【作者】 王磊；

【导师】 闫小喜； 於鑫；

【作者基本信息】 江苏大学 ， 控制科学与工程， 2023， 硕士

【摘要】 时滞现象在控制系统中普遍存在,比如工程控制系统、网络控制系统、生物系统以及数学物理系统等。时滞的存在往往会对系统的稳定性和性能产生负面影响,甚至导致不稳定。输入时滞系统是时滞系统的重要一类,相关问题的研究已得到了国内外学者的广泛关注。由于输入时滞系统是无穷维控制系统,因此,对输入时滞系统进行控制器设计和稳定分析一直是控制领域的一个研究难点,具有重要的理论研究意义和实际应用价值。本文以具有未知输入时滞的控制系统为研究对象,从线性系统和非线性系统两方面分别进行研究。针对具有未知输入时滞的一类线性系统,采用截尾预估反馈方法,设计无记忆状态反馈控制器,实现闭环系统的全局渐近稳定。然后,针对具有未知输入时滞的一类非线性系统,设计了一种基于线性化方法的无记忆反馈控制器,实现了闭环非线性系统的局部渐近稳定。最后,将上述研究结果应用到高速双体船的减纵摇控制中。本文研究内容及创新点包括以下四个方面:(1)针对具有未知输入时滞的一类线性系统,为了避免由传统的无穷维Smith预估控制器带来的实现问题,本文基于截尾预估方法,设计了无记忆状态反馈控制器,利用Razumikhin定理,证明了当未知输入时滞在一定范围内时,闭环控制系统是全局渐近稳定的,并给出了未知输入时滞的变化范围的显式表达式。(2)针对具有未知输入时滞的一类非线性系统,利用线性化方法和非线性分离性质,设计了一个基于截尾预估器的无记忆状态反馈控制器,当未知输入时滞在一定范围内时,利用Razumikhin定理和非线性时滞系统的局部前向完备引理,证明了该无记忆状态反馈控制器能够实现非线性闭环控制系统的局部渐近稳定性。此外,该结果进一步推广到线性化系统的特征值位于左半闭复平面上的情况。(3)针对具有未知输入时滞的一类非线性系统,研究了其无记忆输出反馈局部镇定问题。对线性化的输入时滞系统,设计了一个无记忆输出反馈控制器。当未知输入时滞在一定范围内时,利用Razumikhin定理和非线性时滞系统的局部前向完备引理,证明了所设计的无记忆输出反馈控制器能够实现多输入多输出非线性系统的局部渐近稳定性。另外,该结果对于线性化系统的特征值位于左半闭复平面上的情况依然成立。(4)针对未知输入时滞影响下高速双体船的减纵摇控制问题,将双体船的非线性数学模型进行线性化处理,建立带有T型翼的双体船模型,利用上述研究成果,设计了一个无记忆反馈控制器,实现了减纵摇控制系统的局部渐近稳定。仿真结果验证了所提控制方案的有效性。本文以线性时滞系统和非线性时滞系统为研究对象,针对具有未知输入时滞的控制系统,设计可以使系统渐进稳定的无记忆反馈控制器,将未知输入时滞值与已知输入时滞及其他参数相结合,给出了未知输入时滞范围的显式表达式,设计出能在未知输入时滞的约束范围内对系统进行有效控制的无记忆反馈控制器。此外,还将上述研究结果应用到高速双体船的减纵摇控制中。更多还原

【Abstract】 The phenomenon of time delay is very common in the control system,such as engineering control system,network control system,biological system,mathematical physics system,and so on.The existence of time delay often has a negative impact on the stability and performance of the system,and even leads to instability.Systems with input time-delay are an important class of timedelay systems,and its research on some related issues has been widely concerned by scholars at home and abroad.Because the system with input delay is an infinite dimensional control system,the controller design and stability analysis of the input time delayed system is a difficult problem in the field of control,which has important theoretical research significance and practical application value.In this paper,the control system with unknown input delay is studied from two aspects: linear system and nonlinear system.For a class of linear systems with unknown input delay,a memoryless state feedback controller is designed by using truncated predictor feedback method to achieve global asymptotic stability of the closed-loop system.Then,for a class of nonlinear systems with unknown input delay,a memoryless feedback controller based on linearization method is designed to achieve local asymptotic stability of the closed-loop nonlinear system.Finally,the above research results are applied to the pitch reduction control of high-speed catamaran.In this paper,the four aspects of main results include:(1)For a class of linear system with unknown input delay,in order to avoid the realization problem caused by the traditional Smith predictor controller,which is infinite dimensional,we design a memoryless state feedback controller based on the truncated predictor.By the Razumikhin theorem,it is proved that the closed-loop control system is globally asymptotically stable when the unknown input delay is in a certain range,whose explicit expression is given.(2)For a class of nonlinear systems with unknown input delay,a memoryless state feedback controller based on truncated predictor is designed by using linearization method and nonlinear separation property.We prove that the memoryless state feedback controller can make the nonlinear system with input delay be locally asymptotically stable.In addition,this result is further extended to the case where the eigenvalues of linearized systems lie on the left closed complex plane.(3)For a class of nonlinear systems with unknown input delay,the problem of local stabilization by memoryless output feedback is studied.A memoryless output feedback controller is designed for the linearization systems with input delay.When the unknown input delay is in a certain range,it is proved that the designed memoryless output feedback controller can realize the local asymptotic stability of MIMO nonlinear systems by the use of Razumikhin theorem and the local feedforward complete lemma for nonlinear time-delay systems.In addition,this result still holds for the case where the eigenvalues of the linearization system are located on the left closed complex plane.(4)For the pitch reduction control problem of high-speed catamaran under the influence of unknown input time delay,the nonlinear mathematical model of catamaran is linearized,and the model of catamaran with T-wing is established.Using the above research results,a memoryless feedback controller is designed to realize the local asymptotic stability of the pitch reduction control system.The simulation results verify the effectiveness of the proposed control scheme.In this paper,linear and nonlinear time delay systems are studied.For control systems with unknown input delay,a memoryless feedback controller is designed that can make the system asymptotically stable.The unknown input delay value is combined with the known input time delay and other parameters,and an explicit expression for the range of unknown input delay is given.Design a memoryless feedback controller that can effectively control the system within the constraint range of unknown input delay.In addition,the above research results are also applied to the pitch reduction control of high-speed catamaran.更多还原