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IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY 1

Switching Control of Buck Converter Based on Energy Conservation PrincipleL. Wang, Q. H. Wu, Fellow, IEEE, Y. K. Tao, and W. H. Tang, Senior Member, IEEE

Abstract— This brief presents a switching controlscheme (SCS) based on the energy conservation principlefor buck converters. The concept of the SCS is based on theconservation of energy in circuit. It keeps the balance betweenthe energy that is injected into a circuit and the sum of theenergy that is consumed by the load and stored in reactivecomponents. The SCS not only regulates the output voltage ofthe buck converter accurately under static conditions, but alsoimproves its dynamic responses to disturbances of input voltageand load current. Furthermore, the SCS is capable of operatingin both the continuous current mode and the discontinuouscurrent mode, and the stability analysis undertaken usingthe Lyapunov stability criterion shows that the SCS is stablein all cases. Simulation and experimental results confirm thepossibility and attractiveness of using this method to controlbuck converters.

Index Terms— Buck converter, dynamic response, energyconservation principle, stability analysis, switching control.

I. INTRODUCTION

W ITH the development of microelectronics andpower electronics, dc–dc converters are widely used.

In addition, as the voltage regulation criteria for digitalcircuit’s supply voltage become more stringent, there is anincreasing demand for high dynamic performance powerconverters. Until now, PID controllers are still one of the mostcommonly used control methods for converters. However,the PID control systems suffer from the limitations ofslow compensator networks, which lead to poor dynamicperformances of converters [1].

As control methods play an important role on improv-ing the dynamic performance of converters, various controlmethods have been proposed to provide improved dynamicperformances. The hysteresis control, as presented in [2]–[4],provides fast dynamic responses, since the conventionalfeedback compensation network is removed. However, thedrawbacks of this method are its variable switching frequencyand nonzero steady-state error. Sliding-mode control (SMC)

Manuscript received July 15, 2015; accepted November 21, 2015.Manuscript received in final form November 25, 2015. This work wassupported in part by the Guangdong Innovative Research Team Program,China, under Grant 201001N0104744201 and in part by the State KeyProgram of National Natural Science of China under Grant 51437006.Recommended by Associate Editor Q.-C. Zhong. (Corresponding author:Q. H. Wu.)

L. Wang, Y. K. Tao, and W. H. Tang are with the School of Electric PowerEngineering, South China University of Technology, Guangzhou 510641,China (e-mail: [email protected]; [email protected];[email protected]).

Q. H. Wu is with the School of Electric Power Engineering, South ChinaUniversity of Technology, Guangzhou 510641, China, and also with theDepartment of Electrical Engineering and Electronics, University of Liverpool,Liverpool L69 3GJ, U.K. (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TCST.2015.2505625

is one of the effective non-linear robust control approaches,since it provides system dynamics with an invariance propertyto uncertainties once the system dynamics are controlled in thesliding mode [5]–[7]. However, there are some problems to besolved, such as chattering phenomena and nonconstant switch-ing frequency, when conventional SMC is used in the powerconverters. As another typical nonlinear control strategy, theone-cycle control (OCC) has been studied for decades [8], [9].While its inhibitory capability to variations of input voltage issatisfactory, the inhibitory capability to load changes is stillpoor. Recently, in [10]–[12], a control algorithm based on theprinciple of capacitor charge balance has been studied fordc–dc converters to achieve optimal dynamic performanceunder load current changes. However, the accurate calculationof the duty-ratio required by this control algorithm is difficultto achieve.

An ideal buck controller would behave linearly duringsteady-state conditions for tight voltage regulation and non-linearly during transient conditions for fast response. It isdemonstrated in [12]–[14] that by employing two separate con-trollers for steady-state operation and for transient operation,the dynamic response can be improved while not sacrificingthe steady-state accuracy. However, the accurate detectionof the time when disturbances occur is not easy. In [15],a hybrid mode-switched control scheme that uses energybalance principle to calculate the reference voltage and currenthas been proposed for dc–dc converters. With this scheme, thedynamic performances of the converters are improved. How-ever, the main drawback of this scheme is that it is designedbased on working in DCM. Under CCM, the reference currentis difficult to calculate, since not all the energy stored by theinductor is transferred to the load in one switching cycle.

In our research, an SCS based on the energy conserva-tion principle is proposed to control buck converters. Thisbrief is organized as follows. In Section II, the SCS isdesigned. Section III illustrates the implementation proceduresof the SCS, including the computation of the energy thatthe inductor stores. The stability analysis of the SCS isstudied in Section IV, and the dynamic response is analyzed inSection V. Simulation and experimental results are presented inSection VI, and the conclusions are presented in Section VII.

II. DERIVATION OF THE SWITCHING CONTROLLER

The structure of a buck converter is shown in Fig. 1,where i� represents the current of inductor L, io represents thecurrent of the load R, and uo represents the output voltage.For the buck converter, the energy conservation in the circuitis expressed as follows:

Win(n) = Wout(n) + �W�(n) + �Wc(n) + Ws(n)

(n = 1, 2 . . .) (1)

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2 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY

Fig. 1. Structure of a buck converter with the SCS.

it means that, during the nth switching cycle [(n − 1)Ts, nTs),the energy that is injected into the circuit Win(n) should beequal to the sum of the output energy Wout(n), the energy thatthe reactive components (L and C) store (�Wc(n)+�W�(n)),and the conduction losses of the switch and the diode Ws(n).

The following proves that �Wc(n) in (1) can be ignored.First, the output voltage uo and capacitor voltage uc aredifferent due to the equivalent series resistance (ESR) of thecapacitor, but if the ESR is negligible, then we can assumethat uc is equal to uo. Then compared with the average outputvoltage, the output voltage ripple is negligible. And as ourpurpose is to ensure that uo is always equal to the referencevoltage uref , which is a constant value, uo can be substitutedby uref . The above assumptions give

uc(t) = uo(t) = uref . (2)

And the energy the capacitor stores is calculated using

�Wc(t) =∫ t

(n−1)Ts

uc(t)ic(t)dt (t ∈ [(n − 1)Ts, nTs)). (3)

As the capacitor C works the entire cycle during eachswitching cycle n, �Wc(n) is calculated in

�Wc(n) =∫ (n−1)Ts+Ts

(n−1)Ts

uc(t)ic(t)dt (4)

where ic(t) represents the capacitor current, which iscalculated in

ic(t) = Cduc(t)

dt. (5)

Based on (2), �Wc(n) can be obtained as

ic(t) = Cduc(t)

dt= C

duref

dt= 0 ⇒ �Wc(n) = 0. (6)

Thus Wc(n) in (1) can be ignored, and then the energyconservation in the circuit can be rewritten as follows:Win(n) = Wout(n)+�W�(n)+Ws(n) (n = 1, 2, 3 . . .). (7)

After obtaining (7), Win, Wout, �W� and Ws of the buckconverter working in CCM and DCM are calculated thoughthe state analysis in the following of this section, respectively.

A. Continuous Conduction Mode

Under the CCM operation mode, the buck converteroperates in two states: 1) state 1—switch S1 is ON and2) state 2—S1 is OFF. Thus, during the nth switching cycle,we have

tON(n) + tOFF(n) = Ts (n = 1, 2, 3 . . .) (8)

where tON(n) and tOFF(n) represent the opening and closingdurations of S1, respectively.

State 1: when S1 is ON, energy is injected into the circuit,and i� flows through the loop (uin → S1 → L → C ‖R → uin). In this switching state, L is charged, and S1 and Rconsume energy, and uAB is obtained using

uAB(t) = uin(t) − usat (t ∈ [(n − 1)Ts, (n − 1)Ts + tON(n)))

(9)

where usat represents the ON-state voltage drop of S1.State 2: when S1 is OFF, no energy is fed into the

circuit, however, i� continues flowing through the loop(D1 → L → C ‖ R → D1). In this switching state, L isdischarged, and D1 and R consume energy, and uAB is obtainedusing

uAB(t) = −ud (t ∈ [(n − 1)Ts + tON(n), nTs)) (10)

where ud represents the ON-state voltage drop of thediode D1.

The above state analysis shows that the voltage sourceworks in the time interval from (n−1)Ts to (n−1)Ts + tON(n),while L and R work in the entire switching cycle. Thus, thevalues of Win(n), Wout(n), �W�(n), and Ws(n) during thenth switching cycle can be obtained as follows:

Win(n) =∫ (n−1)Ts+tON(n)

(n−1)Ts

uin(t)i�(t)dt (11)

Wout(n) =∫ (n−1)Ts+Ts

(n−1)Ts

uo(t)io(t)dt (12)

as uo = uref from (2), (12) becomes

Wout(n) = uref io(t)Ts (13)

�W�(n) and Ws(n) are calculated as follows:

�W�(n) =∫ (n−1)Ts+Ts

(n−1)Ts

u�(t)i�(t)dt (14)

Ws(n) =∫ (n−1)Ts+tON(n)

(n−1)Ts

Usati�(t)dt+∫ nTs

(n−1)Ts+tON(n)udi�(t)dt.

(15)

Substituting the values of Win(n), Wout(n), �W�(n), andWs(n) calculated above into (7), the energy conservation isrewritten as follows after adjusting:∫ (n−1)Ts+tON(n)

(n−1)Ts

(uin(t) − usat)i�(t)dt +∫ nTs

(n−1)Ts+tON(n)−uddt

= uref io(t)Ts +∫ nTs

(n−1)Ts

u�(t)i�(t)dt (n = 1, 2 . . .). (16)


WANG et al.: SWITCHING CONTROL OF BUCK CONVERTER BASED ON ENERGY CONSERVATION PRINCIPLE 3

B. Discontinuous Conduction Mode

Under the DCM operation mode, the buck converter oper-ates in three states, in which switch S1 is ON for a durationof tON(n) and is OFF for durations tOFF1(n) and tOFF2(n), andtON(n) + tOFF1(n) + tOFF2 = Ts(n).

State 1: when S1 is on, energy is injected into thecircuit, and i� flows through the loop (uin → S1 →L → C ‖ R → uin). In this switching state, L ischarged, and S1 and R consume energy, and uAB is obtainedusing

uAB(t)=uin(t)−usat (t ∈ [(n−1)Ts, (n−1)Ts+tON(n))). (17)

State 2: when S1 is OFF, no energy is fed into thecircuit. Energy stored in L is discharged through the loop(D1 → L → C ‖ R → D1). In this switching state,L is discharged, and D1 and R consume energy. uAB isobtained in

uAB(t) = −ud(t ∈ [(n − 1)Ts + tON(n),

(n − 1)Ts + tON(n) + tOFF1(n))). (18)

State 3: when S1 is still OFF and energy stored in L isdischarged out, i� = 0. However, the load still consumesenergy from the capacitor. In this switching state, R consumesenergy, and uAB is obtained using

uAB(t) = 0 (t ∈ [(n−1)Ts + tON(n) + tOFF1(n), nTs)). (19)

By combining state 1, state 2, and state 3, Win(n), Wout(n),�W�(n), and Ws(n) under DCM can be calculated similarlyto that of the CCM operation mode. Then substituting thesecalculated values into (7), we get

∫ (n−1)Ts+tON(n)

(n−1)Ts

(uin(t) − usat)i�(t)dt

+∫ (n−1)Ts+tON(n)+tOFF1(n)

(n−1)Ts+tON(n)−udi�(t)dt

+∫ nTs

(n−1)Ts+tON(n)+tOFF1(n)0i�(t)dt


(n−1)Ts

u�(t)i�(t)dt (n = 1, 2 . . .). (20)

Equations (16) and (20) are the main equations that theduration tON(n) and tOFF(n) must satisfy during each switchingcycle to implement the SCS. Combining the aforementionedstate analysis, it is observed that (16) and (20) can both berealized by controlling the switching variable uAB, which isexpressed in

∫ nTs

(n−1)Ts

uAB(t)i�(t)dt


(n−1)Ts

u�(t)i�(t)dt (n = 1, 2 . . .). (21)

III. IMPLEMENTATION OF THE SCS

A. Calculation of the Control Reference Wout (n) + �W�(n)

As control reference, Wout(n) + �W�(n) should becalculated in the time instant of the beginning of thenth switching cycle and kept during the entire switching cycle.After measuring the variable io, Wout(n) is obtained by (13).And as we know, the energy is absorbed and released equallyby the inductor in a switching cycle under the steady-stateconditions. However, it is not equal under the dynamic stateconditions, since the inductor current cannot change instan-taneously. Therefore, to ensure the dynamic performances,�W�(n) should be considered and calculated as follows:

�W�(t)=∫ t

(n−1)Ts

u�(t)i�(t)dt (t ∈[(n−1)Ts, (n−1)Ts+Ts))

(22)

where i� is the measured variable, and u� is obtained using

u�(t) = Li�(t + Tc) − i�(t)

Tc(23)

where Tc is the sampling cycle.The state analysis shows that the inductor works during the

entire switching cycle, which means the time t of (22) goes tothe end of the nth switching cycle, therefore, �W�(n) is calcu-lated by (14). Note here that the control reference is collectedonly in the time instant of the beginning of each switchingcycle, therefore, �W�(n) used in the control reference of thenth switching cycle is actually �W�(n − 1) calculated inthe (n − 1)th switching cycle, which means �W�(n) used inthe SCS has a switching cycle lag.

B. Implementation Procedure of the SCS

After the computation of Wout(n) + �W�(n), the SCS canbe implemented with simple logic functions (comparison andintegration) as shown in Fig. 1. Here, the implementation forcontrol of a CCM buck converter is described as follows:the integration process starts at the moment when S1 isturned ON by the fixed frequency clock pulse. At this moment,uAB(t) = uin(t) − usat. As time goes on, the integrationvalue Wint(t) increases from its initial value shown in Fig. 2as follows:Wint(t) =

∫ t

(n−1)Ts


+Winitial(n) (t ∈ [(n−1)Ts, (n−1)Ts+Ts)) (24)

and Wint(t) compares with Wout(n)+�W�(n) instantaneously.At the instance when Wint(t) reaches Wout(n) + �W�(n), thecomparator generates a reset pulse to reset the RS flip-flop tobe (Q = 0). Then switch S1 is changed from the ON-stateto the OFF-state. At the same time, the integrator is reset tozero. t at this moment is defined as (n − 1)Ts + dSCS(n)Tsof the present cycle n, which is determined by the followingequation:

Winitial(n) +∫ (n−1)Ts+dSCS(n)Ts

(n−1)Ts


= Wout(n) + �W�(n) = uref io(t)Ts + �W�(n) (25)



Fig. 2. Operation waveform of the SCS of the buck converter.

where dSCS(n) is the duty ratio, which is tON(n)/Ts, andWinitial(n) is the integration value during the OFF-state of S1,in this switching state, no energy is injected into the circuit,and uAB is equal to −ud. Then the integration restarts fromzero with the value of −udi�(t) after the reset, as shownin Fig. 2. The switch S1 is OFF until the arrival of thenext clock pulse, which starts the (n + 1)th switching cycle.Thus

Winitial(n) =∫ nTs

(n−1)Ts+dSCS(n)Ts

−udi�(t)dt . (26)

As the implementation for a DCM buck converter is similarto that of CCM, the details are not presented here.

IV. STEADY-STATE ANALYSIS

A. Steady-State Operation Analysis

Under the steady-state conditions, the inductor absorbs andreleases equal energy, which means �W�(t) = 0. Meanwhile,after reaching the steady state, i�(t) is equal to io(t) byneglecting the current ripple. Thus, (21) becomes

1

Ts

∫ (n−1)Ts+Ts

(n−1)Ts

uAB(t)dt = uref (27)

from (21), it is observed that in each switching cycle, theaverage of the switching variable uAB(t) is exactly equal tothe control reference uref , which ensures the tracking of theoutput voltage to uref in each switching cycle [8].

B. Stability Analysis

Under the steady state, neglecting �W�(t) since�W�(t) = 0 and the conduction losses of S1 and D1,(25) becomes

1

Ts

∫ (n−1)Ts+dSCS(n)Ts

(n−1)Ts

uin(t)i�(t)dt = uref io(t)

�⇒ dSCS(n) = uref io(t)

uin(t)i�(t).

(28)

Then a buck converter with the SCS can be described by thefollowing system of differential equations:

x(t) = Ax(t) + Buin(t)

dSCS = uref io(t)

uin(t)i�(t)(29)

where

x(t) =[

i�(t)

uo(t)

], A =

⎡⎢⎣

− R�

L− 1

L1

C− 1

RC

⎤⎥⎦, B =

⎡⎣

dSCS

L0

⎤⎦

and R� represents the parasitic resistance of the inductor(for simplicity, the parasitic resistance of C wasneglected).

A disturbance to the converter causes the changes uo(t) inthe output voltage, i�(t) in the inductor current, and dSCS inthe duty ratio.

System (29) can be rewritten in terms of disturbances

˙x(t) = Ax(t) + B1Vin

dSCS = Vref

RVin I�uo(t) − D

I�i�(t) (30)

where x(t) =[ i�(t)

uo(t)

], B1 =

[ dSCS

L0

], and Vin, D, and I� are

the steady components.A Lyapunov function is defined as

V = 1

2Li 2

� + 1

2Cu 2

o (31)

where V > 0, and the derivative of this is expressed as follows:dV

dt= Li�

di�dt

+ Cuoduo

dt. (32)

By using (30) and replacing i� with dSCS, one gets

dV

dt= −Ri 2

� − u 2o

R+ VindSCSi�

= −Ri 2� − u 2

o

R− d 2

SCS I�D

+ Vref uodSCS

RD. (33)

In a closed-loop controlled converter, any increase in theoutput voltage (uo > 0), for a static value, causes a decreasein the duty ratio (dSCS < 0) to shorten the opening durationof S1, and thus for bringing down back the output voltageto its static value and vice versa [16]. It is obvious that((Vref uodSCS)/RD) < 0, which satisfies the Lyapunov sta-bility criterion [16], [17]. Hence, the SCS is stable.

V. ANALYSIS OF DYNAMIC RESPONSE

The capacitor voltage drop is reconsidered as �uc(n) herefor the analysis of the transient response. Since the dynamicperformance under a load current change is arguably themost important issue in power converter design, the transientresponse to a positive load current change will be fullydiscussed. Referring to Fig. 3, immediately following the loadcurrent step change io1 → io2, the inductor current cannot



Fig. 3. Inductor current path of a buck converter under a positive load current step.

change instantaneously to supply the step of the load current.Therefore, a portion of the load current must be supplied bythe output capacitor. This, in turn, causes the output capacitorto lose charge and the output voltage to decrease. Beforepoint 2, the inductor current is lower than the load current,the capacitor voltage continues to decrease. At point 2, theinductor current is equal to the load current, and then thecapacitor stops discharging. At this point, the capacitor voltagedrop is at its maximum, which is expressed in

Cduc(t)

dt= ic(t) = i�(t) − io(t) (34)

�uc(n) = 1

C

∫ Point2

Point0(i�(t) − io(t))dt . (35)

Assuming the positive and negative inductor slews areinvariable, in order to minimize �uc(n), the duration t2,which represents the integral period (point 0–point 2), mustbe minimized. It means the inductor current i� should achievethe new load current as soon as possible. Here, three factorsinfluence the inductor current to change:

1) the parameters of the circuits;2) the delay time for responding to the disturbances;3) the duty ratio during the increase of i� from io1 to io2.Under certain circuit parameters, the change of i� is deter-

mined by the other two factors. First, when io steps fromio1 to io2, the tON(n) and tOFF(n) of the SCS will be imme-diately allocated again according to (21); at the same time,the SCS makes the corresponding adjustments immediatelyto the switching pulses. However, using the current-modePID controller, the load changes are firstly responded in theinductor current. Then the switching pulse is adjusted after thechanges of the inductor current get to the comparator throughthe compensation block. This will bring an unpredictablelatency t0, as shown in Fig. 3. Then, during the increase of�i� based on the given �io, the bigger the duty ratio is, themore quickly i� gets to io2. The following is the calculationsand comparison of the duty ratios.

By neglecting the energy losses of S1 and D1 of (25), theduty ratio dSCS(n) of the SCS during t1 (the load current hasbecome io2(t) at this time) is obtained as follows:

1

Ts

∫ (n−1)Ts+dSCS(n)Ts

(n−1)Ts

uin(t)i�(t)dt

= uref io(t) + 1

Ts�W�(n)

⇒ dSCS(n) = uref io2(t)

uin(t)i�(t)+ �u�(n)i�(t)

uin(t)i�(t)

= uref io2(t)

uin(t)i�(t)+ �u�(n)

uin(t)(36)

where �u�(n) represents the average change value of theinductor voltage in the nth switching cycle.

According to the state analysis, the state average model ofthe buck converter is obtained as follows:

d(n) =L

di�(t)

dt+ uref + �uo(t)

uin(t). (37)

The designing principle of the current-mode controller isthat the inner current controller is designed by ignoring theinfluence of the output voltage and the outer voltage controlleris designed under the assumption that the actual current com-pletely tracks the reference current. This shows that, during t1,the purpose that the inner and outer loops adjust the duty ratiois to offset the inductor voltage changes �u�(n), althoughthe outer voltage loop implements this purpose by adjustingthe �uo. Thus, according to (37), the duty ratio dPID(n) isobtained as follows:

dPID(n) = uref + �u�(n)

uin(t)= uref

uin(t)+ �u�(n)

uin(t). (38)

Because i�(t) < io2(t) during t1, the comparison between(36) and (38) shows that dSCS(n) is always greater thandPID(n) until i� reaches io2. Therefore, �uc(SCS) is smallerthan �uc(PID), as shown in Fig. 3. Since i� using the SCS can



Fig. 4. Responses of the inductor current to a positive load current step.

approach the new output current io2 more quickly, the recoverytime can be reduced in such a situation, as shown in Fig. 3.This is demonstrated in Fig. 4, which shows the simulationcomparison results of the inductor current responses usingthe SCS and the PID controller to the load current step bychanging the load from 8 to 4 �. The simulation results showthat the inductor current using the SCS increases to the newsteady-state output current very quickly. However, with thePID controller, the inductor current takes more than 16 ms toget to the new steady state. Under other transient conditions,the analysis is virtually similar to those detailed above.

VI. SIMULATION AND EXPERIMENTAL RESULTS

Simulation and experimental results are used to demon-strate the superior performances of the SCS. For simulationstudies, buck converter A with the low switching frequencyfs = 1 kHz and buck converter B with the high switchingfrequency fs = 40 kHz are configured. To evaluate theperformances of the SCS, the following section presents acomparative study with a current-mode PID controller. A com-parison is made with a current-mode controller because itis most frequently used in voltage regulator module (VRM)applications.

According to the circuit shown in Fig. 1, buckconverter A has the parameters: uin = 15 V, uref = 6 V,�upp = 0.08 V, R = 8 �, L = 2500 μH (CCM)/800 μH (DCM), C = 1200 μF (CCM)/2200 μF (DCM). Theinductances and capacitances are determined by the followingequations:

L(critical) = uref(1 − d)

2io(min) fs

C = uref(1 − d)

8�uppL f 2s

(39)

where L(critical) represents the critical inductance betweenCCM and DCM; L represents the inductance determinedaccording L(critical). The PID controllers are designed by theSISO tool of MATLAB with the crossing frequency of 192 Hzand the phase margin of 50.3°.

Figs. 5–8 show the responses of buck converter A workingin CCM and DCM undergoing step changes of the load currentand input voltage. In Fig. 5, the responses to the load currentsteps of CCM buck converter A are compared with that ofthe PID controller. The results show that under the positive

Fig. 5. Simulation results of output voltage response to the load currentchanges for the buck converter A working in CCM.

Fig. 6. Simulation results of output voltage response to the input voltagechanges (15 V → 18 V → 12 V) for buck converter A working in CCM.

Fig. 7. Simulation results of output voltage response to the load currentchanges for buck converter A working in DCM.

Fig. 8. Simulation results of output voltage response to the input voltagechanges (15 V → 18 V → 12 V) for buck converter A working in DCM.

current step change by changing the load from 8 to 4 �, thevoltage peak undershoot �uo is reduced from −0.35 (with thePID controller) to −0.1 V (with the SCS) and the settlingtime tsettling is reduced from 16 ms to 7 ms.



TABLE I

SIMULATION RESULTS OF BUCK CONVERTER A IN ALL THE DYNAMIC CASES

Fig. 9. Simulation results of output voltage response to the load currentchanges for the buck converter B working in CCM.

Fig. 10. Simulation results of output voltage response to the input voltagechanges (15 V → 18 V → 12 V) for buck converter B working in CCM.

Table I summarizes the simulation comparison results of theresponses of the SCS and the PID controller to all the dynamiccases. It is observed from Table I that, compared with the PIDcontroller, the voltage peak shoot �uo and the settlingtime tsettling with the SCS are significantly reduced in all cases.

In order to further verify the functionality of the SCS,a buck converter B is configured with the parameters:uin = 15 V, uref = 6 V, �upp = 0.08 V, R = 8 �,L = 40 μH (CCM)/20 μH (DCM), C = 100 μF (CCM)/150 μF (DCM). The PID controllers are designed by theSISO Tool of MATLAB with the crossing frequency of 6 kHzand the phase margin of 62°. Figs. 9–12 show the simula-tion waveforms of the buck converter B under CCM opera-tion and DCM operation, respectively. And the comparisonresults of the voltage shoot and settling time are summarizedin Table II. The simulation results demonstrate that the SCSstill has improved dynamic performances when the switchingfrequency increased to 40 kHz.

Fig. 11. Simulation results of output voltage response to the load currentchanges for buck converter B working in DCM.

Fig. 12. Simulation results of output voltage response to the input voltagechanges (15 V → 18 V → 12 V) for buck converter B working in DCM.

Fig. 13. Experimental results of output voltage response to the load currentstep changes (8 � → 4 � → 8 �) for buck converter A working in CCM(Xaxis : 10 ms/div; Yaxis : 200 mV/div).

A prototype is constructed in order to experimentally testthe SCS. In the experiment, the voltage and current mea-surements are made using CHV-25P and CHB-25NP/6 A,



TABLE II

SIMULATION RESULTS OF BUCK CONVERTER B IN ALL THE DYNAMIC CASES

TABLE III

EXPERIMENTAL RESULTS OF BUCK CONVERTER A IN ALL THE DYNAMIC CASES

Fig. 14. Experimental results of output voltage response to the input voltagestep changes (15 V → 18 V → 12 V) for buck converter A working in CCM(Xaxis : 10 ms/div; Yaxis : 200 mV/div).

Fig. 15. Experimental results of output voltage response to the load currentstep changes (8 � → 4 � → 8 �) for buck converter A working in DCM(Xaxis : 10 ms/div; Yaxis : 200 mV/div).

respectively, and sent to dSPACE DS1104 controller. TheIGBT gate drivers are based on SKYPER 32R which arepowered with 0/15 V. All the experimental results are com-pleted under the same conditions. Since the maximum sam-pling step (2 × 10−5 s) of the DS1104 limits the switchingfrequency of the system, buck converter A is constructed with

Fig. 16. Experimental results of output voltage response to the input voltagestep changes (15 V → 18 V → 12 V) for buck converter A working in DCM(Xaxis : 10 ms/div; Yaxis : 200 mV/div).

the parameters identical to that of the simulation model inour experimental test bench. Experimental results presentedthereafter are obtained from the oscilloscope (Tektronix)directly.

Figs. 13–16 show the experimental results of buck con-verter A working in CCM and DCM undergoing the stepchanges of the input voltage and the load current, respectively.The comparison results of the voltage shoot and settling timeunder all the dynamic cases are summarized in Table III. It canbe observed from the figures and table that the experimentalresults are consistent with the simulation results. Significantdynamic performance improvements are observed.

VII. CONCLUSION

The SCS is based on the energy conservation principlein circuit and it has been designed and implemented tocontrol buck converters. The SCS is capable of operatingin both CCM and DCM. And it has a simple structure,which can be easily implemented. Furthermore, the stabilityof the converter controlled by the SCS has been provedusing Lyapunov stability criterion. The dynamic response to



a positive load current step change demonstrates the SCS hassuperior dynamic performances.

Simulation and experimental results show that comparedwith the PID controller, the SCS produces superior dynamicperformance, in terms of smaller voltage shoots and shortersettling times under the step changes of input voltage andload current. These results demonstrate that the SCS canbe a substitute for classic controllers in power converterapplications where a quick dynamic response is required. Inaddition, the SCS is here discussed for the buck converters andit can be easily extended to other converter topologies, suchas boost converters, buck-boost converters and even inverters,which will be reported in the future.

REFERENCES

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