using delta operator.A T-S fuzzy rule is designed to further obtain a comprehensive fuzzy control law which satisfies desired control performance for the closed-loop system.Using a Lyapunov method in delta domain,a global asymptotic stability criterion is given for the spacecraft attitude actuator saturation system.A convex hull method is used to transform a fuzzy state feedback controller design problem into a linear matrix inequality problem.Thirdly,stability analysis is investigated for a networked control system with actuator saturation under a high frequency constraint.Through a delta operator method,the high frequency networked control system is discretized into a delta operator actuator saturation system with a high frequency constraint.By an extended integral quadratic constraint framework,the closed-loop system with time-varying delay and actuator saturation is transformed into a double closed-loop feedback configuration form,and its frequency domain inequality criterion is obtained in high frequency domain.Using a generalized KYP lemma,frequency domain inequality conditions is transformed into some linear matrix inequality conditions which are easy to solve.Finally,a static output feedback controller is designed based on a decentralized event trigger mechanism for a low frequency networked control system with a disturbance input.The decentralized event trigger mechanism is adopted so that only measurement outputs that satisfy trigger conditions are transmitted at each sampling instance,and network resources are saved by reducing unnecessary data transmissions.By an integral quadratic constraint method and a generalized KYP lemma,a linear matrix inequality criterion is obtained for the closed-loop system to satisfy a desired low frequency H_?performance.Moreover,a heuristic algorithm is designed to deal with bilinear matrix inequality problems in the criterion to obtain a static output feedback controller.更多还原