融合通信参量的网络系统跟踪性能极限研究
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摘要
跟踪性能是系统跟踪能力的一种定量描述,而跟踪性能极限是控制系统无论选取何种控制器,其跟踪性能无法逾越的一个极限值。在传统控制系统中,跟踪性能极限不仅与被控对象结构特征,如非最小相位零点和不稳定极点位置,以及他们的方向有关,同时还与跟踪信号特征和系统内部时延有着密切联系。该极限值对控制系统设计有着至关重要的参考价值。而由于实际应用中物理设备的限制,控制能量是有限的,于是跟踪误差能量与控制能量之间的权衡问题变的十分重要。跟踪性能极限与控制能量极限分别得到了较好的结果,而控制能量限制下的跟踪性能极限与控制系统本质特征之间的关系如何?网络无处不在,网络打破了传统控制系统点对点连接的格局,降低了控制系统复杂度和成本。在网络为控制系统带来便利的同时,也带来了新的挑战。网络的引入,不可避免地出现了网络诱导时延、信道噪声、数据丢包、量化噪声等影响因素。这些因素的存在甚至可能会导致控制系统失稳,从而使得性能极限值无法得到。那么如何建立跟踪性能极限值与网络通信参量和控制系统内部特征之间的联系,是一项十分有意义的课题。本论文在总结前人工作的基础上,融合通信参量系统研究了网络系统的跟踪性能极限,建立了跟踪性能极限与控制系统特征和网络通信参量之间的纽带。全文的研究内容概况如下：研究了上行通道和下行通道均存在脉冲扰动的跟踪性能极限。研究结果揭示了跟踪性能极限与被控对象内部特征如非最小相位零点,不稳定极点之间的关系。同时,新的非最小相位零点影响跟踪性能极限。这就意味着双通道噪声影响下的跟踪性能极限要大于仅仅在单通道噪声影响下的跟踪性能极限。在单通道噪声中,双自由度控制器能抵消不稳定极点对跟踪性能极限的影响,但在双通道噪声中,双自由度控制器却不能完全抵消不稳定极点的影响。研究了被控对象能量限制下的采样数据系统的跟踪性能极限。参考输入信号分别考虑了阶跃信号、实正弦信号、复正弦信号和斜坡信号。研究结果表明,跟踪性能极限不仅与连续被控对象的非最小相位零点和不稳定极点有关,同时,还与由采样器和保持器所产生的非最小相位零点有关。另外,与连续系统结论相比,被控对象离散化后所产生的非最小相位零点和不稳定极点造成了额外的性能极限。此外,跟踪性能极限还与参考输入信号的特征有关。研究了不确定性因素影响下的控制系统的跟踪性能极限。利用随机嵌入方法来描述不确定性,将实际系统与标称系统的传递函数误差的加权H2范数作为性能指标。不确定性的引入可能导致系统不稳定,原先的控制器不能满足稳定性要求。通过调整实际控制器参数来最小化加权性能指标,得到了加权跟踪性能极限,最后通过实例验证了重新设计的控制器加快收敛速度,减小跟踪误差幅值,且验证了控制器的鲁棒性和优越性。研究了单输入单输出连续被控对象在控制能量和信道输入能量限制下的跟踪性能下界。提出新的性能指标,基于不等式约束的最优化方法,得到了跟踪性能的下界以及保证反馈系统稳定的信噪比的最小值的表达式。研究结果揭示了他们与非最小相位零点和不稳定极点之间的内在联系。寻找一种特殊的内外分解形式便于应用,得到新的结果。研究了离散单输入单输出被控对象在控制能量和Erasure信道输入能量限制下的跟踪性能问题。Erasure信道模拟了离散信道的数据丢包,基于不等式约束的最优化方法求得了跟踪性能的下界,且获得了为保证系统稳定的信噪比的最小值。他们均与被控对象的非最小相位零点,不稳定极点和丢包率有关。同时,随着丢包率的增加,最优性能也会随之增加,这是由于丢包率的增加导致了被控对象越来越难以控制,甚至失稳。研究了单输入多输出被控对象的修正跟踪性能极限。针对某些静态跟踪误差不为零,跟踪性能指标无穷大缺点,通过引入修正因子,提出修正跟踪性能指标。采用内外分解方法求得修正跟踪性能极限,并给出修正因子的适当选取范围。结论表明,即使静态跟踪误差不为零,修正跟踪性能极限仍然为有限值。并且消除了被控对象必须含有积分器的严格假设和对参考输入信号方向的假设。最后对全文进行了归纳总结,并对网络系统的跟踪性能极限的研究和发展方向进行了展望。
The tracking performance is a quantitative description of the system tracking capability. The tracking performance limitation is the limiting value that the tracking error performance can not over-take no matter what controller adopting. In the classical control system, the tracking performance limitations depend on the structure features which include the location and direction information of the non-minimum phase zero and unstable pole. In addition, they are closely linked with the reference signal characteristics and the system inner delay. The limitations provide the important reference value for the system design. However, the control energy is limited due to the limit of the physical equipment in the practical application. The trade-off between the tracking error en-ergy and control energy becomes very important, The tracking performance and the control energy performance separately obtained better results. But what is the relationship between the essential characteristics of control system and the tracking performance limits with the finite control energy?Networks commonly exist in the real world. Networks break the traditional pattern of point to point connection and reduce system complexity and control costs. When the networks provided the facility for the control system, it brought new challenges. Introducing networks inevitably produces some effect factors such as network-induced delay, channel noise, data loss, quantization noise and so on. The existence of these effect factors may even cause the instability of control system. And some performance limitations can not be obtained. So how to establish the relationship between tracking performance limitations and internal features of control system and network communica-tion parameters is a very significant issue. Based on the previous works, the tracking performance limitations of network system integrating communication parameters have been systematically stud-ied. The relationship between the tracking performance limitations and the control system features and network communication parameters has been established. The research content of this disserta-tion is outlined as follows.The tracking performance limitation under the constraint of control energy with the impulse disturbances existing in the uplink channel and downlink channel has been studied. The results reveal the relationship between tracking performance limitations and internal characteristics and controlled object. New non-minimum phase zeros affect the tracking performance limitations. This implies that the tracking performance limitation of two-channel disturbance is larger than the case of single channel disturbance. In the case of single disturbance, the two-degree-of-freedom controller offsets the effect of unstable poles. But in the case of two-channel disturbance, the two-degree-of-freedom controller is not effective and can not completely offset the effect.This dissertation studies the tracking performance limitations of the sampled-data system under the control energy constraint. The reference input signals considered in this dissertation include step signal, real sinusoidal signal, complex sinusoidal signal and ramp signal. The results show that the tracking performance limitations depend not only on the non-minimum phase zeros and unstable poles of the continuous system but also on the non-minimum phase zeros generated by the sampler and hold device. In addition, they depend on the non-minimum phase zeros and unstable poles generated by the discretization of the continuous system compared with the results of the continuous systems. Furthermore, the reference signal affects the optimal performance.The uncertainty influencing factor on the tracking performance limitations is discussed. The uncertainty is formulated by utilizing stochastic embedding of uncertainty. The weighted//2 norm for the transfer function error between the actual system and the nominal system is defined as the performance index. The introduction of uncertainty may lead to the instability of system, so the original controller can not meet the stability requirements. The weighted performance index is minimized by adjusting the actual controller parameter. The controller is redesigned to get the tracking performance limitations. Finally, one example verifies that the redesigned controller can improve the convergence speed and reduce the amplitude of the tracking error. Also the simulation can test the robustness and superiority of the controller.The lower bound of the tracking performance of the single-input single-output continuous sys-tem with the constraint of channel input energy and control input energy. A new performance index for the tracking performance is proposed. Based on the optimization method with the inequality constraints, the expressions of the lower bound of the tracking performance index and the minimum value of signal-to-noise ratio guaranteeing the stability of system are obtained. The results reveal the inherent relationship between these expressions and the non-minimum phase zeros and unstable poles. In addition, one special form of inner-outer factorization is found for easy application and the new result is derived. Erasure channel can model the data loss of the discrete channel. Thus this dissertation studies the tracking performance under the constraint of the Erasure channel input energy and control input energy for the single-input single-output discrete system. Based on the optimization method with the inequality constraints, the lower bound of tracking performance and the minimum value of signal-to-noise ratio guaranteeing the stability of system are derived. They are related to the non-minimum phase zeros, unstable poles and dropout rate. The tracking performance becomes bigger with the increasing of dropout rate because the increase of dropout causes that the system is more and more difficult to be controlled and the closed loop system may be unstable.The modified tracking performance limitation of single input multiple output system is dis-cussed. Since in some cases the static tracking error may not be zero, the tracking performance index may be infinite. Based on this disadvantage, by introducing a scaled factor, a new modified tracking performance index is proposed. By adopting inner outer factorization method, this perfor-mance index is minimized and the proper scaled factor is given. The results show that even if the static tracking error is not zero, the modified tracking performance limitation is finite. Also this performance index deletes that severe limit on the plant which must contain the integrator and on the reference input signal direction.Finally, a summary has been proposed for all discussions in this dissertation. The further study and research works are presented for the network systems.
The tracking performance is a quantitative description of the system tracking capability. The tracking performance limitation is the limiting value that the tracking error performance can not over-take no matter what controller adopting. In the classical control system, the tracking performance limitations depend on the structure features which include the location and direction information of the non-minimum phase zero and unstable pole. In addition, they are closely linked with the reference signal characteristics and the system inner delay. The limitations provide the important reference value for the system design. However, the control energy is limited due to the limit of the physical equipment in the practical application. The trade-off between the tracking error en-ergy and control energy becomes very important, The tracking performance and the control energy performance separately obtained better results. But what is the relationship between the essential characteristics of control system and the tracking performance limits with the finite control energy?Networks commonly exist in the real world. Networks break the traditional pattern of point to point connection and reduce system complexity and control costs. When the networks provided the facility for the control system, it brought new challenges. Introducing networks inevitably produces some effect factors such as network-induced delay, channel noise, data loss, quantization noise and so on. The existence of these effect factors may even cause the instability of control system. And some performance limitations can not be obtained. So how to establish the relationship between tracking performance limitations and internal features of control system and network communica-tion parameters is a very significant issue. Based on the previous works, the tracking performance limitations of network system integrating communication parameters have been systematically stud-ied. The relationship between the tracking performance limitations and the control system features and network communication parameters has been established. The research content of this disserta-tion is outlined as follows.The tracking performance limitation under the constraint of control energy with the impulse disturbances existing in the uplink channel and downlink channel has been studied. The results reveal the relationship between tracking performance limitations and internal characteristics and controlled object. New non-minimum phase zeros affect the tracking performance limitations. This implies that the tracking performance limitation of two-channel disturbance is larger than the case of single channel disturbance. In the case of single disturbance, the two-degree-of-freedom controller offsets the effect of unstable poles. But in the case of two-channel disturbance, the two-degree-of-freedom controller is not effective and can not completely offset the effect.This dissertation studies the tracking performance limitations of the sampled-data system under the control energy constraint. The reference input signals considered in this dissertation include step signal, real sinusoidal signal, complex sinusoidal signal and ramp signal. The results show that the tracking performance limitations depend not only on the non-minimum phase zeros and unstable poles of the continuous system but also on the non-minimum phase zeros generated by the sampler and hold device. In addition, they depend on the non-minimum phase zeros and unstable poles generated by the discretization of the continuous system compared with the results of the continuous systems. Furthermore, the reference signal affects the optimal performance.The uncertainty influencing factor on the tracking performance limitations is discussed. The uncertainty is formulated by utilizing stochastic embedding of uncertainty. The weighted//2 norm for the transfer function error between the actual system and the nominal system is defined as the performance index. The introduction of uncertainty may lead to the instability of system, so the original controller can not meet the stability requirements. The weighted performance index is minimized by adjusting the actual controller parameter. The controller is redesigned to get the tracking performance limitations. Finally, one example verifies that the redesigned controller can improve the convergence speed and reduce the amplitude of the tracking error. Also the simulation can test the robustness and superiority of the controller.The lower bound of the tracking performance of the single-input single-output continuous sys-tem with the constraint of channel input energy and control input energy. A new performance index for the tracking performance is proposed. Based on the optimization method with the inequality constraints, the expressions of the lower bound of the tracking performance index and the minimum value of signal-to-noise ratio guaranteeing the stability of system are obtained. The results reveal the inherent relationship between these expressions and the non-minimum phase zeros and unstable poles. In addition, one special form of inner-outer factorization is found for easy application and the new result is derived. Erasure channel can model the data loss of the discrete channel. Thus this dissertation studies the tracking performance under the constraint of the Erasure channel input energy and control input energy for the single-input single-output discrete system. Based on the optimization method with the inequality constraints, the lower bound of tracking performance and the minimum value of signal-to-noise ratio guaranteeing the stability of system are derived. They are related to the non-minimum phase zeros, unstable poles and dropout rate. The tracking performance becomes bigger with the increasing of dropout rate because the increase of dropout causes that the system is more and more difficult to be controlled and the closed loop system may be unstable.The modified tracking performance limitation of single input multiple output system is dis-cussed. Since in some cases the static tracking error may not be zero, the tracking performance index may be infinite. Based on this disadvantage, by introducing a scaled factor, a new modified tracking performance index is proposed. By adopting inner outer factorization method, this perfor-mance index is minimized and the proper scaled factor is given. The results show that even if the static tracking error is not zero, the modified tracking performance limitation is finite. Also this performance index deletes that severe limit on the plant which must contain the integrator and on the reference input signal direction.Finally, a summary has been proposed for all discussions in this dissertation. The further study and research works are presented for the network systems.
引文
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