Small‐signal modelling for time‐length compensation algorithm in current controlled converters

Abstract

A unified small-signal modeling method is proposed for current controlled converters using discrete-time analysis method. The relationship between the controlled current and the duty ratio is performed by discrete-time analysis which automatically incorporates the sample-and-hold effect. The proposed small-signal mode is accurate when the modulation frequency varies from zero to half the switching frequency. It is very easy to apply the proposed model to all current controlled converters. When an amplitude peak in the current-loop gain is observed at half the switching frequency, subharmonic oscillation can be predicted. Based on the proposed model, a time-length compensation algorithm for elimination of subharmonic oscillation can be analyzed while other small-signal modeling methods cannot be applied in this condition. Simulations and experiments are committed to verify the analysis. KEYWORDSdiscrete-time analysis, sample-and-hold effect, small-signal model, subharmonic oscillation, time-length compensation algorithm | INTRODUCTIONCurrent controlled converters such as peak current control and average current control are widely used as better line noise rejection, automatic overload protection, and improved small-signal dynamics. In current controlled converters, the small-signal models based on state-space average model neglect the sample-and-hold effect which only fits for low modulation frequencies. To increase the accuracy of the small-signal models, the sample-and-hold effect is added in the models in. 1-9 The model accuracy is improved from zero to half the switching frequency. However, most of the calculations are always very complicated and hard to understand.To simplify the analysis, a unified model is proposed for current controlled converters based on discrete time analysis which is very easy to implement. The sample-and-hold effect is automatically incorporated, and the relationship between the controlled current and the duty ratio is obtained. Based on state-space average modeling method, small-signal model for current controlled converters can be derived. With the proposed modeling method, a timelength compensation algorithm for elimination of subharmonic oscillation is then analyzed.

The Application of Classical Control in the Design and Analysis of Power Amplifiers for Driving Piezoelectric Stack Actuators

“…In reference [4], the equivalent small parameter method is used to establish the nonlinear mathematical model of the fractional-order buck-boost converter in continuous current mode, and the method has achieved satisfying results. In reference [5], a unified model is proposed for small-signal modelling in current controlled converters using the discrete-time analysis method, and simulations and experiments are committed to verify the proposed model. Reference [6] introduces an additional operational amplifier that is utilized as a buffer to improve the Howland voltage controlled current source, a complete analysis including a new two-port analysis of the circuit is presented, and the results indicate that the method increases output impedance, improves noise performance and achieves stability easily.…”