VOLTAGE MODE CONTROL OF SOFT SWITCHED BOOST CONVERTER BY TYPE II & TYPE III COMPENSATOR

1002 VOLTAGE MODE CONTROL OF SOFT SWITCHED BOOST CONVERTER BY TYPE II & TYPE III COMPENSATOR NIKITA SINGH 1 ELECTRONICS DESIGN AND TECHNOLOGY, M.TECH NATIONAL INSTITUTE OF ELECTRONICS AND INFORMATION TECHNOLOGY (NIELIT) GORAKHPUR, INDIA SHRI. S.K. SINGH 2 SCIENTIST- D NATIONAL INSTITUTE OF ELECTRONICS AND INFORMATION TECHNOLOGY (NIELIT) GORAKHPUR, INDIA SH.NISHANT TRIPATHI 3 SCIENTIST- C NATIONAL INSTITUTE OF ELECTRONICS AND INFORMATION TECHNOLOGY (NIELIT) GORAKHPUR, INDIA ABSTRACT In this paper a comparative study of type II and type III compensator is done for soft switched boost converter. Compensators are the correction subsystems which are introduced to compensate for the deficiency in the performance of a plant. The transfer function for soft switched boost converter is formulated by using system identification toolbox of MATLAB. The analog compensator is first designed based on the parameters of the soft switched boost converter. Then the analog transfer function of the compensator is transposed in the digital domain using the bilinear transformation. The loop gain will give the frequency domain analysis. Next, the simulation model for both type of the compensator in close loop with the converter is presented. The experimental analysis of the model is done in the MATLAB with input voltage varying from 24V-100V. Through the comparative study it is clear that soft switched boost converter attains more stability when it is compensated by using type III compensator. Index Terms soft switched boost converter (SSBC), voltage-mode controller, type II compensator, type III compensator. INTRODUCTION In the modern electronics field dc-dc boost converter is in demand for converting low voltage source to high voltage source. Till now we have seen that conventional boost converter is capable enough to step up the voltages. But conventional boost converter suffers from switching losses and electromagnetic interference at high frequency switching. Due to the advantages gained from the high frequency switching converters, its application in low power compact is increasing in the recent years. Light weight, small size and high power density are the advantages gained from the high frequency switching. In the recent years, continuous-conduction-mode (CCM) boost converters are widely used in the high-power applications such as hybrid electric vehicles and fuel cell power conversion systems. The hard-switched boost converter suffers from severe diode reverse-recovery problem. The problem becomes more severe for high switching frequency at high power level. Due to the reverse-recovery problem, there is significant turn-off loss of the diode, turn-on loss of the main switch and severe electromagnetic interference emission (EMI). Recently many soft switching techniques have been introduced to overcome the switching losses and severe electromagnetic interference emission (EMI) occurring in the conventional dc-dc converters [1],[2]. The most recent soft switched high gain boost converter is reported in the literature [3], [4]. Although controllers for SMPS are well known [5],[6], this paper motive is to present the design of controller for soft switched high gain boost converter. Several compensator design approaches have been studied in the literature. In practice, if a system is to be redesigned so as to meet the required specifications it is necessary to alter the system by adding an external device to it. Such a redesign or alteration of system using an additional suitable device is called compensation of a control system. Compensators are basically external devices which are used to alter the behavior of the system so as to achieve given specifications. The compensator provides whatever is missing in a system, so as to achieve required performance. Depending upon where the compensator is introduced in a system, the various type of compensation are series compensation, parallel compensation (feedback compensation) and series-parallel compensation. In this paper in order to make the output voltage stable and well regulated, compensation circuit in the feedback loop is appropriately designed. Feedback compensation circuit design method is established in the frequency domain by means of bode plots [7]. The designing procedure describes how to decide position of the poles and zeros of the compensator circuit in order to compensate the undesirable characteristics of a electronic power circuit. This design method has been adopted to design practical compensator circuits because of its simple graphical nature. FEEDBACK COMPENSATION CIRCUIT The output voltage v(t) is measured using a sensor with gain H(s). The sensor output signal H(s)v(s) is compared with a reference input voltage v ref (s) keeping in mind that H(s)v(s) should be equal to the v ref (s). This objective is achieved despite the disturbing elements in

1003 the compensator, pulse-width modulator, gate driver or converter power stage. G p (s) and G c (s) represents the transfer functions of power stage (switching converter and PWM combined) and compensator circuit respectively. The output voltage is the function of the control input variations d(t), the power input voltage variations and the load current variations i load (t) and v g (t). The major causes for the disturbances are input voltage variations and load current disturbances which make the output voltage to be deviated from the desired value i.e v- ref(s). The feedback loop must be incorporated with the compensator to regulated the output voltage to be close to the reference input voltage v ref (s). The fig 1 shows the block diagram of the control system. the quasi-resonance. Under such condition different modeling technique is to be considered. For modeling such converter and their corresponding resonant behavior, a generalized state-space method has been studied in previous works. But generalized state-space modeling technique cannot give high level of accuracy [4]. Fig 2(a). Soft Switched Boost Converter Fig.1 Block Diagram of Control System The converter s control-to-output transfer function G vd (s) is predetermined from the chosen converter topology, mode of operation (continuous conduction mode, CCM or Discontinuous Conduction mode, DCM) and control method (voltage mode control or current mode control). In this paper soft switched boost converter operating in continuous conduction mode and controlled in voltage mode fashion is considered. The feedback compensation design involves selection of a suitable compensation circuit configuration and positioning of its poles and zeros to yield an open loop transfer function. I. MODELING THE TRANSFER FUNCTION FOR SOFT SWITCHED BOOST CONVERTER The soft switched boost converter is comprised of an auxiliary circuit and boost converter as a main circuit [3]. Fig 2(a) gives the circuit diagram; rectifier diode in the conventional boost converter is replaced by upper switch S B. Output voltage is regulated by asymmetrical complementary switching of lower switch S A and upper switch S B. An auxiliary circuit is composed of an inductor L B, two capacitors C A and C B and two diodes D A and D B. Output voltage of the converter is formed by the combination of the capacitor C A and C B. The soft switched boost converter uses the auxiliary circuit resonance of L r -C r to reduce the switch turn-off current. Also, auxiliary circuit helps in ZVS turn-on of switch S A and S B. For modeling the soft switched boost converter direct application of the state-space is not a good option. The reason being that during the operating modes of the soft switched boost converter, the converter circuit is under The reason is that the variables of the resonant tank (L r and C r ) are considered as input control variables instead of as variables. Therefore, any disturbance in the input variables will affect the model accuracy. Hence, the model accuracy for soft switched boost converter is low when it is modeled using generalized state-space. In order to improve the accuracy of the model using generalized state-space technique, the requirement is to use large number of harmonics. This procedure will increase the order of the model and hence its mathematical analysis will be very difficult to conduct. To overcome all the demerits of the modeling techniques till now, system identification technique is analyzed. Using system identification technique, discrete-time model of soft switched boost converter is formulated. For the formulation of the soft-switching converter model Box-Jenkins methodology is used. Using this system identification technique discrete-time transfer function for the soft switched converter topology can be obtained [8]. For the formulation of the soft switched converter using the Box-Jenkins methodology, firstly the soft switched converter is modeled in the SIMULINK platform. Next, by varying the range of the pre-defined parameters the response of the desired parameter is generated. For the given values of the converter parameters, shown in the table I below. The values of the converter parameters are inductor L A is 25µH, Inductor L B is 10µH, capacitor C A is 50µF, capacitor C B is 110µF, capacitor C c is 110µF and resistance R is 150Ω. The switching frequency is 50kHz. And the input voltage is 24volts. The range of the duty ratio varies from 0.3 to 0.7, this ratio acts as a control signal. This range of the duty ratio is equally divided into the intermediate points. At each point, the random generator generates the signal having the step time equal to the sampling time period. Next, this signal is used to drive the switching device of the converter when compared to the triangular ramp. Now, in order to generate the discrete transfer function of the converter, the perturbation signal and its corresponding current or voltage signal is transferred on

1004 to the system identification toolbox of the MATLAB [10]. In this toolbox linear parametric model formulation methodology is selected. Once the model is estimated its accuracy is checked by the residual analysis. If the test of the residual analysis of the converter is within the allowable limits, then the model correctly represents the actual behavior of the converter. The control-to-output transfer function G vd (z) of the converter in z-domain is as follows. designed in the z-domain using bilinear transformation method as given below. The frequency response of the soft switched boost converter is studied by plotting the bode plot. The fig 2(a) gives the bode plot of the converter. Fig.3(a) Type II Compensator Network From the transfer function the bode plot obtained is shown in fig 3(b). It can be verified from the figure that phase boost of 90 is obtained. Fig.2(b) Bode Plot of SSBC II. MODELING THE TRANSFER FUNCTION FOR COMPENSATOR In practice, if a system is to be redesigned so as to meet the required specifications, it is necessary to alter the system by adding an external device to it. Such a redesign or alteration of system using an additional suitable device is called compensation of a control system. Soft switched boost converter suffers from sharp slope downward and the gain will have a rather high peak at the double pole [9] as seen in the fig 2(b). Such systems will be more difficult to compensate since the phase will need an extra boost to provide the necessary phase margin for stability. Type II and type III compensators are used to provide the phase boost in order to compensate the system. Type II compensator can provide phase boost of 90. It is also called second order integral lead controller. It has one pole at origin and one zero-pole pair at different frequency. Fig 3(a) shows the network of type II compensator. The transfer function of type II compensator is given as follows. Fig.3(b) Bode plot of Type II Compensator Type III compensator is also called third order integral lead controller. Type III compensator has one pole at origin and two zero-pole pair at different frequencies. Type III compensator can provide maximum phase boost of 180. Fig 3(c) shows the type III compensator network. Fig.3(c) Type III Compensator Network The transfer function of the type III compensator is given as follows. The values of the resistances R 1 and R 2 are 4.12kΩ and 124kΩ respectively and capacitors C 1 and C 2 are 8.2pF and 2.2nF respectively. From these values transfer function of the type II compensator is The values of resistance R 1, R 2 and R 3 are 4.12kΩ, 20.5kΩ and 150Ω respectively. The values of capacitors

1005 are C 1, C 2 and C 3 are 0.22nF, 2.7nF and 6.8nF respectively. From these values transfer function of the type III compensator is designed in the z-domain by using bilinear transformation method as presented below. system is more stable and fast when it is controlled by using type III compensator. Relative high values of phase margin and gain margin marks the stability of the system. And higher the cutoff frequency, the faster is the system s response. From the transfer function the bode plot obtained is shown in fig 3(d). It can be witnessed from the figure that phase boost of 135 is obtained. Fig.4(b) Bode Plot of Loop Gain Fig.3(d) Bode Plot of Type III Compensator III. MODELING TRNSFER FUNCTION FOR THE LOOPGAIN The loop gain T(z) is defined as the product of the gains around the forward and feedback paths of the loop. This transfer function shows how the addition of a feedback loop modifies the transfer function and performance of the system. The loop gain transfer function is given as follows. T L (z) = G vd (z)g c (z) Fig 4(a) shows the loop gain of the system which is controlled by type II compensator. We can deduce from the figure that phase margin is 70, gain margin is 10dB and cutoff frequency is 500Hz. VI. SIMULATION RESULTS In this section simulation models, output voltage waveforms and comparison in terms of overshoot and settling time is established. In Fig 5(a) simulation model of voltage mode controlled soft switched boost converter by type II compensator is represented and its output voltage waveform is shown in fig 5(b). Fig 5(c) show the simulation model of the SSBC controlled by type III compensator and its output voltage waveform is given in fig 5(d). The input voltage given to models is 24volts. The output voltage is boosted up to 30 volts. The circuit s transient response of both the models is analyzed through overshoot as shown in fig 5(e) and settling time as in fig 5(f). All the measurements are made by varying input voltage from 24volts to 100volts. Fig.5(a) Simulation Model of SSBC controlled by Type II compensator Fig.4(a) Bode Plot of Loop Gain Fig 4(b) shows the loop gain of the system which is controlled by type III compensator. We can deduce from the figure that phase margin is 110, gain margin is 24dB and cutoff frequency is 5kHz. From the above bode plots we can deduce that stability margins for the loop gain using type III compensator is good as compared to the type II compensator. The Fig.5(b) Output Voltage Waveform

1006 Fig.5(e) Graph of Overshoot v/s Input Voltage Fig.5(c) Simulation Model of SSBC controlled by Type III compensator Fig.5(f) Graph of Settling Time v/s Input Voltage Fig.5 (d) Output Voltage Waveform The table II gives the comparative study of the soft switched boost converter controlled by type II and type III compensator. It is interesting to notice that system s transient response is good when SSBC is controlled by type III compensator. The overshoot is small and settling time is faster for type III compensator as compared to the type II compensator. For the type II compensated SSBC overshoot is high and settling time is slower. TABLE I. COMPARITIVE ANALYSIS IN TERMS OF OVERSHOOT AND SETTLING TIME S.No. Input Voltage 1. V in =24V 2. V in =36V 3. V in =48V 4. V in =60V 5. V in =72V 6. V in =84V 7. V in =96V SSBC Controlled by Type II Compensator Parameters Over shoot(%) Settling time SSBC Controlled by Type III Compensator Parameters Over shoot(%) Settling time 40% 0.0486 15% 0.0475 37% 0.0481 15% 0.0469 41% 0.0486 14% 0.0464 40% 0.0475 15% 0.0453 34% 0.0480 14% 0.0459 42% 0.0486 13% 0.0469 42% 0.0475 14% 0.0453 VII. CONCLUSION In this paper voltage mode control of soft switched boost converter is done by type II and type III compensator. Simulation results show that type III compensator provide better circuit s transient response. Since, it is capable to provide 180 phase boost, it ensures stability margins. Different order compensators can be designed which can further enhance the stability margins and control. Once controller is designed then it is converted into the real time/simulation implications. REFERENCES [1] K. Liu, R. Oruganti, and F. C. Lee, Resonant switched-topologies and characteristics, IEEE Trans. Power Electron., vol. PE-2, no. 1, pp. 62 74, Jan. 1987. [2] A. Ostadi, X. Gao, and G. Moschopoulos, Circuit properties od zerovoltage-transition PWM converters, J. Power Electron., vol. 8, no. 1,pp. 35 50, Jan. 2008. [3] Sungsik Park, Sewan Choi, Soft Switched CCM Boost Converters With High Voltage Gain For High- Power Applications, IEEE Trans. On Power Electronics, 2010, Vol. 25(5), pp. 1211-1217. [4] Jianping Xu and C.Q.Lee, Unified Averaging Technique for the Modeling of Quasi-Resonant Converters, IEEE Transactions on Power Electronics, Vol. 13(3), 1998, pp. 556-563. [5] Veerachary. M, ``Two-loop voltage-mode control of coupled inductor step-down buck converter,'' IEE Proc. On Electric Power Applications, Vol. 152(6), pp. 1516-1524, 2005. [6] R. D. Middlebrook, Cuk. S, A general unified approach to modeling switching converter power stage, IEEE Power electronics specialists conference, 1976, pp. 13-34. [7] L. H. Dixon, Jr., Closing the feedback loop, UnitrodePower Supply Design Seminar, Unitrode Corporation,1983.

1007 [8] M. Veerachary, R. Shekar, Digital Voltage-mode Controller Design For High gain Soft-switching Boost Converter, IEEE Proc. On PEDES2010, pp. 1-5. [9] K. Kittipeerachon, C. Bunlakasananusorn, Feedback compensation design for switched mode power supplies with a right-half plane (RHP) zero, Power Electronics, Machines and Drives, 2004. (PEMD 2004). Second International Conference on (Conf. Publ. No. 498), vol.1, no., pp.236,241 Vol, 31 March-2 April 2004. [10] MATLAB, user manual, 2010.