Variable Freq Predictive Digital Current Mode Control

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IEEE POWER ELECTRONICS LETTERS, VOL. 2, NO. 4, DECEMBER 2004 113

Variable-Frequency Predictive DigitalCurrent Mode Control

Praneet Athalye , Student Member, IEEE , Dragan Maksimovic , Member, IEEE , and Robert Erickson , Fellow, IEEE

Abstract—A variable-frequency predictive digital controlmethod for the inductor current in switched-mode convertersis introduced in this letter. This method is predictive in naturebecause the transistor off-time required for achieving the targetcurrent is calculated ahead of time. The transistor on-time iskept constant, which results in variable switching frequency. Thecontrol laws for continuous and discontinuous modes of operationof the three basic converters are derived. Stability and robust-ness criteria are presented. The variable-frequency predictivecontrol obviates the need for current-loop compensation andhas the advantages of single-cycle response and relatively simpleimplementation. The control method is demonstrated in a digitalsignal processor (DSP) for a boost power factor corrector (PFC),

which shows excellent current tracking and a very low harmonicdistortion of the line current.

Index Terms—Current control, dc–dc power conversion, digitalcontrol, predictive control, switched mode power supplies.

I. INTRODUCTION

FOLLOWING the trends of increasing speed and processingpower of digital devices, including micro-controllers, dig-

ital signal processors, programmable logic, or custom dig-ital integrated circuits, high-performance digital control forswitched-mode power converters is becoming increasingly fea-sible and practical[1]. In order to improve dynamic performance

in the presence of processing delays, discrete-time control tech-niques specifically tailored for high-frequency switched-modepower converters are receiving increased attention. In partic-ular, predictive current control techniques have been proposedfor dc–dc converters [2] and power factor correctors [3]. Inthe predictive dead-beat current control, the switch duty ratioin the current cycle is computed so that the current reachesthe target in a finite number of cycles. Constant-frequencypredictive valley current control has been described in [2] and[3]. This technique has been extended to constant-frequencypredictive peak or average current control in [4]. The pro-posed constant-frequency predictive controllers require two orthree switching cycles to achieve the current target and thecontrol laws apply only to converters operating in continuousconduction mode (CCM). Recently, operation in discontinuousconduction mode (DCM) with predictive current control hasbeen addressed [5], which requires evaluation of a square-rootor a look-up table implementation.

Manuscript received June 26, 2004; revised November 30, 2004. Recom-mended by Associate Editor D. J. Perreault.

P. Athalye is with National Semiconductor, Santa Clara, CA 95052 USA(e-mail: [email protected]).

D. Maksimovic and R. Erickson are with the Department of Electrical andComputer Engineering, University of Colorado, Boulder, CO 80309-0425 USA(e-mail: [email protected]; [email protected]).

Digital Object Identifier 10.1109/LPEL.2004.841493

Fig. 1. Digital control of a boost converter.

Fig. 2. Variable-frequency (constant on-time) predictive digital current modecontrol.

In this letter, we describe a constant on-time/variable-fre-quency predictive current control technique, which can achievethe target current in just one switching cycle. Operation inCCM or DCM is supported without significantly increasingthe computational requirements. Furthermore, the constanton-time operation is advantageous for implementation of cur-rent sensing and A/D conversion.

The proposed control method is introduced in Section II,stability and robustness are discussed in Section III, DCMoperation in Section IV, and experimental results in Section V.Conclusions are given in Section VI.

II. CONTROL IN CONTINUOUS CCM

A typical setup for a digitally controlled boost converter is

shown in Fig. 1. In the proposed control scheme, illustrated by

the waveforms shown in Fig. 2, the transistor on-time is

constant by design and is selected by considering the allowed

range of switching frequency variation and the minimum com-

putation time required. The current can be sampled anywhere

during , by allowing sufficient time for A/D conversion and

calculation of the transistor off time .

1540-7985/04$20.00 © 2004 IEEE



114 IEEE POWER ELECTRONICS LETTERS, VOL. 2, NO. 4, DECEMBER 2004

TABLE ICCM CONTROL LAWS FOR THREE BASIC CONVERTERS

The inductor current waveform is shown in Fig. 2. Assuming

that the current is sensed at the valley, let us consider the th

switching interval. The equation for the inductor current can be

written as follows:

(1)

where is the sampled current, is the target current, and

, are the current slopes during and respectively.

The current slopes are functions of the input voltage and/or

the output voltage as shown in Table I. The required

to achieve the target current is given by

(2)

Equation (2) is the basic control law for the variable-fre-

quency predictive digital control in continuous conduction

mode. The control laws are tabulated in Table I for three basic

converters. If the output voltage is fairly constant, the division

by “ ” can be avoided, by replacing it with a constant dc value

, for a simpler digital implementation in the cases of buck

and buck-boost converters.

III. STABILITY AND ROBUSTNESS

Let us consider the boost control law, as shown in Table I. Let

us also rewrite the basic current equation as

(3)

Then, let be the nominal inductance value, and let be the

actual inductance value in the practical implementation. The

calculated is then

(4)

and the actual is given by the following equation with

from (4) as

(5)

Fig. 3. Stability conditions.

Subtracting from both sides and rearranging the terms gives

(6)

where

(7)

This means that the error at the end of the period will decrease

with time (as shown in Fig. 3) provided that the right-hand side

of (6) is less than unity. The condition for stability is

(8)

This is not dif ficult to meet in practice.

Next, let us suppose that there is an error or an offset in

the sampled output voltage. The current at the end of the period

is then given as

(9)

This translates into

(10)



ATHALYE et al.: VARIABLE-FREQUENCY PREDICTIVE DIGITAL CURRENT MODE CONTROL 115

TABLE IIDCM CONTROL LAWS FOR THREE BASIC CONVERTERS

There are two terms in (10). If is less than , which is

the case in a well-designed system, the first term decreases with

time. The second term is responsible for a constant offset error.

The steady-state offset error in the current can be written as

(11)

In conclusion, the proposed control law is relatively immune

to parameter tolerances or sensing errors. A similar analysis can

be extended to other topologies.

IV. CONTROL IN DCM

The inductor current waveform in the boundary conduction

mode followed by the discontinuous conduction mode is shown

in Fig. 4. In DCM, only the average current control applies in the

proposed method. DCM operation is detected when the control

objective is less than half the ripple current or .In steady state, we have

(12)

The area under the current waveform is given by

(13)

which can also be written as

(14)

Hence, is given by

(15)

which is the control law in DCM. Implementation of this law

in conjunction with the CCM control law (3) can be done in

two ways. In one implementation, the CCM/DCM boundary

condition is checked first, before deciding which control law

computation to perform [(3) for CCM or (15) for DCM]. In

the second method, one can compute for both CCM and

DCM control laws, and then select the larger of the two.

The control laws for DCM are summarized for the basic con-

verters in Table II. It can be seen that there is an additional divi-

sion operation by but a square-root operation is not required.An advantage of the constant-on-time operation in DCM is that

Fig. 4. Variable-frequency predictive average current control in DCM.

the switching frequency decreases as the load is reduced, which

further causes a reduction in the switching losses.

In DCM there is no inner current loop and the tracking per-

formance is ensured by a relatively slow outer voltage loop. Fol-

lowing the analysis similar to the analysis in Section III, we find

that an error in the inductance value results in a current offset

error given by

(16)

This results in an output voltage error, which is corrected by

adjusting the control variable .

V. EXPERIMENTAL IMPLEMENTATION AND RESULTS

The boost control law shown in Table I has been implemented

in a power factor corrector (PFC) to demonstrate its current-

tracking ability. An Analog Devices ADSP401 evaluation board

with a 26-MHz clock has been used. Theinput voltage, the output voltage, and the inductor current are

sensed and digitized. The inductance value mH and

are constants in the implementation. The A/D con-

version and calculations (integer arithmetic) are completed in

approximately 4 . The division operation is the most time

consuming with 16 clock cycles. The minimum (approx-

imately 308 ns) is dictated by the software implementation in

the DSP. This puts a limit on the maximum duty cycle to about

94%.

The input voltage is 110 V rms, while the output is adjusted

to 380 V dc with a resistive load of 100 W. The maximum

switching frequency is approximately 190 kHz near the line

zero-crossings, and the minimum switching frequency is ap-proximately 120 kHz at the peak of the line. The line voltage



116 IEEE POWER ELECTRONICS LETTERS, VOL. 2, NO. 4, DECEMBER 2004

Fig. 5. Experimental line waveforms for a DSP-controlled boost PFCrectifier:rectified line voltage (Ch 1 at 50 V/div) and line current (Ch 4 at 1 A/div).

and the line current waveforms are shown in Fig. 5. A total har-

monic distortion of 2.8% has been achieved for the line current.

VI. CONCLUSION

The proposed variable-frequency predictive digital current

control method has several advantages. The control objective

is achieved in one switching cycle, which results in high-per-

formance current tracking capability. The transistor on-time is

kept constant, which is advantageous for the implementations

of current sensing and A/D conversion. The control laws for

CCMor DCMoperation, as well as checking for the CCM/DCM

boundary, are relatively simple and easy to implement using in-

teger arithmetic. In DCM operation, the switching frequencyand the switching losses decrease when the load is reduced. Ex-

perimental results show excellent current shaping for a 100-W,

DSP-controlled PFC boost rectifier operating at switching fre-

quencies in the range from 120 to 190 kHz.

REFERENCES

[1] D. Maksimovic, R. Erickson, and R. Zane, “Impact of digital control in

power electronics,” in Proc. IEEE ISPSD Conf., 2004, pp. 13–22.

[2] S. Bibian and H. Jin, “High performance predictive dead-beat digital

controller for DC power supplies,” IEEE Trans. Power Electron., vol.

17, pp. 420–427, May 2002.

[3] , “Digital control with improved performance for boost powerfactor correction circuits,” in Proc. IEEE APEC Conf., 2001, pp.

137–143.

[4] J. Chen, A. Prodic, R. Erickson, and D. Maksimovic, “Predictive digital

current programmed control,” IEEE Trans. Power Electron., vol. 18, pp.

411–419, Jan. 2003.

[5] M. Ferdowsi and A. Emadi, “Estimative current mode control technique

for dc-dc convertersoperating in discontinuousconduction mode,” IEEE

Power Electron. Lett., vol. 2, Mar. 2004.

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Variable Freq Predictive Digital Current Mode Control