CPS中一类非线性MIMO系统观测器辅助实时控制方法研究
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摘要
CPS (Cyber Physical Systems,信息物理系统)是集计算、通信、控制于一体的下一代智能系统,是计算进程和物理进程的统一体。该系统使用网络化空间以远程的、可靠的、实时的、安全的、协作的方式操控一个物理实体。CPS是物联网的智能化扩展,也是下一代网络化机电一体化控制系统的核心技术。CPCS(信息物理控制系统)是CPS的一个重要分支；多个分立的SISO(单输入单输出)型闭环控制系统经网络接入CPS后,可以建模成一个具有网络诱导时延的MIMO(多输入多输出)闭环CPCS。
网络诱导时延是影响闭环CPCS稳定性和实时性的重要因素；严重时,在无时延环境下设计的控制器甚至不能在网络环境下工作。所以,研究CPCS中的MIMO系统,尤其是对时延一般比较敏感的非线性MIMO系统的网络诱导时延补偿和网络化实时控制技术具有巨大的学术价值,对推动CPS在控制领域的实际应用具有重要意义,目前已经成为CPS相关前沿研究中的热点问题。
本文旨在寻求以2DOF(两自由度)直升机模型为代表一类非线性MIMO系统的网络化实时控制方法,目的是使在无时延环境下为之设计的就地控制器,仍然可以使用在具有网络诱导I/O时延的CPCS中；这样,就可以用无时延环境下的控制器设计方法来为CPCS中的该类非线性MIMO系统设计网络控制器。
论文首先以著名的Wood-Berry模型为例,研究了线性MIMO系统的网络I/O时延补偿技术,提出了一种新的基于虚拟观测器的时延补偿方法。然后将本文研究的一类非线性MIMO系统通过局部线性化方法近似成一线性MIMO系统,从而构建一个时延合并的虚拟系统；基于该虚拟系统为实际的时延非线性MIMO系统设计了一个观测器,在该虚拟观测器的辅助下,利用在无时延环境下设计的控制器实现了对该类非线性MIMO系统的网络化实时控制。对2DOF直升机模型的实际测试结果证明了该方法正确有效。
论文的主要内容有：
1)为线性MIMO系统提出了一种构建等效虚拟系统的方法。即将网络诱导的I/O(输入和输出)时延进行合并,并分配到输出通道或系统状态向量中,从而从数学上构建了一个虚拟线性MIMO系统。具有合并时延的该虚拟MIMO系统,在输入-输出关系上与原来具有I/O时延的系统等效。而且,该虚拟系统可以用状态空间模型来描述,并证明了该模型具有可观测性,满足观测器设计条件。
2)提出了一种改进的Luenberger观测器设计方法,并基于该方法简便地实现了线性MIMO系统的网络时延补偿。即,基于合并时延的虚拟MIMO系统设计一种含有时延项的Luenberger观测器,观测器的状态反馈到无时延环境下设计的状态反馈控制器,如LQR(线性二次型优化控制器)。由于观测器的状态位于合并的输出时延项之前,从而剥离了时延的影响,保证了闭环控制系统的稳定,实现了状态反馈闭环控制系统的时延补偿。论文以对时延敏感的著名Wood-Berry线性MIMO系统模型为例,仿真表明,在无时延环境中设计的状态反馈控制器,即就地控制器,在网络环境中由于网络诱导时延的存在不能正常工作,而利用本文提出的虚拟观测器时延补偿方法,原状态反馈控制器又恢复到了良好的工作状态。
3)为了更有效地补偿不同大小的时延,论文提出用一个比例因子ε修正该观测器的增益矩阵Jo,并给出了求解ε最优值的系统方法。即,将观测器特征方程中的时延用其Pade近似值替代,然后取不同的ε值求解方程的特征根,距离虚轴最远的主特征根对应的ε值即为当前时延下的ε的最优值。
4)由2DOF(两自由度)直升机模型的网络化控制引出了一类CPCS中的非线性MIMO系统的网络控制问题。首先,对拉格朗日方法得到的直升机模型的非线性动态方程进行准线性化,得到要讨论的一类非线性MIMO系统的准线性无时延状态空间模型。基于该模型设计了就地控制器,即LQR+FF+I控制器(线性二次型优化控制器+前向控制器+积分器)。然后,对引入时延的该状态空间模型进行数学变换,将非线性项进一步简化后合并到线性部分,构建一个等效的具有I/O时延的线性MIMO系统；最后,基于该等效系统利用线性MIMO系统时延补偿办法进行虚拟观测器辅助实时控制。对2DOF的直升机模型的控制仿真和实际测试表明,本方法对该类非线性MIMO系统的网络化实时控制十分有效,使网络时延导致失稳的直升机模型网络闭环系统重新归于稳定。
5)最后讨论了实际应用在CPCS中需要注意的几个事项。如：有界随机时延可以通过时延堆栈转化成固定时延,以简便地实现基于虚拟观测器的时延补偿。对时延合并构建的虚拟系统的维数可能增加,导致基于虚拟系统设计的观测器的状态不能直接反馈到原来的LQR控制器的问题,本文提出了用状态输出矩阵Ω对观测器状态进行降维的办法。对输入或输出通道上的时延大小相差较大的系统,ε可以取值为一个合适的矩阵,这将有利于提高时延补偿的效果。
Cyber Physical Systems (CPS), the unity of computing and physical process, is the next generation intelligent system which is the integration of computation, communication and control. The system manipulates the physical entity remotely, reliably, real-time, safely, and collaboratively via networked space. CPS is the argument in telligence of Internet of Things, and also is the key technology of next generation networked mechatronics control systems. Cyber Physical Control System (CPCS) is one of important parts of CPS; multiple closed loop control systems of Single Input-Single Output (SISO) systems can be modeled as a closed loop CPCS of Multiple Inputs-Multiple Outputs (MIMO) system with network induced delays since they are inter-connected into CPS.
Network induced delay is one of the vital factors influencing the real-time performance of CPCS; and even worse, the controller designed in delay-free environment doesn't work in network anymore. So, research on real-time control and delay compensation technology for networked MIMO system, especially for nonlinear MIMO system, is of great scientific value and very important for the applications of CPS in control field, and now it has been the advanced hot research area in the field of CPCS.
This dissertation is to find a networked real-time control method for a class of networked nonlinear MIMO systems by taking2DOF helicopter model as the representative, and the goal is to assure that the local controller designed in delay-free environment still can be used in the CPCS with network induced I/O delays, thus, the networked controller of a class of nonlinear MIMO system in CPCS can be designed by the method of controller design in delay-free environment.
This dissertation begins with delay compensation technology of linear MIMO system based on a novel virtual observer by taking famous Wood-Berry model as an example. And then, a class of nonlinear MIMO sytem addressed in this dissertation was transformed to a linear MIMO system approximately by the method of local linearization; furthermore, a virtual MIMO system with combined delays was constructed; based on the virtual MIMO system, an observer was designed for the actual delayed nonlinear MIMO systems. With the aid of such a virtual observer, the networked nonlinear system can still be controlled well by the controller designed in delay free environment. The simulation and actual test results of2DOF helicopter networked control system proved the correctness and effectiveness of this method.
The main content is as bellow.
1) A method of construction of an equivalent virtual linear system was proposed in this dissertation. Network induced Input/Output (I/O) delays are firstly combined, and then the combined delay is allocated to output channels or system states, which results in the mathematical construction of a virtual linear MIMO system. It is proved that the virtual system with combined delay is equivalent to the original system with I/O delays in terms of system input-output relationship. Furthermore, the observability of the virtual system in the form of state space model was also proved, which is required to design the virtual observer.
2) A modified Luenberger observer was designed, and delay compensation of linear MIMO system is realized based on the modified observer. Firstly, the modified Luenberger observer was designed based on the equivalent virtual system with combinded delay; and the estimated states of the original I/O delayed system were obtained by the modified observer. Secondly, the estimated states were fed back to the state-feedback-controller (for example, LQR) which was designed for the corresponding delay-free system. Because that the observer states were output in ahead of the combined delay, the stability of the closed loop control system with the observer is almost the same as delay free. So the delay compensation for the state-feedback control system was realized. Finally, taking the famous delay-sensitive Wood-Berry model as an example, the simulation shows that the local state-feedback controller designed in delay-free environment cannot work yet in the network due to the network induced delays, but it can resume working well when the virtual observer-based delay compensation method is applied.
3) In order to compensate the delay of variable time constant, this dessertation proposed a proportional factor namely ε to modify observer gain Jo. And the optimal solution of ε was presented as well. Firstly, approximate the delay in characteristic equation of observer with Pade method. Then, solve the equation with different value of ε to obtain the characteristic poles of observer. Finally, the value of ε with which the principal pole of observer is farthest from imaginary axis can be considered as the optimal value corresponding to the current delay.
4) The problem of delay compensation for a class of nonlinear MIMO system is drew forth from the issue of networked control of two Degree of Freedom (2DOF) helicopter model. Firstly, the nonlinear dynamic equations of a2DOF helicopter model were obtained by means of Lagrange method. Then, the dynamic equations were un-completely linearized, which results in delay-free simi-linearized state space model of a class of nonlinear MIMO systems. The next, local delay free controller, that is LQR+FF+I controller (Linear Quadratic Regulator+Forward Feed controller+Integrator) was designed based on the simi-linearized state space model. The next, network induced I/O delays were introduced into the state feedback control system, and then by mathematical transformation the nonlinear item in the delayed semi-linearized state space model was converted and combined into the linear part, which leads to an equivalent I/O delayed linear MIMO system. Finally, following the delay compensation method for linear MIMO system, the delay compensation for the delayed nonlinear MIMO system was implemented. Simulation and hardware control of the2DOF helicopter model proves the effectiveness of the method, that is, the unstable networked closed loop control system of helicopter due to the network induced I/O delays resumes being stable with the aid of the virtual observer.
5) Several issues relative to the application of networked control technology into actual CPCS were also discussed. For example, limited random delay can be converted into fixed delay by means of delay stack to realize the delay compensation simply; the state number of virtual system with combined delay may increase and as a result the observer state cannot be fed back to the original state-feedback controller directly, so this dissertatin proposed to use matrix Ω to decrease the observer order; at last, it is pointed out that it would be better if ε is a proper matrix when the difference of time constant of input or output delays is considerable large, and it will improve the effectiveness of corresponding delay compensation.
网络诱导时延是影响闭环CPCS稳定性和实时性的重要因素；严重时,在无时延环境下设计的控制器甚至不能在网络环境下工作。所以,研究CPCS中的MIMO系统,尤其是对时延一般比较敏感的非线性MIMO系统的网络诱导时延补偿和网络化实时控制技术具有巨大的学术价值,对推动CPS在控制领域的实际应用具有重要意义,目前已经成为CPS相关前沿研究中的热点问题。
本文旨在寻求以2DOF(两自由度)直升机模型为代表一类非线性MIMO系统的网络化实时控制方法,目的是使在无时延环境下为之设计的就地控制器,仍然可以使用在具有网络诱导I/O时延的CPCS中；这样,就可以用无时延环境下的控制器设计方法来为CPCS中的该类非线性MIMO系统设计网络控制器。
论文首先以著名的Wood-Berry模型为例,研究了线性MIMO系统的网络I/O时延补偿技术,提出了一种新的基于虚拟观测器的时延补偿方法。然后将本文研究的一类非线性MIMO系统通过局部线性化方法近似成一线性MIMO系统,从而构建一个时延合并的虚拟系统；基于该虚拟系统为实际的时延非线性MIMO系统设计了一个观测器,在该虚拟观测器的辅助下,利用在无时延环境下设计的控制器实现了对该类非线性MIMO系统的网络化实时控制。对2DOF直升机模型的实际测试结果证明了该方法正确有效。
论文的主要内容有：
1)为线性MIMO系统提出了一种构建等效虚拟系统的方法。即将网络诱导的I/O(输入和输出)时延进行合并,并分配到输出通道或系统状态向量中,从而从数学上构建了一个虚拟线性MIMO系统。具有合并时延的该虚拟MIMO系统,在输入-输出关系上与原来具有I/O时延的系统等效。而且,该虚拟系统可以用状态空间模型来描述,并证明了该模型具有可观测性,满足观测器设计条件。
2)提出了一种改进的Luenberger观测器设计方法,并基于该方法简便地实现了线性MIMO系统的网络时延补偿。即,基于合并时延的虚拟MIMO系统设计一种含有时延项的Luenberger观测器,观测器的状态反馈到无时延环境下设计的状态反馈控制器,如LQR(线性二次型优化控制器)。由于观测器的状态位于合并的输出时延项之前,从而剥离了时延的影响,保证了闭环控制系统的稳定,实现了状态反馈闭环控制系统的时延补偿。论文以对时延敏感的著名Wood-Berry线性MIMO系统模型为例,仿真表明,在无时延环境中设计的状态反馈控制器,即就地控制器,在网络环境中由于网络诱导时延的存在不能正常工作,而利用本文提出的虚拟观测器时延补偿方法,原状态反馈控制器又恢复到了良好的工作状态。
3)为了更有效地补偿不同大小的时延,论文提出用一个比例因子ε修正该观测器的增益矩阵Jo,并给出了求解ε最优值的系统方法。即,将观测器特征方程中的时延用其Pade近似值替代,然后取不同的ε值求解方程的特征根,距离虚轴最远的主特征根对应的ε值即为当前时延下的ε的最优值。
4)由2DOF(两自由度)直升机模型的网络化控制引出了一类CPCS中的非线性MIMO系统的网络控制问题。首先,对拉格朗日方法得到的直升机模型的非线性动态方程进行准线性化,得到要讨论的一类非线性MIMO系统的准线性无时延状态空间模型。基于该模型设计了就地控制器,即LQR+FF+I控制器(线性二次型优化控制器+前向控制器+积分器)。然后,对引入时延的该状态空间模型进行数学变换,将非线性项进一步简化后合并到线性部分,构建一个等效的具有I/O时延的线性MIMO系统；最后,基于该等效系统利用线性MIMO系统时延补偿办法进行虚拟观测器辅助实时控制。对2DOF的直升机模型的控制仿真和实际测试表明,本方法对该类非线性MIMO系统的网络化实时控制十分有效,使网络时延导致失稳的直升机模型网络闭环系统重新归于稳定。
5)最后讨论了实际应用在CPCS中需要注意的几个事项。如：有界随机时延可以通过时延堆栈转化成固定时延,以简便地实现基于虚拟观测器的时延补偿。对时延合并构建的虚拟系统的维数可能增加,导致基于虚拟系统设计的观测器的状态不能直接反馈到原来的LQR控制器的问题,本文提出了用状态输出矩阵Ω对观测器状态进行降维的办法。对输入或输出通道上的时延大小相差较大的系统,ε可以取值为一个合适的矩阵,这将有利于提高时延补偿的效果。
Cyber Physical Systems (CPS), the unity of computing and physical process, is the next generation intelligent system which is the integration of computation, communication and control. The system manipulates the physical entity remotely, reliably, real-time, safely, and collaboratively via networked space. CPS is the argument in telligence of Internet of Things, and also is the key technology of next generation networked mechatronics control systems. Cyber Physical Control System (CPCS) is one of important parts of CPS; multiple closed loop control systems of Single Input-Single Output (SISO) systems can be modeled as a closed loop CPCS of Multiple Inputs-Multiple Outputs (MIMO) system with network induced delays since they are inter-connected into CPS.
Network induced delay is one of the vital factors influencing the real-time performance of CPCS; and even worse, the controller designed in delay-free environment doesn't work in network anymore. So, research on real-time control and delay compensation technology for networked MIMO system, especially for nonlinear MIMO system, is of great scientific value and very important for the applications of CPS in control field, and now it has been the advanced hot research area in the field of CPCS.
This dissertation is to find a networked real-time control method for a class of networked nonlinear MIMO systems by taking2DOF helicopter model as the representative, and the goal is to assure that the local controller designed in delay-free environment still can be used in the CPCS with network induced I/O delays, thus, the networked controller of a class of nonlinear MIMO system in CPCS can be designed by the method of controller design in delay-free environment.
This dissertation begins with delay compensation technology of linear MIMO system based on a novel virtual observer by taking famous Wood-Berry model as an example. And then, a class of nonlinear MIMO sytem addressed in this dissertation was transformed to a linear MIMO system approximately by the method of local linearization; furthermore, a virtual MIMO system with combined delays was constructed; based on the virtual MIMO system, an observer was designed for the actual delayed nonlinear MIMO systems. With the aid of such a virtual observer, the networked nonlinear system can still be controlled well by the controller designed in delay free environment. The simulation and actual test results of2DOF helicopter networked control system proved the correctness and effectiveness of this method.
The main content is as bellow.
1) A method of construction of an equivalent virtual linear system was proposed in this dissertation. Network induced Input/Output (I/O) delays are firstly combined, and then the combined delay is allocated to output channels or system states, which results in the mathematical construction of a virtual linear MIMO system. It is proved that the virtual system with combined delay is equivalent to the original system with I/O delays in terms of system input-output relationship. Furthermore, the observability of the virtual system in the form of state space model was also proved, which is required to design the virtual observer.
2) A modified Luenberger observer was designed, and delay compensation of linear MIMO system is realized based on the modified observer. Firstly, the modified Luenberger observer was designed based on the equivalent virtual system with combinded delay; and the estimated states of the original I/O delayed system were obtained by the modified observer. Secondly, the estimated states were fed back to the state-feedback-controller (for example, LQR) which was designed for the corresponding delay-free system. Because that the observer states were output in ahead of the combined delay, the stability of the closed loop control system with the observer is almost the same as delay free. So the delay compensation for the state-feedback control system was realized. Finally, taking the famous delay-sensitive Wood-Berry model as an example, the simulation shows that the local state-feedback controller designed in delay-free environment cannot work yet in the network due to the network induced delays, but it can resume working well when the virtual observer-based delay compensation method is applied.
3) In order to compensate the delay of variable time constant, this dessertation proposed a proportional factor namely ε to modify observer gain Jo. And the optimal solution of ε was presented as well. Firstly, approximate the delay in characteristic equation of observer with Pade method. Then, solve the equation with different value of ε to obtain the characteristic poles of observer. Finally, the value of ε with which the principal pole of observer is farthest from imaginary axis can be considered as the optimal value corresponding to the current delay.
4) The problem of delay compensation for a class of nonlinear MIMO system is drew forth from the issue of networked control of two Degree of Freedom (2DOF) helicopter model. Firstly, the nonlinear dynamic equations of a2DOF helicopter model were obtained by means of Lagrange method. Then, the dynamic equations were un-completely linearized, which results in delay-free simi-linearized state space model of a class of nonlinear MIMO systems. The next, local delay free controller, that is LQR+FF+I controller (Linear Quadratic Regulator+Forward Feed controller+Integrator) was designed based on the simi-linearized state space model. The next, network induced I/O delays were introduced into the state feedback control system, and then by mathematical transformation the nonlinear item in the delayed semi-linearized state space model was converted and combined into the linear part, which leads to an equivalent I/O delayed linear MIMO system. Finally, following the delay compensation method for linear MIMO system, the delay compensation for the delayed nonlinear MIMO system was implemented. Simulation and hardware control of the2DOF helicopter model proves the effectiveness of the method, that is, the unstable networked closed loop control system of helicopter due to the network induced I/O delays resumes being stable with the aid of the virtual observer.
5) Several issues relative to the application of networked control technology into actual CPCS were also discussed. For example, limited random delay can be converted into fixed delay by means of delay stack to realize the delay compensation simply; the state number of virtual system with combined delay may increase and as a result the observer state cannot be fed back to the original state-feedback controller directly, so this dissertatin proposed to use matrix Ω to decrease the observer order; at last, it is pointed out that it would be better if ε is a proper matrix when the difference of time constant of input or output delays is considerable large, and it will improve the effectiveness of corresponding delay compensation.
引文
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