Closed Loop Control Using PWM
Under this section, the closed-loop control of the ideal circuit is considered.
For both the buck converter and the boost converter, the output voltage increases
as the duty cycle of the switch increases and hence the same PWM circuit can
be used. The block diagram is also similar, but the transfer function is only
slightly different. The block diagram is shown in Fig. 8.
A more detailed block diagram is shown in Fig. 9.
The transfer function of the circuit in open loop is obtained as outlined
below by using an approximate method. Even though it is difficult to justify
the approximation, it is presented. The output voltage is expressed by equation
(8). Let the quiescent duty cycle be assumed to be D and let the small increment
to duty cycle be d. Then equation (8) can be presented as:
If d<< (1-D), then the above equation can be approximated using the
binomial expansion and retaining only the first two terms. That is,
The change in output, denoted as DVo,
can be expressed to be
The transfer function can then be obtained as:
The design of the controller is based on the block diagram in Fig. 10. The
third applet has been developed based on this block diagram. The difference
between the inductor current and the load current is the capacitor current
and the current through the capacitor is proportional to the derivative of
the capacitor voltage and the derivative feedback is obtained as shown. .
The third applet presented below displays the location of poles and zeros
for the selected parameters. If any poles happen to be in the right-half side
of s-plane, the program may not work
click here to open the applet
For simulation of the power circuit using PWM, closed loop scheme used is
shown in Fig. 9. As long as the inductor current is less than the maximum
current, the feedback signal is the sum of the output voltage filter output
and a derivative signal obtained from the inductor current and the load current.
When the inductor voltage exceeds the set maximum value, the feedback signal
contains an additional element proportional to the amount by which the inductor
current exceeds the maximum current. The output of the PI controller determines
the duty cycle.
The simulation of the power circuit with closed-loop control and pulse-width
modulation mode is presented in the fourth applet. One of the five responses
can be selected and the program interface is similar to many of the preceding
applets.
click here to open the applet
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