Analysis And Design Of Structural Controllability For The Active Network Over F(z)

The traditional control theory on research the systematic features such as the stability, controllability or observability of the system are based on the actual system model just like the mathematical or physical model, which means this sort of research method depends on the parameter values of the system, in other words, the system properties are over the real field R. However, the analysis and design of control system primarily need to analyze the whole structure of the system, and the matrix of the real area is not convenient to analyze structure properties of the system. Based on this, Professor Lu Kai-Sheng uses Rational function systems with multi-parameters over F(z) as the new method to study the system structure. Knowing the basic concepts of Rational function systems and the controllability decision theorem of active network over F(z), this paper analyzes and designs the second-order RC active network by use of the conclusions concerning the structural controllability for the active network over F(z). In addition, on basis of linear system theory, it can realize the pole allocation to meet the requirements of the stability and dynamic performances by the design of state feedback.The papers were made following several aspects:Firstly, introduced the research background and significance for the structural controllability of the system over F (z), and the research situation at home and abroad; Secondly, more thorough introduction to the electric network theory and the analysis of the active network controllability by use of the controlling flow graph; Then the analysis and synthesis for linear system leaded to the pole allocation algorithm based on the state feedback system; Thirdly, TAP-II controlling theory experiment device for the design of the active network was introduced, which included detailed description of the experiment device and the control theory software for the experiment; Then the step responses of the typical links for control system were gotten through the design of the corresponding experiment circuit; Thirdly, a detailed description of the active network based on the inertial links, and analyzed the structure controllability of the active network, besides, the state equation of the active network were obtained, then, parameter values of the active network were taken in the real field according to the stability and divergent two situations for the active network, the calculation of the pole allocation including the performance features of the active network in the real domain values were finished by using the MATLAB software, and its step response simulation curves were also gotten. According to the results of pole calculation and stimulation, design the state feedback circuit to realize the arbitrary pole assignment and get the step response curves on the control theory experimental device; Fourthly, another kind of common active network that is based on Differential Circuit were introduced in detail. For this sort of network, the state feedback circuit that is to achieve the capacitor voltage value needs to design the special feedback circuit. This paper firstly choose the difference proportion circuit as a feedback circuit, and tested the relationship between the input and output voltage signals, then connected the feedback circuit with the active network to realize the pole allocation for the active network. According to the pole allocation experiment, the step responses for the feedback active network were obtained. finally, this paper introduced another feedback circuit based on linear optical coupling isolated amplifier, which could commendably separated the feedback circuit with the active network, Unfortunately, in the test experiment for the relationship between the input and output signals of the active network can’t meet the requirements for the state feedback circuit, which needs thorough study in the future.