Stability of Cascaded Voltage Control Systems of DC-DC Converters
DOI:
https://doi.org/10.31649/1997-9266-2021-159-6-51-57Keywords:
DC-DC boost converter, voltage controller, regulation error, stability proof, singular perturbation systems theoryAbstract
The paper is devoted to research and development of the cascaded DC-link voltage control systems for DC-DC boost converters whose mathematical model is highly nonlinear and non-minimum phase. The relevance of the analysis method for classic control systems for DC-DC boost converters is substantiated, which are similar to vector-controlled electric drives systems if the speed controller is replaced by DC-link voltage controller.
It is shown that the reduced-order solution of initial nonlinear system dynamics can be obtained giving the time-scale separation between the input current and the DC-link voltage control processes based on the singular perturbation systems theory. In its turn, it is concluded that the reduced-order system dynamics is locally (asymptotically) stable if cascaded control algorithm is applied. The similarity of the time-scale separation conditions for the cascaded control systems with proportional and proportional-integral DC-link voltage controller is shown. The time-scale separation of the control processes is achieved if inner current regulation loop is much faster than the outer voltage regulation loop.
The simulation study demonstrates that if the time-scale separation conditions between the input current and the DC-link voltage regulation are met then the full-order system dynamics of the DC-link voltage regulation of DC-DC boost converters is close to the reduced-order system dynamics. The control algorithm has a typical structure of the modern controlled converters applied in hybrid energy storage systems for electric vehicles. From the results of the simulation study, it follows that the influence of the inner resistance of the input inductance on the system stability and quality indicators of the DC-link voltage control process is insignificant for the investigated DC-DC boost converter.
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