含有控制时滞离散时间系统的最优控制及其应用研究
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摘要
由于对系统动态性能期望的提高，所建立的系统模型需要更加真实地反映实际系统的特性。由控制信号的计算、传输以及控制力的产生所引起的控制时滞普遍存在于实际控制系统中。同时，外界持续扰动是普遍存在的。控制时滞和扰动的存在可能会引起系统性能的下降，甚至导致系统不稳定。在车辆主动悬挂系统的最优减振控制问题中考虑控制时滞的影响，可以更加有效地抑制由路面不平整度引起的车体振动问题，并且提高车辆的乘坐舒适性和操作稳定性。离散时间协同自适应巡航控制系统通过感知周围环境以及应用相关车辆的信息，可以有效地提高道路通行能力以及行驶的安全性，同时对车辆的乘坐舒适度、燃料耗费以及实现驾驶员所期望的驾驶行为等性能有明显的改善。因此，针对含有控制时滞离散时间系统的最优跟踪控制、扰动抑制控制及其应用研究具有重要的理论价值和实际意义。
全文主要研究内容以及创新点如下：
1.研究了一类含有控制时滞离散时间系统基于二次性能指标的最优跟踪控制问题，其中参考输入的动态特性由外系统给定的。此类跟踪问题会导致既含有超前项又含有滞后项的两点边值（Two Point Boundary Problem, TPBV）问题。针对含有单个和多个控制时滞的离散时间系统的最优跟踪控制问题，提出两种不同的变量代换方法，将含有控制时滞离散时间系统转化为标准的无时滞系统，并将二次性能指标简化为与转化后无时滞系统相对应的形式，从而获得更加精确地性能指标。此时，此类跟踪问题转化为不含时滞项和超前项的TPBV问题。利用极大值原理，通过求解Riccati和Stein方程，得到系统的最优输出跟踪控制律，并验证了控制律的存在唯一性。利用构造参考输入外系统状态向量的降维观测器，解决了控制律中前馈补偿器的物理不可实现问题。仿真实例验证了针对含有控制时滞离散时间系统所设计的最优跟踪控制律的有效性。
2.研究无限时域情形下在持续外部扰动作用下含有控制时滞离散时间系统的最优跟踪控制问题。首先研究了在正弦扰动影响下含有单个控制时滞离散时间系统的最优跟踪控制，根据正弦扰动的动态特性并利用扩维方法，原系统转化为不显含扰动的标准系统。基于上述对于含有单个控制时滞离散时间系统的变量代换，将此类问题转化为不含超前项和滞后项的TPBV问题。应用极大值原理，得到前馈反馈最优控制（Feedforward and FeedbackOptimal Control law, FFOC）律，保证了闭环系统的稳定性和性能，并且验证了FFOC的唯一性和最优性。在此控制律中，前馈控制项由扰动外系统和参考输入外系统的状态向量组成。进一步将外部扰动模型由正弦扰动推广到更一般的由线性外系统描述的已知动态特性的扰动模型，研究了在此类扰动作用下含有多控制时滞离散时间系统的最优跟踪控制问题。仿真结果表明所设计的FFOC不仅仅能减小扰动对系统性能的影响，而且有效地提高了被控系统的跟踪精度。
3.研究路面扰动作用下含有控制时滞汽车主动悬挂离散时间系统的最优减振控制。考虑控制时滞存在的情况下，建立了二自由度四分之一汽车主动悬挂系统和路面随机激励输入的离散时间模型。根据汽车驾驶舒适性和操控稳定性的性能指标，设计了汽车主动悬挂系统前馈-反馈最优减振控制（Feedforward and Feedback Optimal Vibration Control,FFOVC）律。通过求解Riccati方程和Sylvester方程得到FFOVC控制律，并证明了最优解的存在唯一性。仿真算例说明了FFOVC律的有效性。
4.研究离散时间协同自适应巡航控制(Cooperative Adaptive Cruise Control, CACC)系统中与被控车辆相对位置有关的分布式纵向最优跟踪控制。考虑由不同车辆组成的交通流中纵向控制问题。根据车辆的特性、交通状况以及驾驶员所期望的驾驶行为，构建了与车辆速度、加速度以及前车车间距相关的跟踪目标，并将混杂交通流纵向控制问题规划为基于二次性能指标的最优跟踪控制问题。根据车辆间的通信结构，利用极大值原理，得到最优纵向跟踪控制律，其中包括由被控车辆状态组成的反馈项以及由相关车辆的预测信息组成的前馈项，从而权衡了三个相互矛盾的跟踪目标。另外，通过引入“虚拟期望速度”以及“虚拟期望加速度”的概念，设计了与车辆相对位置有关的期望速度以及加速度，从而规划了相关期望目标，并构建了相对应的跟踪问题。计算机仿真实验验证了所提出的跟踪控制律的可行性和有效性。
With the increasing expectations of dynamic performances, engineers need their models tobehave more like the real process. In actual control systems, the time-delay in control input isinevitable, which is caused by calculating and transporting the control singnal, building up therequired control force. External distuabance exists widely and inevitably. In general, theexistence of time-delay and disturbance usually deteriorate the performance of closed-loopsystems and maybe a source of instability. Taking into account control delays in activesuspension systems, the vibration problem for vehicles could be solved by using active force sothat ride comfort and driving safety are improved, in which the vibration is caused by persistentdisturbance of roughness road. In vehicle longitudianl control, the cooperative operation in avehicle platoon could be realized by using the information about the related vehicles andembient environment. Then, the traffic flow, driving safety, ride comfort, fuel comsumpation,and the drivers’ respond are significantly improved in CACC system. Therefore, the optimaltracking control, optimal rejection control, and application for discrete-time systems withcontrol delays are very important and significant in the field of theory research and actualpractice.
The main results and contributions of this disseration are summarized as follows.
1. The optimal trakcing control problem for discrete-time systmes with control delayswith quadratic performance index is studied, in which the referecen is given by an exosystem.The TPBV problems with both time-delay and time-advance terms is induced in this type problem. For the optimal tracking control problem with signal and multiple control delayss, twokinds of variable transformations are introduced. Then, the systems with control delays aretransformed into a non-delayed system, and the quadratic performance index of the optimaltracking control is transformed into a relevant format. The original TPBV problems aretransformed into a sequence of linear TPBV problem without time-delay and time-advanceterms. By using the maximum principle, the optimal tracking control law is constructed by thesolution of a Riccati matrix equation and a Stein matrix equation. A reduced-order observer isconstructed to solve the physically realizable problem of the feedforward compensator.Simulation results demonstrate the effectiveness of the proposed optimal tracking control law.
2. The optimal trakcing control problem for discrete-time system with control delaysunder persistant disturbance is researched. Firstly, the optimal tracking controller fordiscrete-time system with signal input delay under sinusoidal disturbance is presented.According to the dynamic characters of sinusoidal and argument method, the originaldiscrete-time system is reformed into a transformed system without disturbance. Based on theabove variable transformation, this problem is transformed into a TPBV problem withouttime-delay and time-advance items. The feedback and feedforward control law is designed byusing the maximum prinpicle so that the stability and performance index of closed-loop systemare ensured. The feedforward items of this controller contant the states of disturbance exosystemand the reference exosystem. The conditions of existence and uniqueness of the control law arepresneted. Furthermore, the external disturbances model is generalized from the sinusoidaldisturbance form to more general deterministic disturbance that described by a linear exosystem.The optimal trakcing control problem for discrete-time systems with multiply control delayswith persistant disturbances is studied. Simulation results demonstrate the effectiveness of theoptimal tracking control law, which not only reduces the influence of virbation, but also improve the tracking precision.
3. The problem of optimal vibration control for vehicle active suspension discrete-timesystems with actuator time delay under random road disturbance is considered. Firstly, thediscrete-time model for the two-degree-freedom vehicle active suspension system with actuatortime delay under random road disturbance is presented and the random road disturbance causedby road roughness is considered as the output of an exosystem. Based on the requirements ofride comforable and handing stability, the FFOVC law is obtained from Riccat and Steinequations by using maximum principle. The existence and uniqueness of the optimal control lawis proved. Numerical simulations illustrate the effectiveness of the optimal control law.
4. Longitudinal tracking controller for discrete-time CACC systems are designed that cancomprehensively enable tracking of various spacing policies, designed desired velocity, anddesigned desired acceleration. Taking into account heterogeneous traffic, i.e., a platoon ofvehicles with possibly different characteristics, the longitudinal control problem is formulated asan output tracking control problem with a quadratic function so that the contradictions amongthe different tracking requirements are realized, which include inter-vehicle spacing, velocityand acceleration. Then, the optimal tracking longitudinal controller is proposed by using alimited communication structure and maximum prinpicle, in which the feedback items arecomposed of the states of host vehicles, and additional information of the nearest precedingvehicle and leading vehicle are used as feedforward items. In additional, the concepts of “virtualdesired velocity” and “virtual desired acceleration” are introduced to design the desired velocityand acceleration, realize additional objectives, and formulate the tracking problem. Numeroussimulation results show that the proposed tracking controller provides a reliable tool for asystematic and efficient design of a platoon controller within CACC systems.
Finally, the main work in this dissertation is summarized and a proposition is indicated on the research work in the future.
全文主要研究内容以及创新点如下：
1.研究了一类含有控制时滞离散时间系统基于二次性能指标的最优跟踪控制问题，其中参考输入的动态特性由外系统给定的。此类跟踪问题会导致既含有超前项又含有滞后项的两点边值（Two Point Boundary Problem, TPBV）问题。针对含有单个和多个控制时滞的离散时间系统的最优跟踪控制问题，提出两种不同的变量代换方法，将含有控制时滞离散时间系统转化为标准的无时滞系统，并将二次性能指标简化为与转化后无时滞系统相对应的形式，从而获得更加精确地性能指标。此时，此类跟踪问题转化为不含时滞项和超前项的TPBV问题。利用极大值原理，通过求解Riccati和Stein方程，得到系统的最优输出跟踪控制律，并验证了控制律的存在唯一性。利用构造参考输入外系统状态向量的降维观测器，解决了控制律中前馈补偿器的物理不可实现问题。仿真实例验证了针对含有控制时滞离散时间系统所设计的最优跟踪控制律的有效性。
2.研究无限时域情形下在持续外部扰动作用下含有控制时滞离散时间系统的最优跟踪控制问题。首先研究了在正弦扰动影响下含有单个控制时滞离散时间系统的最优跟踪控制，根据正弦扰动的动态特性并利用扩维方法，原系统转化为不显含扰动的标准系统。基于上述对于含有单个控制时滞离散时间系统的变量代换，将此类问题转化为不含超前项和滞后项的TPBV问题。应用极大值原理，得到前馈反馈最优控制（Feedforward and FeedbackOptimal Control law, FFOC）律，保证了闭环系统的稳定性和性能，并且验证了FFOC的唯一性和最优性。在此控制律中，前馈控制项由扰动外系统和参考输入外系统的状态向量组成。进一步将外部扰动模型由正弦扰动推广到更一般的由线性外系统描述的已知动态特性的扰动模型，研究了在此类扰动作用下含有多控制时滞离散时间系统的最优跟踪控制问题。仿真结果表明所设计的FFOC不仅仅能减小扰动对系统性能的影响，而且有效地提高了被控系统的跟踪精度。
3.研究路面扰动作用下含有控制时滞汽车主动悬挂离散时间系统的最优减振控制。考虑控制时滞存在的情况下，建立了二自由度四分之一汽车主动悬挂系统和路面随机激励输入的离散时间模型。根据汽车驾驶舒适性和操控稳定性的性能指标，设计了汽车主动悬挂系统前馈-反馈最优减振控制（Feedforward and Feedback Optimal Vibration Control,FFOVC）律。通过求解Riccati方程和Sylvester方程得到FFOVC控制律，并证明了最优解的存在唯一性。仿真算例说明了FFOVC律的有效性。
4.研究离散时间协同自适应巡航控制(Cooperative Adaptive Cruise Control, CACC)系统中与被控车辆相对位置有关的分布式纵向最优跟踪控制。考虑由不同车辆组成的交通流中纵向控制问题。根据车辆的特性、交通状况以及驾驶员所期望的驾驶行为，构建了与车辆速度、加速度以及前车车间距相关的跟踪目标，并将混杂交通流纵向控制问题规划为基于二次性能指标的最优跟踪控制问题。根据车辆间的通信结构，利用极大值原理，得到最优纵向跟踪控制律，其中包括由被控车辆状态组成的反馈项以及由相关车辆的预测信息组成的前馈项，从而权衡了三个相互矛盾的跟踪目标。另外，通过引入“虚拟期望速度”以及“虚拟期望加速度”的概念，设计了与车辆相对位置有关的期望速度以及加速度，从而规划了相关期望目标，并构建了相对应的跟踪问题。计算机仿真实验验证了所提出的跟踪控制律的可行性和有效性。
With the increasing expectations of dynamic performances, engineers need their models tobehave more like the real process. In actual control systems, the time-delay in control input isinevitable, which is caused by calculating and transporting the control singnal, building up therequired control force. External distuabance exists widely and inevitably. In general, theexistence of time-delay and disturbance usually deteriorate the performance of closed-loopsystems and maybe a source of instability. Taking into account control delays in activesuspension systems, the vibration problem for vehicles could be solved by using active force sothat ride comfort and driving safety are improved, in which the vibration is caused by persistentdisturbance of roughness road. In vehicle longitudianl control, the cooperative operation in avehicle platoon could be realized by using the information about the related vehicles andembient environment. Then, the traffic flow, driving safety, ride comfort, fuel comsumpation,and the drivers’ respond are significantly improved in CACC system. Therefore, the optimaltracking control, optimal rejection control, and application for discrete-time systems withcontrol delays are very important and significant in the field of theory research and actualpractice.
The main results and contributions of this disseration are summarized as follows.
1. The optimal trakcing control problem for discrete-time systmes with control delayswith quadratic performance index is studied, in which the referecen is given by an exosystem.The TPBV problems with both time-delay and time-advance terms is induced in this type problem. For the optimal tracking control problem with signal and multiple control delayss, twokinds of variable transformations are introduced. Then, the systems with control delays aretransformed into a non-delayed system, and the quadratic performance index of the optimaltracking control is transformed into a relevant format. The original TPBV problems aretransformed into a sequence of linear TPBV problem without time-delay and time-advanceterms. By using the maximum principle, the optimal tracking control law is constructed by thesolution of a Riccati matrix equation and a Stein matrix equation. A reduced-order observer isconstructed to solve the physically realizable problem of the feedforward compensator.Simulation results demonstrate the effectiveness of the proposed optimal tracking control law.
2. The optimal trakcing control problem for discrete-time system with control delaysunder persistant disturbance is researched. Firstly, the optimal tracking controller fordiscrete-time system with signal input delay under sinusoidal disturbance is presented.According to the dynamic characters of sinusoidal and argument method, the originaldiscrete-time system is reformed into a transformed system without disturbance. Based on theabove variable transformation, this problem is transformed into a TPBV problem withouttime-delay and time-advance items. The feedback and feedforward control law is designed byusing the maximum prinpicle so that the stability and performance index of closed-loop systemare ensured. The feedforward items of this controller contant the states of disturbance exosystemand the reference exosystem. The conditions of existence and uniqueness of the control law arepresneted. Furthermore, the external disturbances model is generalized from the sinusoidaldisturbance form to more general deterministic disturbance that described by a linear exosystem.The optimal trakcing control problem for discrete-time systems with multiply control delayswith persistant disturbances is studied. Simulation results demonstrate the effectiveness of theoptimal tracking control law, which not only reduces the influence of virbation, but also improve the tracking precision.
3. The problem of optimal vibration control for vehicle active suspension discrete-timesystems with actuator time delay under random road disturbance is considered. Firstly, thediscrete-time model for the two-degree-freedom vehicle active suspension system with actuatortime delay under random road disturbance is presented and the random road disturbance causedby road roughness is considered as the output of an exosystem. Based on the requirements ofride comforable and handing stability, the FFOVC law is obtained from Riccat and Steinequations by using maximum principle. The existence and uniqueness of the optimal control lawis proved. Numerical simulations illustrate the effectiveness of the optimal control law.
4. Longitudinal tracking controller for discrete-time CACC systems are designed that cancomprehensively enable tracking of various spacing policies, designed desired velocity, anddesigned desired acceleration. Taking into account heterogeneous traffic, i.e., a platoon ofvehicles with possibly different characteristics, the longitudinal control problem is formulated asan output tracking control problem with a quadratic function so that the contradictions amongthe different tracking requirements are realized, which include inter-vehicle spacing, velocityand acceleration. Then, the optimal tracking longitudinal controller is proposed by using alimited communication structure and maximum prinpicle, in which the feedback items arecomposed of the states of host vehicles, and additional information of the nearest precedingvehicle and leading vehicle are used as feedforward items. In additional, the concepts of “virtualdesired velocity” and “virtual desired acceleration” are introduced to design the desired velocityand acceleration, realize additional objectives, and formulate the tracking problem. Numeroussimulation results show that the proposed tracking controller provides a reliable tool for asystematic and efficient design of a platoon controller within CACC systems.
Finally, the main work in this dissertation is summarized and a proposition is indicated on the research work in the future.
引文
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