Contents
% Asignatura: Filtros y Convertidores de señal. % Autor: Alejandro Fernández Hernández
Práctica 1 (Ejercicio 3): Control de un convertidor Buck-Boost.
Enunciado: Diseñar el regulador en tiempo continuo más apropiado para controlar la tensión de salida del convertidor frente a variaciones en el ciclo de trabajo d. Representar el diagrama de Bode y la respuesta en el tiempo. Posteriormente realizar un modelo Simulink en el que se vea la respuesta ante una onda cuadrada.
clear all; close all; clc; % Filtros y Convertidores de Señal
Definir Parámetros
Definimos los parámetros del convertidor Buck-Boost:
Vg=30; L=260*10^(-6); R=10; C=160*10^(-6); D=0.6; Leq=L/(1-D)^2; Vo=Vg*(D/(1-D)); fc=150*10^(3); % Definimos la función de transferencia del convertidor Buck-Boost: s=tf('s'); Gd=(-(Vg*D/(1-D)^2)/(1+Leq*s/R+s^2*Leq*C))+((Vg+(Vg*D)/(1-D))/(1-D))*(1/(1+Leq*s/R+s^2*Leq*C)) figure; bode(Gd) LazoCerrado=Gd/(1+Gd) figure step(LazoCerrado)
Gd =
0.00195 s^2 + 1.219 s + 7500
------------------------------------------------------------
6.76e-12 s^4 + 8.45e-09 s^3 + 5.464e-05 s^2 + 0.0325 s + 100
Continuous-time transfer function.
LazoCerrado =
1.318e-14 s^6 + 2.472e-11 s^5 + 1.675e-07 s^4 + 0.0001933 s^3
+ 0.6444 s^2 + 365.6 s + 7.5e05
-----------------------------------------------------------------------------
4.57e-23 s^8 + 1.142e-19 s^7 + 1.399e-14 s^6 + 2.608e-11 s^5 + 1.724e-07 s^4
+ 0.0001986 s^3 + 0.6564 s^2 + 372.1 s + 7.6e05
Continuous-time transfer function.
Estudio en Discreto
% Introducimos en el script el regulador calculado por SISOTOOL: PID=36.793*((1+0.0007*s)*(1+0.0022*s))/(s*(1+3.2e-5*s)); Ts=1/(150e3); % A continuación, discretizamos el convertidor y el regulador por los % métodos ZOH y TUSTIN: Gdzoh=c2d(Gd,Ts,'zoh') PIDzoh=c2d(PID,Ts,'zoh') GdTustin=c2d(Gd,Ts,'Tustin') PIDTustin=c2d(Gd,Ts,'Tustin') % Representamos en una misma gráfica, el diagrama de bode del sistema % contínuo, y el diagrama de bode de los sistemas discretos equivalentes, % por ZOH y TUSTIN. PlantaC=Gd*PID PlantaDzoh=Gdzoh*PIDzoh PlantaDTustin=GdTustin*PIDTustin figure; hold on, bode(PlantaC), bode(PlantaDzoh), bode(PlantaDTustin), legend show, hold off,
Gdzoh =
0.006401 z^3 - 0.006382 z^2 - 0.006382 z + 0.006366
---------------------------------------------------
z^4 - 3.991 z^3 + 5.974 z^2 - 3.975 z + 0.9917
Sample time: 6.6667e-06 seconds
Discrete-time transfer function.
PIDzoh =
1.771 z^2 - 3.521 z + 1.751
---------------------------
z^2 - 1.812 z + 0.8119
Sample time: 6.6667e-06 seconds
Discrete-time transfer function.
GdTustin =
0.003198 z^4 + 1.384e-05 z^3 - 0.006382 z^2 - 1.275e-05 z + 0.003185
--------------------------------------------------------------------
z^4 - 3.991 z^3 + 5.974 z^2 - 3.975 z + 0.9917
Sample time: 6.6667e-06 seconds
Discrete-time transfer function.
PIDTustin =
0.003198 z^4 + 1.384e-05 z^3 - 0.006382 z^2 - 1.275e-05 z + 0.003185
--------------------------------------------------------------------
z^4 - 3.991 z^3 + 5.974 z^2 - 3.975 z + 0.9917
Sample time: 6.6667e-06 seconds
Discrete-time transfer function.
PlantaC =
1.105e-07 s^4 + 0.0002771 s^3 + 0.6267 s^2 + 845.1 s + 2.759e05
-------------------------------------------------------------------------
2.163e-16 s^6 + 7.03e-12 s^5 + 1.02e-08 s^4 + 5.568e-05 s^3 + 0.0357 s^2
+ 100 s
Continuous-time transfer function.
PlantaDzoh =
0.01133 z^5 - 0.03384 z^4 + 0.02238 z^3 + 0.02257 z^2 - 0.03359 z
+ 0.01114
------------------------------------------------------------------------
z^6 - 5.803 z^5 + 14.02 z^4 - 18.04 z^3 + 13.04 z^2 - 5.024 z + 0.8052
Sample time: 6.6667e-06 seconds
Discrete-time transfer function.
PlantaDTustin =
1.023e-05 z^8 + 8.855e-08 z^7 - 4.082e-05 z^6 - 2.583e-07 z^5
+ 6.111e-05 z^4 + 2.51e-07 z^3 - 4.066e-05 z^2 - 8.123e-08 z
+ 1.014e-05
------------------------------------------------------------------------
z^8 - 7.983 z^7 + 27.88 z^6 - 55.64 z^5 + 69.41 z^4 - 55.41 z^3
+ 27.65 z^2 - 7.884 z + 0.9835
Sample time: 6.6667e-06 seconds
Discrete-time transfer function.
Diagrama de Bode
% Introducimos los reguladores calculados con Sisotool y representamos el % diagrama de bode de las distintas plantas: z=tf('z'); w=(z-1)/Ts; Czoh=22.979*(((1+0.0066*w)*(1+0.00041*w))/(w*(1+2.5e-5*w))) CTustin=34.106*(((1+0.0053*w)*(1+0.00045*w))/(w*(1+2.5e-5*w))) PlantaD2zoh=Gdzoh*Czoh PlantaD2Tustin=GdTustin*CTustin figure; hold on, bode(PlantaC), bode(PlantaD2zoh), bode(PlantaD2Tustin), legend show, hold off,
Czoh =
2.764e-15 z^2 - 5.479e-15 z + 2.716e-15
---------------------------------------
1.111e-15 z^2 - 1.926e-15 z + 8.148e-16
Sample time: unspecified
Discrete-time transfer function.
CTustin =
3.615e-15 z^2 - 7.172e-15 z + 3.557e-15
---------------------------------------
1.111e-15 z^2 - 1.926e-15 z + 8.148e-16
Sample time: unspecified
Discrete-time transfer function.
PlantaD2zoh =
1.769e-17 z^5 - 5.271e-17 z^4 + 3.472e-17 z^3 + 3.523e-17 z^2
- 5.222e-17 z + 1.729e-17
------------------------------------------------------------------------
1.111e-15 z^6 - 6.361e-15 z^5 + 1.514e-14 z^4 - 1.917e-14 z^3
+ 1.362e-14 z^2 - 5.149e-15 z + 8.081e-16
Sample time: 6.6667e-06 seconds
Discrete-time transfer function.
PlantaD2Tustin =
1.156e-17 z^6 - 2.289e-17 z^5 - 1.18e-17 z^4 + 4.578e-17 z^3 - 1.11e-17 z^2
- 2.289e-17 z + 1.133e-17
----------------------------------------------------------------------------
1.111e-15 z^6 - 6.361e-15 z^5 + 1.514e-14 z^4 - 1.917e-14 z^3
+ 1.362e-14 z^2 - 5.149e-15 z + 8.081e-16
Sample time: 6.6667e-06 seconds
Discrete-time transfer function.
