chap12.pdf

Current Programmed Control

So far, we have discussed duty ratio control of PWM converters, in which the converter output is con-

trolled by direct choice of the duty ratio d ( t ) . We have therefore developed expressions and small-signal

transfer functions that relate the converter waveforms and output voltage to the duty ratio.

Another control scheme, which finds wide application, is current programmed control [1–13],

in which the converter output is controlled by choice of the peak transistor switch current The

control input signal is a current and a simple control network switches the transistor on and off, such

that the peak transistor current follows The transistor duty cycle d ( t ) is not directly controlled, but

depends on as well as on the converter inductor currents, capacitor voltages, and power input volt-

age. Converters controlled via current programming are said to operate in the current programmed mode

(CPM).

The block diagram of a simple current programmed controller is illustrated in Fig. 12.1. Control

signal and switch current waveforms are given in Fig. 12.2. A clock pulse at the Set input of a

latch initiates the switching period, causing the latch output Q to be high and turning on the transistor.

While the transistor conducts, its current is equal to the inductor current this current increases

with some positive slope that depends on the value of inductance and the converter voltages. In more

complicated converters, may follow the sum of several inductor currents. Eventually, the switch cur-

rent becomes equal to the control signal . At this point, the controller turns the transistor switch

off, and the inductor current decreases for the remainder of the switching period. The controller must

measure the switch current

with some current sensor circuit, and compare

using an ana-

log comparator. In practice, voltages proportional to

and

are compared, with constant of propor-

tionality

When

the comparator resets the latch, turning the transistor off for the remainder

of the switching period.

As usual, a feedback loop can be constructed for regulation of the output voltage. The output

voltage v ( t ) is compared to a reference voltage

to generate an error signal. This error signal is applied

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Current Programmed Control

12.1 Oscillation for D > 0.5

441

to the input of a compensation network, and the output of the compensator drives the control signal

To design such a feedback system, we need to model how variations in the control signal

and

in the line input voltage affect the output voltage v ( t ) .

The chief advantage of the current programmed mode is its simpler dynamics. To first order, the

small-signal control-to-output transfer function contains one less pole than Actually,

this pole is moved to a high frequency, near the converter switching frequency. Nonetheless, simple

robust wide-bandwidth output voltage control can usually be obtained, without the use of compensator

lead networks. It is true that the current programmed controller requires a circuit for measurement of the

switch current however, in practice such a circuit is also required in duty ratio controlled systems,

for protection of the transistor against excessive currents during transients and fault conditions. Current

programmed control makes use of the available current sensor information during normal operation of

the converter, to obtain simpler system dynamics. Transistor failures due to excessive switch current can

then be prevented simply by limiting the maximum value of This ensures that the transistor will turn

off whenever the switch current becomes too large, on a cycle-by-cycle basis.

An added benefit is the reduction or elimination of transformer saturation problems in full-

bridge or push–pull isolated converters. In these converters, small voltage imbalances induce a dc bias in

the transformer magnetizing current; if sufficiently large, this dc bias can saturate the transformer. The dc

current bias increases or decreases the transistor switch currents. In response, the current programmed

controller alters the transistor duty cycles, such that transformer volt-second balance tends to be main-

tained. Current-programmed full-bridge isolated buck converters should be operated without a capacitor

in series with the transformer primary winding; this capacitor tends to destabilize the system. For the

same reason, current-programmed control of half-bridge isolated buck converters is generally avoided.

A disadvantage of current programmed control is its susceptibility to noise in the or

signals. This noise can prematurely reset the latch, disrupting the operation of the controller. In particu-

lar, a small amount of filtering of the sensed switch current waveform is necessary, to remove the turn-on

current spike caused by the diode stored charge. Addition of an artificial ramp to the current-programmed

controller, as discussed in Section 12.1, can also improve the noise immunity of the circuit.

Commercial integrated circuits that implement current programmed control are widely avail-

able, and operation of converters in the current programmed mode is quite popular. In this chapter, con-

verters operating in the current programmed mode are modeled. In Section 12.1, the stability of the

current programmed controller and its inner switch-current-sensing loop is examined. It is found that this

controller is unstable whenever converter steady-state duty cycle D is greater than 0.5. The current pro-

grammed controller can be stabilized by addition of an artificial ramp signal to the sensed switch current

waveform. In Section 12.2, the system small-signal transfer functions are described, using a simple first-

order model. The averaged terminal waveforms of the switch network can be described by a simple cur-

rent source, in conjunction with a power source element. Perturbation and linearization leads to a simple

small-signal model. Although this first-order model yields a great deal of insight into the control-to-out-

put transfer function and converter output impedance, it does not predict the line-to-output transfer func-

tion of current-programmed buck converters. Hence, the model is refined in Section 12.3. Section

12.4 extends the modeling of current programmed converters to the discontinuous conduction mode.

12.1

OSCILLATION FOR D > 0.5

The current programmed controller of Fig. 12.1 is unstable whenever the steady-state duty cycle is

greater than 0.5. To avoid this stability problem, the control scheme is usually modified, by addition of an

artificial ramp to the sensed switch current waveform. In this section, the stability of the current pro-

grammed controller, with its inner switch-current-sensing loop, is analyzed. The effects of the addition of

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Current Programmed Control

the artificial ramp are explained, using a simple first-order discrete-time analysis. Effects of the artificial

ramp on controller noise susceptibility is also discussed.

Figure 12.3 illustrates a generic inductor current waveform of a switching converter operating

in the continuous conduction mode. The inductor current changes with a slope during the first sub-

interval, and a slope – during the second subinterval. For the basic nonisolated converters, the slopes

and – are given by

Buck converter

Boost converter

Buck–boost converter

With knowledge of the slopes and –

we can determine the general relationships between

and

During the first subinterval, the inductor current

increases with slope

until

reaches

the control signal . Hence,

Solution for the duty cycle d leads to

In a similar manner, for the second subinterval we can write

In steady-state,

and

Insertion of these relationships into Eq. (12.4)

yields

12.1 Oscillation for D > 0.5

443

Or,

Steady-state Eq. (12.6) coincides with the requirement for steady-state volt-second balance on the induc-

tor.

Consider now a small perturbation in

is a steady-state value of

which satisfies Eqs. (12.4) and (12.5), while

is a small perturba-

tion such that

It is desired to assess the stability of the current-programmed controller, by determining whether this

small perturbation eventually decays to zero. To do so, let us solve for the perturbation after n switching

periods, and determine whether tends to zero for large n.

The steady-state and perturbed inductor current waveforms are illustrated in Fig. 12.4. For clar-

ity, the size of the inductor current perturbation is exaggerated. It is assumed that the converter

operates near steady-state, such that the slopes and are essentially unchanged. Figure 12.4 is

drawn for a positive the quantity is then negative. Since the slopes of the steady-state and per-

turbed waveforms are essentially equal over the interval

the difference between the

waveforms is equal to

for this entire interval. Likewise, the difference between the two waveforms

is a constant

over the interval

since both waveforms then have the slope –

Note that

is a negative quantity, as sketched in Fig. 12.4. Hence, we can solve for

in terms of

by considering only the interval

as illustrated in Fig. 12.5.

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