Discrete-time Modeling And Digital Silding Model Control Of A Zeta Converter Based On The Variational Integrator

With the gradual deepening study on nonlinear behavior and control of the DC-DC converter, people take more and more attention on modeling method for DC-DC converter, the excellent modeling method can take into account both the accuracy and simplicity, can yield twice the result with half the effort of the nonlinear and control study of DC-DC converter. There is often unstable phenomenon in DC-DC converter, and the DC-DC converter has a stable output and strong anti-interference ability in engineering practice. So it is necessary to search for an excellent modeling method, and analyze the system’s nonlinear and closed-loop control strategy based on the modeling.Firstly, this paper studies the constructing method of discrete Lagrangian model based on variational integrator, then use the Boost converter as an example, compared with discrete Lagrangian model and the traditional iterative model output voltage and inductor current waveform in time domain when the Boost converter is open loop or closed loop. The results show that, discrete Lagrangian modeling method has a very high accuracy in DC-DC converter modeling. Then analyzes the characteristics of boost converter’s Jacobian matrix values with discrete Lagrangian model in different reference current, calculated the bifurcation points of boost converter.Zeta converter belongs to the typical four-step converter, it has the advantages of the lifting voltage, small output ripple, easy output filter, etc. However, it has more complex structure than ordinary two-step converter, so it need to study its modeling and nonlinear behavior, but it is seldom studied. Therefore, this paper use Zeta converter as the object of the study, established the discrete Lagrangian model of zeta converter, then use the model to study the zeta converter’s Jacobian matrix characteristic value trajectory and the stability region by change different parameters of the converter, and the compared the stability region with the traditional modeling method, through the PSIM simulation to study the nonlinear dynamic characteristics of the system. It is proved that the correctness of the discrete Lagrangian modeling method in the analysis of high order DC-DC converter, and zeta converter exists in the analysis of the stability region.With the development of digital control chip, digital control will be the development direction of DC-DC converter control. Therefore this paper based on the zeta converter discrete Lagrangian model to establish the zeta converter’s discrete sliding mode control strategy, and builds a platform for the circuit experiment by using the software of Matlab/ Simulink, then preliminary analysis of discrete sliding mode dynamic response characteristics and robustness.At last, the peak current control of Boost converter, peak current control of Zeta converter and Zeta converter digital control experimental platform are built, and the correctness of theoretical analysis is verified. The practicability of the discrete Lagrange modeling method based on variational integral in modeling and analyzing of DC-DC converter is proved.The results of this article have important guiding significance for modeling, stability analysis and control research of DC-DC converter system.