Current Programmed Control

So far, we have discussed duty ratio tontrol of PWM converters, in which the converter outptit is con-troiied by direct choice of the duty ratio d(l}. We have therefore developed expressions and smaii-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 converteroutput is controlled by choice ofthe pealt transistor switch current peak(;,(/)). The control input signal is a current (,(/), and a simple control network switclies the trimsistor on and off, such that the peak transistor current follows The transistor duty cycle rf(f) is not directly controlled, but depends on /.(f) as well as on the converter inductor currents, capacitor voltages, and power input voltage. Converters cttntroiled via curtent programming are said to operate in the currem programmed mode (CPM).

The block diagram of a simple current programmed controller is illustrated in Fig. 12.1. Control signal it) and switch current ((t) 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 condticts, its current /,.(0 is equal to the inductor current f,(f); this current increases with some positive siope m, that depends on the value of inductance and the converter voltages. In more complicated converters, f/f) may follow the stmi of several inductor currents. Eventtiaiiy, the switch current /,(() becomes equal to the control signal iit). 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 cmreiit senstir circuit, and compare ifl) to iXt) using an analog comparator. In practice, voltages proportional to l,(0 and ijj) are compared, with constant of propor-tioniUity Яу. When i/f) 5: (fO, 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 otitptit voltage vif) is compared to a reference voltage f y, to generate an eiTor signal. This error signal is applied

Buck converter

Measure sviitck

11 D,

Control input

0 r.

Analog coinparator

Latcfi

Current-programmed controller

Conventiortal output voUage coritroller

Fig. 12.1 Cutrent-programnned control of a huck converter. The peak tian.iistor cuirent replaces the duty cycle as tlie control input.

Fig. t2,2 Switch cuiTeni ij{i) and coiitiol input (,.(t) waveforms, for the current-programmed system ofPig. 12.1.

Transistor status;

Clock turns Comparator tefTiT

iratsistor on transistor off

to the input of a compensation net:worl;, and the output of the compensator drives t:he control signal lJj)Rp To design such a feedbaclc system, v/e need to model how variations in the control signal iJX) and in the line input voltage vj,t) affect the output voltage t(r).

The chief advantage of the current programmed mode is its simpler dynamics. To first order, the sinali-signal contiol-to-output transfer fuuctitm v(.v)/i,(i) contains one less pole than ii-sytiis). Actually, this pole is moved to a high frequency, near the converter sv/itching frequency. Nonetheless, simple robust vt-ide-bandwidth output voltage control can usually be obtained, without the use of compensator lead networlcs. It is true that the current programmed controller requires a circuit for measurement ofthe switch current /,(г); however, in practice such a circuit is also required in duty ratio controlled systems, for protection ofthe 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 ij,t). This ensures that the transistor will turn [)ff whenever the switch current becomes too iiirge, on a cycle-by-cycie biLsis.

An added benefit is the reduction or elimination of transformer saturation problems in full-bridge or push-pull is[)lated converters. In these converters, small voltage imbalances induce a dc bias in the transformermagnetizing 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 maintained. 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 ijt) or il) signals. This noise can prematurely reset the latch, disrupting the operation ofthe controller. In particular, a small amount of filtering ofthe sensed switch current waveform is necessary, to remove the turn-on current spike caused by the diode stored chiirge. .-Addition of an artificial riimp to the current-programmed controller, as discussed in Section 12.1, can also improve the noise immunity ofthe circuit.

Commercial integrated circuits that implement current programmed control are widely available, and operation of converters in the current programmed mode is quite popular. In this chapter, converters [ipeiating in the cunent piogiammed mode are mtideled. In Section 12.1, the stability ttf 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 programmed controllercan be stabilized by addition of an artificial ramp signal to the sensed switch current waveform. In Section 12.2, the system small-signal transferfunctions are described, using a simple first-order model. The averaged terminal wavefrirms ofthe switch network can be described by a simple current source, in ctinjunction with a power source element. Perturbation and linearization leads to a simple smali-signal model. Although this first-order model yields a great deal of insight into the controi-to-out-put transfer function and converter output impedance, it does not predict the line-to-output transfer liinc-tion G{s)oi current-programmed buck converters. Hence, the model is refuted 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 ofthe current programmed controller, with its inner switch-current-sensing 1сюр, is analyzed. The effects of the addition of