Study On Tracking Performance Limitation Of Network System Integrating Communication Parameters

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.