At the moment the concept of the dynamical profile is mainly applied only in the academia. The natural interest should be, however, to make practical the use of the dynamical profile and to promote its superiority as a valuable tool in analyzing and ensuring performance and stability. The lack of understanding and knowledge of the dynamical issues among the engineers are the main obstacles in making the use of the dynamical profile as a common tool in the industry. Training courses and seminars should be organized and targeted on the industry.
This thesis analyzed only the buck converter under the three different control modes.
However, there are numerous topologies and control principles which are used in various applications without completely understanding their dynamical behavior.
Therefore, at least a boost and buck/boost converter and their (isolated) derivates should be analyzed. Consequently, the dynamical profiles should be derived to every new topology and/or control principle that is introduced.
The cascaded control was not considered in the thesis. The proposed methods provide a facility to analyze the dynamics of a converter, where the voltage and current loops are cascading. Also, the relation between the frequency and time domains associated with transient response should be studied.
The use of digital control has begun to replace its analog counterparts. The digital control can provide e.g. adaptive control, but the effects of the digitalization of the control block on the converter dynamics have not been extensively analyzed. The analog and corresponding digital dynamical profile should be compared and analyzed in order to understand the effects of digital control.
A potential research topic is also the effect of the excitation signal on the transfer functions, when making the measurements. A sinusoidal signal is typically used as the excitation signal, but it is observed to cause phase lag in higher frequencies if the signal goes through the modulator. This effect should be put in a mathematical form and different excitation signals should be used to compare the phase lags and other properties in order to find the best type of signal to be injected into a loop in order to get accurate frequency responses.
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Appendix A
% Inductor and capacitor values and their ESRs C=316e-6;
r_c=33.3e-3;
L=108e-6;
r_L=60e-6;
% Switch on-time resistance r_ds r_ds=0.4;
% Diode on-time resistance r_d and max forward voltage Ud r_d=0.055;
Ud=0.3;
Uin=50; % Input voltage 20V-50V Uout=10;
Iout=2.5; % Nominal load
R=Uout/Iout; % Value of the load resistor needed to obtain the nominal load current Ts=1/(100000); % Switching period
D=(Uout+(r_L+r_d)*Iout+Ud)/(Uin+Ud+(r_d-r_ds)*Iout); % Duty-ratio IL=Iout;
%Controller component values and transfer function Rb=3.3e3;
% Denominator of the transfer functions i.e. g-parameters:
den=(s^2+((s*(r_L+r_c+(r_ds*D)+(r_d*(1-D))))/L)+(1/L/C));
% Nominal/internal open-loop g-parameters:
Gco_vmc_ccm_nom=(((((Uin+Ud+(r_d-r_ds)*IL)*(1+s*r_c*C))/L/C)/den)/Vm);
% Nominal/internal closed-loop parameters:
Loop_nom=Gcc*Gco_vmc_ccm_nom;
YinC_vmc_ccm_nom=Yino_vmc_ccm_nom-(Loop_nom/(1+Loop_nom))*((Gioo_vmc_ccm_nom*Gci_vmc_ccm_nom)/Gco_vmc_ccm_nom);
ToiC_vmc_ccm_nom=Toio_vmc_ccm_nom-(Loop_nom/(1+Loop_nom))*((Zoo_vmc_ccm_nom*Gci_vmc_ccm_nom)/Gco_vmc_ccm_nom);
% Special admittance parameters:
Yinf=(Yino_vmc_ccm_nom-((Gioo_vmc_ccm_nom*Gci_vmc_ccm_nom)/Gco_vmc_ccm_nom));
Yinf_real=-D*IL/Uin;
Yinsc=Yino_vmc_ccm_nom+((Gioo_vmc_ccm_nom*Toio_vmc_ccm_nom)/Zoo_vmc_ccm_nom);
Yinsc_real=(D^2)/(r_L+D*r_ds+(1-D)*r_d+s*L);
% Load circuit parameters:
L_L=108e-6;
C_L=2.350e-3;
r_C_CL=100e-3;
r_8k=80e-3;
% Load transfer functions
Z_L100=(s*L_L+((1/(s*C_L))+3*r_C_CL)); % Resonance at 100 Hz Z_L400=(s*3*L_L+((1/(s*0.2*C_L))+0.1*r_C_CL)); % Resonance at 400 Hz Z_L500=(s*2*L_L+((1/(s*0.2*C_L))+r_C_CL)); % Resonance at 500 Hz
% Filter transfer functions
% Resonance at 680 Hz
GioC_vmc_ccm_Snom=Gioo_vmc_ccm_Snom/(1+Loop_Snom);
ZoC_vmc_ccm_Snom=Zoo_vmc_ccm_Snom/(1+Loop_Snom);
% Double interactions
%%%%%%%%%%%%%%%%%%%%%%%
% Open-loop:
Yino_vmc_ccm_SL=Yino_vmc_ccm_L/(1+Zs*Yino_vmc_ccm_L);
Toio_vmc_ccm_SL=Toio_vmc_ccm_L/(1+Zs*Yino_vmc_ccm_L);
Gioo_vmc_ccm_SL=Gioo_vmc_ccm_L/(1+Zs*Yino_vmc_ccm_L);
Zoo_vmc_ccm_SL=((1+Zs*Yinsc)/(1+Zs*Yino_vmc_ccm_L))*Zoo_vmc_ccm_L;
Gci_vmc_ccm_SL=Gci_vmc_ccm_L/(1+Zs*Yino_vmc_ccm_L);
Gco_vmc_ccm_SL=((1+Zs*Yinf)/(1+Zs*Yino_vmc_ccm_L))*Gco_vmc_ccm_L;
% Closed-loop:
Loop_SL=((1+Zs*Yinf)/(1+Zs*Yino_vmc_ccm_L))*Loop_L;
YinC_vmc_ccm_SL=Yino_vmc_ccm_SL-(Loop_SL/(1+Loop_SL))*((Gioo_vmc_ccm_SL*Gci_vmc_ccm_SL)/Gco_vmc_ccm_SL);
ToiC_vmc_ccm_SL=Toio_vmc_ccm_SL-(Loop_SL/(1+Loop_SL))*((Zoo_vmc_ccm_SL*Gci_vmc_ccm_SL)/Gco_vmc_ccm_SL);
GioC_vmc_ccm_SL=Gioo_vmc_ccm_SL/(1+Loop_SL);
ZoC_vmc_ccm_SL=Zoo_vmc_ccm_SL/(1+Loop_SL);
Appendix B
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Mixed-Data Controller Design %
% Copyright Mikko Hankaniemi %
% Tampere University of Technology %
% Institute of Power Electronics %
% 2007 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Measured control-to-output transfer function data are converted to % a complex number
gain_1=10.^((gain)./20);
phase_fii=(phase/180)*pi;
Gco_compx=gain_1.*(cos(phase_fii)+j*sin(phase_fii));
% Analytically designed controller transfer function Gcc is
% converted to a complex number w=2.*pi.*f;
[mag ang]=bode(Gcc, w);
mag1=mag(:,:);
ang1=ang(:,:);
ang1_fii=(ang1/180)*pi;
f1=w/2/pi;
Gcc_compx=mag1.*(cos(ang1_fii)+j*sin(ang1_fii));
% Calculating the loop gain Loop=Gcc_compx.*Gco_compx;
% Extracting the magnitude in decibels and phase in degrees from the % complex number
“Loop”
Loop_g=abs(Loop);
Loop_gdB=20*log10(Loop_g);
Loop_ang_fii=atan2(imag(Loop),real(Loop));
Loop_ang=180*Loop_ang_fii/pi;
Appendix C
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Nominal Gco Calculation from Measured Data %
% Based on Mixed-Data Method %
% Copyright Mikko Hankaniemi %
% Tampere University of Technology %
% Institute of Power Electronics %
% 2007 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Resistive load R=4;
% Measured control-to-output transfer function (with resistive load)
% data are converted to a complex number gain_1=10.^((gain)./20);
phase_fii=(phase/180)*pi;
GcoR_compx=gain_1.*(cos(phase_fii)+j*sin(phase_fii));
% Measured open-loop output impedance (nominal)
% data are converted to a complex number gain_2=10.^(gain2./20);
phase_fii2=(phase2/180)*pi;
Zoo_compx=gain_2.*(cos(phase_fii2)+j*sin(phase_fii2));
% Computing the nominal/internal Gco basing on the load interaction
% formalism
Gco=GcoR_compx.*(1+(Zoo_compx./R));
% Extracting the magnitude in decibels and phase in degrees from the % complex number
“Loop”
Gco_g=abs(Gco);
Gco_gdB=20*log10(Gco_g);
Gco_ang_fii=atan2(imag(Gco),real(Gco));
Gco_ang=180*Gco_ang_fii/pi;
Appendix D
Fig. D.1. Laboratory test setup.
Fig. D.2. Power stage and control circuits of the experimental buck converter.
Auxiliary power supplies
Oscilloscope
Current probes
Electronic load
Frequency response analyzer and linear amplifier
Injection transformers Buck converter
Computer interface
Power stage
PCMC &
PCMC-OCF
VMC & PCMC of current-output converter VMC-CCM
& VMC-DCM
Fig. D.3. Example schematics of the experimental VMC-CCM buck converter.
Tampere University of Technology