Control Weight-Based Stability Mechanism Of Multi-loop COT Controlled Buck Converter

Multi-loop constant on-time(COT)control combines the advantages of current-mode COT control and COT-V~2 control.The control signal in its inner loop is generated by the superposition of inductor current signal and output voltage signal,and different control performance can be flexibly realized by configuring the weights of control loop.However,when the equivalent series resistance(ESR)of the output capacitor is small,the weights of the control loop not only affect the stability of the multi-loop COT controlled buck converter,but also affect its transient performance.In addition,when the voltage ripple in the outer voltage loop is not negligible,the gain of the outer voltage loop will also affect the stability of the converter.Therefore,this paper will take multi-loop COT controlled buck converter using proportional integral(PI)compensator in the outer voltage loop as an example to study the stability mechanism of control weight configuration when the output capacitance of small ESR.The results can be used to provide a basis for the parameter design of this kind of converter.Firstly,the piecewise linear model of multi-loop COT controlled buck converter with PI compensator is derived,and the bifurcation behaviors of the converter with variation of the circuit parameters and the two-dimensional dynamic distribution are analyzed by using the ODE algorithm in MATLAB.Thus,the effect of control weights on the dynamic characteristics of the converter is studied.Then,the approximate reduced-order discrete-time model is established,and the approximate stability conditions of the converter and the instability boundary in different parameter planes are given.The simulation results verify the correctness of the theoretical analyses.Secondly,when the output capacitor ESR is small,the larger inductor current weight is required for multi-loop COT controlled buck converter with PI compensator to ensure stable operation.However,if the inductor current weight is too heavy,which deteriorates the load transient performance.Therefore,the effects of inductor current weight and output voltage weight on the transient performance of multi-loop COT controlled buck converter with PI compensator is analyzed in this paper.Based on the capacitor charge balance,inductor current weights for optimal transient performance under load step-up and step-down were derived by time-domain analysis.Furthermore,the control weight configuration for optimal load transient performance was proposed.The simulation results verify the correctness of the theoretical analyses.Finally,experimental prototype of the multi-loop COT controlled buck converter was implemented,and the hardware circuit experiment was carried out.And,the experimental results are consistent with the PSIM simulation results,which well verifies the correctness of the theoretical analyses and simulation results.