Controller Design Converters

IEEE TRANSACTIONS ON EDUCATION, VOL. 45, NO. 4, NOVEMBER 2002 307

Learning Feedback Controller Design of SwitchingConverters Via MATLAB/SIMULINK

Juing-Huei Su, Member, IEEE, Jiann-Jong Chen, Member, IEEE, and Dong-Shiuh Wu, Member, IEEE

Abstract—The application of MATLAB/SIMULINK is devel-oped for simulation and learning feedback controller design ofdc–dc switching converters. With the help of its intuitive graphicaluser interface and some basic circuit theories, the correspondingSIMULINK models of the switching converter circuits can beeasily constructed. Students can then use these models to learnand evaluate the closed-loop behavior of the entire system in theMATLAB/SIMULINK environment, after feedback controllersare devised by any classical or modern control theory. The accu-racy of this approach is also verified by comparing the simulationresults with the responses obtained from a buck-type dc–dcswitching converter circuit and existing experimental results [4].

Index Terms—dc–dc switching converter, feedback controller,MATLAB/SIMULINK.

I. INTRODUCTION

T HE SWITCHED-mode dc–dc converters are power elec-tronic systems that convert one level of electrical voltage

into another level by switching action. They are very popularthese days because of their high efficiency and smaller size [1],[7], [15]. Switched-mode dc–dc converters are used extensivelyin personal computers, computer peripherals, and adapters ofconsumer electronic devices to provide dc voltages. The wide-spread use of switched mode dc–dc converters in many elec-tronic systems makes the fundamental understanding of them anecessity for many electronic system design engineers.

Unfortunately, learning the design philosophy of the dc–dcswitching converters is interesting but difficult, because it in-cludes many areas of knowledge, e.g., the converter circuits andelectronics, linear and nonlinear control system theory [7], [15],magnetics, etc. Teaching the dc–dc switching converters is achallenging undertaking because one cannot assume that all stu-dents enrolled in the class have solid prerequisite knowledgein so many areas. Therefore, to speed up the learning process,the application of user-friendly and powerful computer-aidedsimulation software tools to help students get acquainted withthe dynamic behavior of the dc–dc switching converter circuitsis inevitable [1]–[3], [5], [10], [13]. Although the simulationprogram SPICE is quite popular among electronic engineers,the software package focuses primarily on the circuit level inconstructing the entire circuit for simulation. Furthermore, thecomplexity of device models and the switching nature of theswitching converter circuits make simulation difficult to con-

Manuscript received August 25, 2001; revised December 27, 2001.The authors are with the Department of Electronic Engineering, Lunghwa

University of Science and Technology, 330, Taiwan, R.O.C. (e-mail:[email protected]).

Digital Object Identifier 10.1109/TE.2002.803403

Fig. 1. Boost-type dc–dc switching converter.

verge unless some of the default values of parameters are suit-ably changed [10]. Thus, SPICE is not suitable for studentswho need to learn quickly what the system dynamics are andto acquire the system viewpoints in linear and even nonlinearfeedback controller designs. In this regard, the simulation en-vironment MATLAB/SIMULINK is quite suitable for studentsto learn the feedback controller design techniques if the corre-sponding simulation models of dc–dc switching converters canbe constructed without too much effort and still give accurateresults. It is, therefore, the purpose of this paper to propose analternative way of teaching feedback controller designs of dc–dcswitching converters to students, so that it would be less diffi-cult to learn.

SIMULINK is a window-oriented dynamics modelingsoftware package built on top of the MATLAB numericalworkspace. An advantage is that models are entered as blockdiagrams with an intuitive graphical interface when the cor-responding mathematical descriptions are available for thetarget systems. This application is not difficult to do for basictopologies of dc–dc switching converters. Furthermore, a setof blocks with signal interconnections could be masked as asubsystem for convenience in the SIMULINK environment.The parameters of masked subsystems are then entered indialog windows and can be changed interactively during a sim-ulation. Simulation results can be viewed during the simulationvia a virtual oscilloscope and then exported to the MATLABworkspace for subsequent off-line analysis. As stated in [6]and [13], the abundant library blocks that the SIMULINKmodeling environment provides make construction of simpledynamical systems quite easy. This construction is also truefor the design and verification of feedback controllers for dy-namical systems. If the mathematical way of using Kirchhoff’slaws to construct the corresponding dynamical systems is notfavored, the MATLAB environment can also be used to developmathematical models from input–output data via the systemidentification tools [2].

0018-9359/02$17.00 © 2002 IEEE

308 IEEE TRANSACTIONS ON EDUCATION, VOL. 45, NO. 4, NOVEMBER 2002

Fig. 2. The constructed boost-type converter block in SIMULINK.

II. SIMULINK M ODEL’S CONSTRUCTION OFdc–dcSWITCHING CONVERTERS

The boost-type dc–dc switching converter with an idealsingle-pole double-throw switch is an example of a SIMULINKmodel (Fig. 1). The dynamics of this converter operating in thecontinuous conduction mode (CCM) can be easily understoodby applying Kirchhoff’s voltage law on the loop containingthe inductor and Kirchhoff’s current law on the node withthe capacitor branch connected to it [7], [15]. When the idealswitch is at position 1, the dynamics of the inductor current

and the capacitor voltage are

(1)

When the ideal switch is at position 2, the dynamics of the circuitare

(2)

In both cases, capacitor voltage and output voltageare related via the following equation:

(3)

The intuitive signal flow interface in SIMULINK makes thismathematical model and its corresponding masked subsystemvery easy to create (see Fig. 2). The constraints that the inductor

Fig. 3. Comparisons of simulation results obtained from SPICE andSIMULINK.

current and the capacitor voltage can only bepositive in the circuit are fulfilled by setting the integrationblocks in the SIMULINK model to give only positive outputs.Therefore, the SIMULINK model for the boost-type dc–dcswitching converter is also valid when operating in the discon-tinuous conduction mode (DCM). To facilitate the subsequentsimulation analysis and feedback controller verification, thepulse-width-modulation signal to control the ideal switch canalso be built into the masked subsystem. Therefore, the inputsfor the masked subsystem are duty ratio and input voltage, andthe outputs are chosen to be inductor current, capacitor voltage,and output voltage. When double-clicking the pointer on themasked subsystem, students can enter parameter values of theswitching converter circuit in a dialog window.

The circuit parameters of the above boost-type switching con-verter circuit are as follows: switching frequency 5 kHz,

15 V, 0.25, 500 H, 200 F,0.5 , 0.25 , and 10 . The simulation resultscan be seen to agree closely with those provided by SPICE inFig. 3. These results validate the usefulness of the correspondingSIMULINK model of the boost-type switching converter.

The nonidealities of the single-pole double-throw switchwhen realized via a transistor and diode could also be builtinto the corresponding SIMULINK subsystem. This processis accomplished by first modifying (1)–(3) with simplifiedmodels of transistors and diodes and then constructing thesubsystem in the SIMULINK environment accordingly. Forexample, MOSFETs would behave like a resistor and diodeand can be modeled as a forward voltage drop in series with aresistor when they are in theON-state.

It is also possible to construct a SIMULINK model for zero-current-switching quasi-resonant converters (ZCS-QRCs), butit is not easy to construct simulation circuits in SPICE [10]. Thebuck-type half-wave ZCS-QRC model in SIMULINK is con-structed without too much effort when the operating modes areidentified. Fig. 4 (with parameters 20 V, 1.6 H,

SU et al.: LEARNING FEEDBACK CONTROLLER DESIGN OF SWITCHING CONVERTERS 309

(a)

(b)

(c) (d)

Fig. 4. (a) The buck-type half-wave ZCS-QRC converter circuit. (b) The constructed buck half-wave ZCS-QRC converter block in SIMULINK. (c) Inductorcurrents in buck-type half-wave ZCS-QRC circuit. (d) Inductor currents and capacitor voltages in buck-type half-wave ZCS-QRC circuit.

310 IEEE TRANSACTIONS ON EDUCATION, VOL. 45, NO. 4, NOVEMBER 2002

0.064 F, 0.1 H, 0, 0, 0,0, 0.1 F, 5 , and the switching fre-

quency at 200 kHz) shows the buck-type half-wave ZCS-QRCcircuit and its corresponding SIMULINK model. The simula-tion results also agree closely with those provided in [10].

Since the SIMULINK models for dc–dc switching convertersprovide reasonably accurate simulation results, they could alsobe used to verify the modeling techniques for dc–dc switchingconverters in both CCM and DCM operating conditions [7], [9],[11], [15].

Since the MATLAB toolboxes are abundant and the typicallearning time for the manipulation of SIMULINK’s intuitivegraphical interface is short, the simulation tool is well suited toeducational use. Also, the purpose of this paper is to provide analternative way of learning the dynamic behavior and feedbackcontroller designs of dc–dc switching converters [14].

III. FEEDBACK CONTROLLER DESIGNS OF

SWITCHING CONVERTERS

Now is the time to learn the design philosophies of linearaveraged and nonlinear feedback controllers for the dc–dcswitching converters, after the corresponding SIMULINKmodels of the basic dc–dc switching converters are created.

A. Linear Averaged Feedback Controller Design

For the sake of simplicity, the following discussion will belimited to the voltage-mode linear averaged feedback controllerdesigns.

Voltage-mode linear averaged feedback controllers for dc–dcswitching converters are mostly designed in the frequency do-main, though some feedback controllers with more advancedcontrol theory have been developed in the time domain recently[4], [12]. The design guidelines for the voltage-mode linear av-eraged feedback controllers of a given dc–dc switching con-verter on a given operating condition could be summarized asthe following steps.

1) Determine the steady-state operating condition to becontrolled. The steady-state information of the switchingconverter circuit is then used to construct the corre-sponding linearized small signal mathematical modeland its frequency response. The methods provided in[7]–[9], [11], and [15] may be used in this step.

2) Decide what the value of the 0-dB crossover frequencyof the closed-loop gain should be. This value generallydetermines the bandwidth of the control to the outputclosed-loop system. Since the averaged mathematicalmodels are accurate only up to one-third of the switchingfrequency [11], the value of the 0-dB crossover fre-quency should be lower than one-third of the switchingfrequency.

3) Choose an appropriate phase margin at the crossover fre-quency for the compensator to provide to meet both thestability and performance requirements. This task maytake some iterations for students to check on different op-erating conditions.

4) Enlarge the gain below the crossover frequency of theloop gain so that the influences of disturbances (e.g., input

Fig. 5. Buck-type switching converter.

voltage variations and load variations) would be kept assmall as possible. Output voltage steady-state error couldbe eliminated if an integrator is included in the feedbackcontroller.

5) Verify whether the linear averaged feedback controllercould deal with all the operating conditions in the speci-fications.

Following the guidelines above, the voltage-mode linearaveraged feedback controller can then be constructed by usingany existing controller type—for example, phase lead, phaselag, or combined compensator—to meet the stability andperformance requirements. Fortunately, these steps of feedbackcontroller design could be accomplished quickly and easilyin the MATLAB/SIMULINK environment. The “sisotool(‘bode’)” command in the control system toolbox providesa graphical user interface so that the closed-loop frequencyresponse can be interactively changed by online modifyingof the pole-zero pattern of the feedback controller. Whenthe desired frequency is obtained, users are also given thecorresponding transfer function of the feedback controller inthe same interface.

Since the design of the linear averaged feedback controller isbased only on a given operating condition, simulations or exper-imental prototypes should be conducted to see whether it couldcope with the other operating conditions given in the specifi-cations. Experimental prototype construction is usually a time-consuming task; therefore, simulations are often taken to verifythat the specifications are fulfilled to save time in the conceptdesign stage. Since the SIMULINK models were introduced inSection II, students can easily see how the devised feedback con-troller works in the MATLAB/SIMULINK environment.

The entire design procedure is illustrated in the following ex-ample, and the result is compared with an experimental circuitby using the voltage-mode PWM control IC TL494.

Consider the buck-type switching converter in Fig. 5, withinput voltage 12 V, 5 V, 0.25 ,0.25 , 150 H, 200 F, and 20 . If theswitching frequency is set to 55 kHz, the circuit would operatein the CCM.

The steady-state operating point and dutycycle of the above switching converter operating in CCMcan be calculated via the following formula:

(4)

Equation (4) is derived by assuming that the derivatives of theaveraged inductor current and capacitor voltage arezero without resorting to the method in [8]. The matrixes in

SU et al.: LEARNING FEEDBACK CONTROLLER DESIGN OF SWITCHING CONVERTERS 311

Fig. 6. Open-loop frequency response of buck converter in MATLAB/SIMULINK.

Fig. 7. Closed-loop frequency response of buck converter in MATLAB/SIMULINK.

(4) represent different operating modes (subscript 1 stands fortransistor on, and subscript 2 stands for transistor off) of theswitching converter circuit. Therefore

(5a)

(5b)

(5c)

Using the element values of the above buck-type switchingconverter, the steady-state operating conditions can be simplycalculated via (5) in MATLAB as 0.25 A, 5 V,and 0.4219. The frequency response of the linearizedcontrol to the output transfer function of the example switchingcircuit can then be plotted via the sisotool (“bode”) commandand the switching converter’s linearized average model [7], asin Fig. 6.

According to the above design guidelines, the 0-dBcrossover frequency of the entire closed-loop frequencyresponse is chosen to be about one-eighth of the switching

312 IEEE TRANSACTIONS ON EDUCATION, VOL. 45, NO. 4, NOVEMBER 2002

(a)

(b)

Fig. 8. (a) Verification setup in the SIMULINK environment for buck converter. (b) Parameters setting dialog box for the masked buck converter subsystem.

Fig. 9. Closed-loop control of buck-type converter via TL494.

frequency, i.e., 8 kHz. The linear averaged feedback controlleris then designed to stabilize the linearized switching converterin the same interface provided by the “sisotool” command by

adjusting the pole-zero locations of the feedback controller.The corresponding transfer function of the feedback controllerand gain/phase margins of the closed-loop system would also

SU et al.: LEARNING FEEDBACK CONTROLLER DESIGN OF SWITCHING CONVERTERS 313

Fig. 10. Practical realization of feedback controller defined in (6).

be shown in the interface. Therefore, after some adjustmentsin the design environment, students can easily construct thefollowing type 1 feedback controller

(6)

which gives a phase margin of about 34at a 0-dB crossover fre-quency of about 8.5 kHz. The closed-loop frequency responseis shown in Fig. 7.

For the above linear averaged feedback controller, studentsought to check whether it still stabilizes the switching converterat different operating conditions, e.g., light load, heavy load,and different input voltages. To verify whether the linear aver-aged feedback controller meets the performance requirements,students can construct a SIMULINK model like the one inFig. 8(a) with load change built into the SIMULINK switchingconverter model. Feedback controller design at this stage mayrequire some iterations to tune the control parameters so thatthe closed-loop system gives satisfactory results during startupand abrupt load or input changes. The approach proposedin this paper could help save quite some time at this stage.If the simulation results meet the stability and performancerequirements, the feedback controller is feasible.

To assure students that this approach really works, the ac-curacy of the simulation results is then compared with the re-sponses obtained from an experimental switching converter cir-cuit constructed by using TL494 [16], which is shown in Fig. 9.The linear averaged feedback controller defined in (6) is real-ized in Fig. 10 via the error operation amplifier in TL494.

The input–output relation of the circuit is

(7)

It can be seen from (7) that the circuit implements the desiredlinear averaged feedback controller in small signal. The simu-lation results and the experimental circuit output are comparedin Fig. 11, showing close resemblance in the transient behaviorwhen load abruptly changes from 2 Kto 20 .

B. Nonlinear Feedback Controller Design

The framework described above is also quite suitable forlearning feedback controller designs by applying more ad-vanced control theory, as is illustrated in the following example.

Example: In [4], several nonlinear feedback controllers fora boost-type dc–dc switching converter are compared. One ofthe nonlinear feedback controllers, the sliding-mode controllerillustrates how the above-mentioned approach could be appliedto help students quickly get acquainted with the method and findout what the controller’s strong and weak points are. A brief

(a)

(b)

Fig. 11. (a) Output response simulation of the feedback controlled buckconverter with load change at 8 ms. (b) Output response of the experimentalfeedback controlled buck converter with load change (using TL494).

introduction of the theoretical background and implementationissues of designing sliding-mode controllers would be given tostudents first, according to [17].

By using the previously developed boost-type dc–dcswitching converter subsystem, the authors constructed thedigital sliding-mode controller [4] with a 60-s samplingperiod shown in Fig. 12(a). The sliding surfaceis chosen to be

(8)

and the corresponding control signal for the ideal switch inFig. 1 is

(9)

To reduce the chattering phenomenon caused by the inputsignal (9) around the switching surface (8), hysteresis controlmethod [17] is used. The entire feedback control system withinput voltage variations in the SIMULINK environment is

314 IEEE TRANSACTIONS ON EDUCATION, VOL. 45, NO. 4, NOVEMBER 2002

(a)

(b)

(c)

Fig. 12. (a) Sliding-mode control of a boost-type converter with input voltagevariations. (b) Step responses of a boost-type converter with a sliding-modecontroller. (c) Simulation results of the sliding-mode control of a BOOSt-typeconverter with input voltage variations.

shown in Fig. 12(a). The parameters for the digital boost-typeswitching converter are nominal input voltage 10 V,reference voltage 20 V, 170 mH, 1000 F,

0.1 , 0.25 , and 100 . The inputvoltage changes to 13 V at 0.3 s and returns to the nominalvalue when 0.35 s. The simulation results in Fig. 12(b) and(c) agree with the experimental results in [4].

This example helps students not only learn the sliding modecontrol theory but also get acquainted with some practical issuesin implementation, e.g., the effect when the feedback controlleris implemented digitally and the relay in Fig. 12(a) as a hys-teresis controller to reduce the chattering phenomenon.

IV. CONCLUSION

The need for undergraduate students to learn to apply com-puter-aided design tools to speed up the learning process in thedc–dc switching converter design is increasing because the topicintegrates many areas of knowledge. The computer-aided designsoftware tool MATLAB/SIMULINK is shown in this paper to bequite useful in providing a simulation and verification environ-ment for the feedback controller designs of the dc–dc switchingconverters. Students can not only learn quickly to acquire thesystem viewpoint about the entire dc–dc switching converter de-sign process but also explore more advanced control techniques[4], [12], [17].

REFERENCES

[1] S. S. Ang, “A practice-oriented course in switching converters,”IEEETrans. Educ., vol. 39, pp. 14–18, Feb. 1996.

[2] K.-T. Chau, “A software tool for learning the dynamic behavior of powerelectronics circuits,”IEEE Trans. Educ., vol. 39, pp. 50–55, Feb. 1996.

[3] T. H. Sloane, “Laboratories for an undergraduate course in power elec-tronics,” IEEE Trans. Educ., vol. 38, pp. 365–369, Nov. 1995.

[4] G. Escobar, R. Ortega, H. Sira-Ramirez, J.-P. Vilain, and I. Zein, “Anexperimental comparison of several nonlinear controllers for power con-verters,”IEEE Control Syst. Mag., pp. 66–82, Feb. 1999.

[5] L. K. Wong, F. H. Leung, and P. K. S. Tam, “A simple large-signalnonlinear modeling approach for fast simulation of zero-current-switchquasiresonant converters,”IEEE Trans. Power Electron., vol. 12, pp.437–442, May 1997.

[6] E. Allen, N. LaWhite, Y. Yoon, J. Chapman, and M. Ilic, “Interactiveobject-oriented simulation of interconnected power systems usingSIMULINK,” IEEE Trans. Educ., vol. 44, pp. 87–95, Feb. 2001.

[7] R. W. Erickson,Fundamentals of Power Electronics. Norwell, MA:Kluwer-Academic, 1999.

[8] B. K. H. Wong and H. S. Chung, “Steady-state analysis of PWM DC/DCswitching regulators using iterative cycle time-domain simulation,”IEEE Trans. Ind. Electron., vol. 45, pp. 421–432, June 1998.

[9] , “A systematic graphing technique for small-signal low-frequencycharacterization of PWM DC/DC converters,”IEEE Trans. Ind. Elec-tron., vol. 47, no. 1, pp. 45–54, Feb. 2000.

[10] J. Xu and M. Grotzbach, “Time-domain analysis of half-wave zero-cur-rent switch quasiresonant converters by using SPICE,”IEEE Trans. Ind.Electron., vol. 40, pp. 577–579, Dec. 1993.

[11] J. Sun, D. M. Mitchell, M. F. Greuel, P. T. Krein, and R. M. Bass, “Av-erage modeling of PWM converters operating in discontinuous conduc-tion mode,” IEEE Trans. Power Electron., vol. 16, pp. 482–492, July2001.

[12] P. Midya, P. T. Krein, and M. F. Greuel, “Sensorless current modecontrol—An observer-based techniques for DC–DC converters,”IEEETrans. Power Electron., vol. 16, pp. 522–526, July 2001.

[13] D. Logue and P. T. Krein, “Simulation of electric machinery and powerelectronics interfacing using MATLAB/SIMULINK,” in7th WorkshopComputers in Power Electronics, 2000, pp. 34–39.

[14] J.-H. Su, “Power electronics course,” Lunghwa Univ. of Science andTechnology, Taiwan, R.O.C..

[15] M. H. Rashid,Power Electronics, Circuits, Devices and Applications,2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 1993.

[16] Texas Instruments, “Design switching voltage regulators with TL494,”,Application Rep., 1998.

[17] J. Y. Hung, W. Gao, and J. C. Hung, “Variable structure control: Asurvey,”IEEE Trans. Ind. Electron., vol. 40, pp. 2–22, Feb. 1993.

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Juing-Huei Su (S’87–M’93) was born in Tainan, Taiwan, R.O.C., on February17, 1965. He received the B.S., M.S., and Ph.D. degrees in electrical engineeringfrom the National Taiwan University, Taipei, Taiwan, in 1987, 1989, and 1993,respectively.

From 1993 to 1995, he was a Military Officer in the army. In 1995, he was aSenior Engineer with Taian Electric Co., Ltd. Since 1996, he has been an Asso-ciate Professor in the Department of Electronic Engineering, Lunghwa Univer-sity of Science and Technology, Taiwan. Currently, his research interests includerobust control theory and power electronic systems.

Jiann-Jong Chen(S’94–M’96) was born in Keelung, Taiwan, R.O.C., on July23, 1966. He received the M.S. and Ph.D. degrees in electrical engineering fromNational Taiwan University, Taipei, Taiwan, in 1992 and 1995, respectively.

During 1986–1988, he was an MP in the Chinese army. During 1994–1995,he was a Teacher in the Department of Electronic Engineering, Lunghwa Uni-versity of Science and Technology, Taiwan, where he has been an AssociateProfessor since 1995. He has received one U.S. patent and one R.O.C. patent.His research interests are in analog and digital integrated circuits and systems.

Dong-Shiuh Wu (S’94–M’96) was born in Yunlin, Taiwan, R.O.C., onSeptember 1, 1964. He received the M.S. and Ph.D. degrees in electricalengineering from National Taiwan University, Taipei, Taiwan, in 1991 and1995, respectively.

From 1984 to 1986, he was a Second Lieutenant in the army of Taiwan. Since1995, he has been an Associate Professor in the Department of Electronic Engi-neering, Lunghwa University of Science and Technology, Taiwan. His researchinterests are in analog and digital integrated circuits and systems.