The basis for feedback control is illustrated with the flow diagram of Fig。 3 where the goal is for the output to follow the reference predictably and for the effects of external perturbations, such as input voltage variations, to be reduced to tolerable levels at the output Without feedback, the reference-to-output transfer function y/u is equal to G, and we can express the output asy Gu

With the addition of feedback (actually the subtraction of the feedback signal)y Gu yHG

and the reference-to-output transfer function becomesy/u=G/1+GH

If we assume that GH __ 1, then the overall transfer function simplifies toy/u=1/H

Fig。 3。 Flow graph of feedback control

Not only is this result now independent of G,it is also independent of all the parameters of the system which might impact G (supply voltage, temperature, component tolerances, etc。) and is determined instead solely by the feedback network H (and, of course, by the reference)。Note that the accuracy of H (usually resistor tolerances) and in the summing circuit (error amplifier offset voltage) will still contribute to an output error。 In practice, the feedback control system, as modeled in Fig。 4, is designed so thatG __ H and GH __ 1 over as wide a frequency range as possible without incurring instability。 We can make a further refinement to our generalized power regulator with the block diagram shown in Fig。 5。 Here we have separated the power system into two blocks – the power section and the control circuitry。 The power section handles the load current and is typically large, heavy, and subject to wide temperature fluctuations。 Its switching functions are by definition, large-signal phenomenon, normally simulated in most stability analyses as just a two states witch with a duty cycle。 The output filter is also considered as a part of the power section but can be considered as a linear block。 论文网

Fig。 4。 The general power regulator

IV。 THE BUCK CONVERTER

    The simplest form of the above general power regulator is the buck – or step down – topology whose power stage is shown in Fig。 6。 In this configuration, a DC input voltage is switched at some repetitive rate as it is applied to an output filter。 The filter averages the duty cycle modulation of the input voltage to establish an output DC voltage lower than the input value。 The transfer function for this stage is defined by

tON=switch on -timeT = repetitive period (1/fs)d = duty cycle

Fig。 5。 The buck converter。

    Since we assume that the switch and the filter components are lossless, the ideal efficiency ofThis conversion process is 100%, and regulation of the output voltage level is achieved bycontrolling the duty cycle。 The waveforms of Fig。6 assume a continuous conduction mode (CCM)

Meaning that current is always flowing through the inductor – from the switch when it is closed,And from the diode when the switch is open。 The analysis presented in this topic will emphasizeCCM operation because it is in this mode that small-signal stability is generally more difficult

to achieve。 In the discontinuous conduction mode (DCM), there is a third switch condition in which the inductor, switch, and diode currents are all 5-4 zero。 Each switching period starts from the same state (with zero inductor current), thus effectively reducing the system order by one and making small-signal stable performance much easier to achieve。 Although beyond the scope of this topic, there may be specialized instances where the large-signal stability of a DCM system is of greater concern than small-signal stability。    There are several forms of PWM control for the buck regulator including,• Fixed frequency (fS) with variable tON and variable tOFF

• Fixed tON with variable tOFF and variable fS