THE MODELING and control of power electronic systems

Transcription

1 2530 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 6, JUNE 2008 A Hybrid Control Algorithm for Voltage Regulation in DC DC Boost Converter C. Sreekumar and Vivek Agarwal, Senior Member, IEEE Abstract A new switching control algorithm based on state trajectory approximation is proposed to regulate the output voltage of a representative second-order dc dc converter the boost converter. The essence of the proposed algorithm is to trap the system into a stable limit cycle while ensuring the required voltage regulation. Unlike some of the earlier algorithms, the concept is applicable to both continuous and discontinuous current modes of operation, making it viable over a wide operating range under various load and line disturbances. A hybrid-automaton representation of the converter is used to perform the analysis, and the control problem is simplified to a guard-selection problem. Guard conditions, governing the transition of the converter operation from one discrete state to the other in a hybrid-automaton representation, are derived. The hybrid-automaton-based control system is implemented by using the state flow chart feature of MATLAB, and extensive simulations are carried out to check the suitability of the algorithm. The hybrid control law is also validated in real time by using a laboratory prototype. The experimental and simulation results prove the effectiveness of the proposed control law under varying line and load conditions. Index Terms Hybrid control, limit cycle, modeling, power converters, stability, state feedback, switching systems. I. INTRODUCTION THE MODELING and control of power electronic systems has been a challenging task for researchers and engineers working in this field. Second-order dc dc converters, with which this paper deals, are no exception. The last few decades have witnessed a number of contributions in the area of modeling and control of these converters [1] [24]. Like any other power electronic system, these converters are highly nonlinear, discontinuous in time, and variable structure systems. Being variable structure systems, they assume different topologies depending on their mode of operation [governed by the operation of the controllable device(s)]. The matter is further complicated due to the existence of continuous-current-mode (CCM) and discontinuous-current-mode (DCM) operations, which require different models for analysis. As the complete operating range of a converter may involve both the CCM and DCM operations, there is a need for a common representation that is applicable over the entire operating range [25]. An early approach to mathematical modeling was the transfer function approach where the states of the system are averaged around a nominal operating point and linearized [1] [3]. It has Manuscript received June 15, 2007; revised January 22, C. Sreekumar is with the Government College of Engineering, Kannur , India ( sreeku.gcek@gmail.com). V. Agarwal is with the Department of Electrical Engineering, Indian Institute of Technology, Bombay , India ( agarwal@ee.iitb.ac.in). Digital Object Identifier /TIE also been proved that the same state averaged model can be obtained from a Lagrangian approach [4]. In a recent work [5], a numerical state-space average-value model is used for control design. The model, which describes the dynamics around the designed operating point, may fall short when there are disturbances in the system [6]. The advent of modern control theory has also been utilized in control design using the statespace models, including the sliding-mode techniques [7] [9], H-infinity technique [10], linear-quadratic-regulator method [11], fuzzy control [12] [16], and optimal control method [17], to name just a few. An important point to note here is that, in many of the modeling techniques, different models are required to represent the converter operating in CCM and DCM, and in the literature previously described, the DCM operation is overlooked. The control techniques, which are generally implemented through pulsewidth modulation (PWM), can be classified into voltage mode control or current mode control. The current mode control has a definite advantage over the voltage mode control in that the system response to disturbances is much faster [18]. However, both techniques have problems of inherent instability and subharmonic oscillations when they operate under constant frequency PWM scheme, and a compensator network is usually required. The control design is usually carried out by using the linear system design techniques in the frequency domain [1] [3]. The major constraint in this method is the presence of a right-handplane (RHP) zero in many of the averaged models. As the location of this zero is inversely proportional to the average inductor current, an increase in the inductor current shifts the zero toward low frequencies in the RHP, causing considerable phase lag, which, in turn, limits the available bandwidth for a stable operation of the converter. Some time-domain techniques have also been proposed and successfully implemented (e.g., sliding-mode scheme [7] [9]). However, in most cases, this method presumes CCM operation of the converter, and the regulation is lost when it enters DCM operation. The other time-domain techniques, such as H-infinity control [10], fuzzy control [12] [16], and nonlinear multiloop control [19], have also considered only the CCM operation. As an attempt to rectify the problem of model inaccuracy and control limitations previously discussed, the hybrid modeling technique was presented [20], [21] in the literature as a natural representation of power electronic converters. The hybrid model is a large signal model where the exact behavior of the circuit is used for controller design. Matthew et al. [20] have used an exact model to represent a boost converter as a hybrid automaton. They have designed a controller to regulate /$ IEEE

2 SREEKUMAR AND AGARWAL: CONTROL ALGORITHM FOR VOLTAGE REGULATION IN DC DC BOOST CONVERTER 2531 TABLE I SYSTEM MATRICES UNDER DIFFERENT MODES Fig. 1. Typical boost-converter circuit. the output voltage of a boost converter. However, extensive computations are required to implement this type of control. In addition to this, the switching frequency is very high, causing difficulty in practical implementation. Furthermore, this scheme is demonstrated only for the CCM operation of the converter, and the experimental investigations are not done. Another hybrid control scheme, involving energy-based algorithm, is proposed for the voltage regulation of a boost converter [22]. However, this algorithm is naturally suited for DCM, resulting in high inductor-current peak. Thus, it is clear that the existing hybrid control algorithms have some limitations. Hence, there is a need to develop a simple computationally viable control algorithm to be implemented in real time by using a general hybrid-automaton representation which includes both CCM and DCM operations. In this paper, a new hybrid control algorithm is derived from the basic circuit laws and implemented for regulating the output voltage in a boost converter. The algorithm is simple, and the computations involved are minimal. Hence, it is quite suitable for real-time implementation. Its applicability to both the CCM and DCM operations is a useful feature, considering that the operating mode of a power converter may change from CCM to DCM and vice versa depending upon the variation in line and load conditions. Such a situation may occur if the converter is designed to operate in CCM at the rated conditions and in DCM under light load conditions to realize an overall higher efficiency. This would be specifically advantageous in certain applications, for example, battery-powered systems [23]. The proposed control law ensures that the system rests in a stable limit cycle around the steady-state point and is free from any nonlinear characteristics [25]. The remainder of this paper is organized as follows. Section II describes the hybrid-automaton representation of a boost converter system operating in CCM/DCM. Controller design is explained in Section III. Simulation and experimental details, along with the results, are given in Sections IV and V, respectively. Finally, the major conclusion of this paper is summarized in Section VI. II. HYBRID MODELING AND AUTOMATON REPRESENTATION Typical boost-converter circuit is shown in Fig. 1. A general hybrid automaton [20], [26] for a CCM/DCM-operated boost converter is developed by using the following definitions. Let X R n be a continuous state space, and let Q = q 1,...,q N be a finite set of discrete states. The continuous state space specifies the possible values of the continuous states for all q s, where q Q represents the on/off configuration of the switches in the circuit. For each q Q, the continuous dynamics is modeled by differential equations of the form ẋ(t) =A q x(t)+b q = f q (x(t)) (1) where x X, A q R n n, and B q R n 1. The operation of a subsystem given by (1), which corresponds to a discrete state q, is known as the mode of the system. A hybrid automaton can be defined as a six-tuple collection H =(Q, X, F, I, E, G), where F :(Q X) R n assigns to every discrete state a Lipschitz continuous vector field on X; I : Q 2 X assigns each q Q an invariant set; E Q Q is a collection of discrete transitions; and G : E 2 X, e = (q, q ) E, is a guard. In any converter system with k switching elements, 2 k discrete states are possible. Hence, in a second-order boost converter [6], four discrete states are possible, namely, q 1 (SW1 on, SW2 off), q 2 (SW1 off, SW2 on), q 3 (SW1 off, SW2 off), and q 4 (SW1 on, SW2 on), where SWi, i =1, 2, represents the main controllable device (power MOSFET, insulatedgate bipolar transistor, etc.) and the power diode, respectively. Out of these, q 4 is redundant as it is not feasible. Then, the set of possible discrete states Q =(q 1,q 2,q 3 ) leads to the set of possible events as E =[(q 1,q 2 ), (q 2,q 1 ), (q 2,q 3 ), (q 3,q 1 )]. The first two events {(q 1,q 2 ), (q 2,q 1 )} correspond to the CCM operation, and the event set {(q 1,q 2 ), (q 2,q 3 ), (q 3,q 1 )} corresponds to the DCM operation of boost converter. For the analysis, let the states of the system be defined as x(t) =(i L,v o ), where i L is the instantaneous value of inductor current, and v o is the instantaneous output voltage. Let V in be the input voltage, v L be the inductor voltage, v c be the capacitor voltage, L be the input inductor, C be the output capacitor, and R be the load resistance of the boost converter. The system can be represented in terms of three state equations corresponding to q i (i =1, 2, 3). The system matrices for various operating modes are shown in Table I. The boost converter under closed-loop control can be considered as an interacting combination of two hybrid automatons [20], [21], as shown in Fig. 2. The discrete evolution depends on the continuous signal x(t), and the continuous evolution is based on the discrete symbol σ = {σ 1,σ 2,σ 3 }. The control problem is to determine the guard conditions G ij which cause transition from the ith discrete state to the jth discrete state while satisfying the system requirements on control. In other words, the hybrid control problem is to restrict the state

3 2532 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 6, JUNE 2008 Fig. 3. Approximate variation of state variables in CCM. Fig. 2. Hybrid-automaton representation of the boost converter. i.e., trajectories within the limits specified by the guard conditions. In this paper, the approach is to determine appropriate switching guards for trapping the system into a limit cycle satisfying the voltage-regulation constraint. III. CONTROLLER DESIGN A GUARD-SELECTION PROBLEM In a hybrid control perspective, the control-design problem is essentially a guard-selection problem satisfying the voltage regulation. The guard conditions governing intermode transfer can be derived by using a circuit theoretical approach, as discussed next for the CCM and DCM operations. For the CCM operation, it is required to determine two guards, i.e., G 12 and G 21, and the DCM operation involves proper selection of three guards, i.e., G 12, G 23, and G 31. The generation of control pulses for both the DCM and CCM operations is on similar lines based on the respective guards except that, in the CCM mode, the third mode is not present, and the transitions from mode 2 to mode 3 and from mode 3 to mode 1 are not defined. Transition from one mode to another takes place when the sensed state variables exceed the relevant guard condition. A. CCM Operation The approximated waveforms of the inductor current and the output voltage of a boost converter operating in CCM are shown in Fig. 3 [6]. In Fig. 3, I p, I L, i L, V o, and v o are the peak value of i L, the average value of i L, the ripple in I L, the average value of v o, and the ripple in V o, respectively. dt is the time at which the system dynamics change from mode 1 to mode 2, and T is the time at which the system switches back to mode 1. T is also the inverse of converter-operating frequency f. From Fig. 3, during 0 t dt di L dt = V in L (2) 2 i L = V in dt. (3) L Similarly, during the same interval, the change in capacitor voltage is i.e., dv o dt = V o RC From (3) and (5), it follows that (4) 2 v o = V o dt. (5) RC i L = RCV in LV o v o. (6) The ripples in the output voltage and the inductor current are related by (6). In CCM, for a given output voltage swing, the current swing along with the average inductor current is used to define the guard conditions, which governs the transition between the two modes of operation. The average inductor current can be determined by equating the converter input power with the converter output power as follows: I L = V o 2. (7) RV in By using (6) and (7), the guard conditions G 12 and G 21 are defined as i L I L + i L and i L I L i L, respectively. These guards cause the system to settle in some limit cycle, depending upon the load condition of the system. The load current and the output voltage have to be sensed to determine the guards. As the load on the system decreases, the average inductor current reduces and becomes exactly half of the current ripple at the CCM DCM boundary. Thereafter, the voltage regulation is lost. Hence, the algorithm is modified for the DCM operation as described next.

4 SREEKUMAR AND AGARWAL: CONTROL ALGORITHM FOR VOLTAGE REGULATION IN DC DC BOOST CONVERTER 2533 From the ongoing analysis, by using (11), one can easily deduce the dependence of the inductor peak current on the frequency of switching as follows: I p = 2 V o (V o V in ). (15) RfL Fig. 4. Variation of state variables in DCM. B. DCM Operation The inductor current and the output voltage of the boost converter for DCM are shown in Fig. 4. Interval d 1 T is the duration for which the system stays in mode 1, d 2 T is the duration for which the system stays in mode 2, and (1 d 1 d 2 )T is the duration for which the system stays in mode 3. From the output-voltage waveform V o = V in(d 1 + d 2 ). (8) d 2 The average inductor current is given by I L = V o(d 1 + d 2 ). (9) Rd 2 In terms of the peak current, the average inductor current is I L = I p(d 1 + d 2 ). (10) 2 From Fig. 4, the peak inductor current is From (8) (11) d 2 = fl Rd 1 I p = d 1TV in L. (11) Rd2 1 fl. (12) By noting that the average load current is equal to the average current through SW2, an expression for the voltage gain of the boost converter operating in DCM is given by V o V in = 1 2 By rearranging (13) d 1 = 1 V in Rd2 1 fl. (13) [ ] 2 flvo (V o V in ). (14) R To define a guard condition G 12 based on the current I p, (15) should hold. The guard G 12, thus defined, directly depends on f. The constraint that the output voltage swing should never go beyond ± v o can be effectively used to select this frequency f. The resulting system is trapped into a limit cycle of frequency f within the allowed voltage range. Hence, the selected frequency, satisfying the aforementioned constraints, is referred to as the trap frequency f T. Referring to Fig. 4, the voltage swing constraints are [ IL C V o RC ] d 2 T 2 v o (16) V o RC (d 1 + d 3 )T 2 v o. (17) By using the aforementioned inequalities, the condition on the trap frequency can be obtained as f T > (V o V in ) 2 v o RC. (18) In the limiting case, the limit-cycle operation is such that the output voltage swing is at its maximum. In short, the guard condition G 12 is determined by I p, as per (15). The transition from mode 2 to mode 3 is autonomous in the system, and hence, i L =0 can be characterized as the natural guard G 23. The reference voltage v o = V o can be selected as the guard condition G 31 to ensure equal v o swings during the voltage decay. The guard condition in (15) can be calculated by fixing the trap frequency as per (18) and using it as the frequency of operation f. Hence, the DCM operation under the proposed control is of constant frequency. During a load change, the output voltage ripple gets adjusted to satisfy the constant frequency operation in DCM. IV. SIMULATION RESULTS AND DISCUSSION The proposed algorithm is tested in MATLAB for a boost converter with the following specifications: V in =15V, V o = 30 V (desired value), R =20 Ω, L = 350 µh, C =10 µf, and v o =0.5V. The continuous transitions are implemented by using SIMULINK blocks, and the discrete transitions are implemented by using the state flow (chart) feature of MATLAB to replicate the representation in Fig. 2. The simulation waveforms are shown in Figs. 5 and 6. These waveforms demonstrate the effectiveness of the proposed scheme under various load and line conditions in the system. A. Operation in CCM At t =0, the system is switched on with the rated load resistance R =20Ωand the input voltage V in =15V, as shown in Fig. 5(a). The converter works in CCM for this operating

5 2534 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 6, JUNE 2008 Fig. 5. Simulation results under disturbances. Variations in (a) load resistance and input voltage, (b) inductor current, and (c) output voltage. Fig. 6. Magnified view of the v o and i L waveforms during various disturbances (expanded from Fig. 5). (a) v o corresponding to the load change at t =6ms, causing transition from CCM to CCM DCM boundary. (b) i L variation corresponding to (a). (c) Output-voltage response for a load change at t =9ms, causing transition from CCM DCM boundary to DCM. (d) Inductor-current variation corresponding to (c). condition. It is observed that v o quickly reaches and settles at 30 V. There is no voltage overshoot, and the oscillations around the set point are limited to ±0.5 V. A load change from R =20to 45 Ω is applied at t =3ms. The converter output voltage settles to the set value of 30 V after an overshoot while operating in the CCM. The variations in v o and i L are shown in Fig. 5(b) and (c), respectively. B. Operation at CCM DCM Boundary At t =6ms, the load is abruptly changed from R =45to 95 Ω. Figs. 5(b) and 6(b) show that the system enters the just DCM operation. Figs. 5(c) and 6(a) show the response of v o. Due to the sudden change in load, the output voltage jumps to 31.2 V but soon settles around the desired value of 30 V,

6 SREEKUMAR AND AGARWAL: CONTROL ALGORITHM FOR VOLTAGE REGULATION IN DC DC BOOST CONVERTER 2535 Fig. 7. Steady-state waveforms for higher trap frequency f T =30kHz with R = 440 Ω. (a) Inductor current. (b) Output voltage. as shown in Figs. 5(c) and 6(a) and (c). Hence, the transient response when the mode of operation changes from CCM to DCM is found to be satisfactory, and the system does not become unstable. C. Operation in DCM The load resistance is further increased from R =95 to 220 Ω at t =9ms for the converter to operate in perfect DCM. The guard condition G 12 depends on the trap frequency, and hence, a suitable value is to be selected for f T. By using (18), it is determined that the trap frequency for a load of 95 Ω should be greater than or equal to 16.6 khz. As the load varies, the minimum trap frequency decreases to f T =3.9 khz at a load of 400 Ω. A trap frequency of 20 khz is used for this paper. The impact of trap-frequency change is discussed later in this section. From the DCM waveforms shown in Fig. 6(c) and (d), it is seen that the controller is fast enough to respond to the load changes. The change in output voltage during the load change is negligible. The load is further increased to 440 Ω at 12 ms and to 1090 Ω at t =15ms. It is found that the controller action causes the output voltage to remain at the set value. D. Operation Under Input-Voltage Disturbances In order to test the controller performance over a wide range of operating conditions, disturbances, such as a step rise in the input voltage V in by 5 V at t =18 ms and a sinusoidal disturbance of peak 2 V and a frequency 4000 rad/s in the input voltage at t =21ms, are applied, as shown in Fig. 5(a). It is observed that the controller is able to respond to the disturbances appropriately to regulate the output voltage at 30 V, as shown in Fig. 5(c). E. Impact of Higher f T The algorithm is also implemented for a higher trap frequency of 30 khz. The steady-state waveforms at this trap frequency with the input voltage V in =15V and load resistance R = 440 Ω are shown in Fig. 7. As expected, the ripple in output voltage and inductor current is reduced for a similar loading condition [can be compared with Fig. 6(c) and (d)]. Thus, a higher trap frequency is desirable as far as the speed of response, voltage ripple, current ripple, and regulation are considered. However, such a higher frequency can be selected if and only if the other circuit conditions, such as power loss, driver-circuit limitations, device speed, etc., permit. V. E XPERIMENTAL VERIFICATION OF THE CONTROL SCHEME The proposed hybrid control scheme is implemented in real time using analog and digital ICs and other discrete components. A detailed circuit schematic of the implemented scheme, showing the power circuit and the control stage, is shown in Fig. 8. The control scheme involves both feedforward and feedback of signals. The inductor current, output voltage, load current, and input voltage are measured for control computation. Although the control involves measurement of more number of variables, the best features of both current mode and voltage mode control schemes can be used in the proposed hybrid control scheme. The instantaneous values of inductor current and output voltage are used to compare with the threshold values given by the guard conditions to switch from one discrete state to the other. The control signal thus generated is fed into the gate of the main switching device (MOSFET) through the gate driver circuit which provides the necessary isolation of the switching signal ground and the power ground. In the laboratory prototype, IRF450 MOSFET is used as the main switching device; SW1 and CSD10030 ultrafast diode is used as SW2. An LEM sensor is used to sense the current. In the controller part, all the calculations are done by using the MPY 634, which is a multifunction IC that gives good results for multiplication, division, and square rooting. Proper scaling is done by using potentiometers and amplifiers to limit the voltage level in the range of 0 10 V, which is compatible with the ICs used. Signal amplification is done by using TL 082 Op-Amp IC, and all comparisons are done by using KA 319 fast comparator or LM311 comparator. The 4013 flip-flop IC is used for control-pulse generation, and IC 3120 is used as the MOSFET driver. The load and input disturbances are applied by using toggle switches. Following the procedure used in simulations, the load resistance of the converter system is varied in steps using a

7 2536 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 6, JUNE 2008 Fig. 8. Detailed circuit diagram showing the power and control stages of the implemented scheme. toggle switch, and the steady-state response under the proposed control scheme is shown in Fig. 9. From the simulation results, it is observed that the simulated inductor current has a sharp rise. As the power supply used in the laboratory has current limiting protection, the input voltage is increased in steps during startup. In Fig. 9(a), the switching pulses (control signal) and the inductor-current waveforms are shown for the CCM operation of the converter with a load resistance of 20 Ω. From the waveforms shown [Fig. 9(b)], it is clear that the required output voltage of 30 V is maintained under the proposed control scheme. The switching signal and the inductor-current waveforms corresponding to the just DCM operation and the perfect DCM operation are shown in Fig. 9(c) and (e), respectively. The corresponding variations in output voltage are shown in Fig. 9(d) and (f), respectively. The control law is tested under disturbances in load and input voltage, and the results are shown in Figs. 10 and 11, respectively. The load is varied from 20 to 45 Ω and back. Corresponding variations in output voltage and inductor current are shown in Fig. 10(a). It is observed that the operation of the converter still remains in the CCM. The output voltage exhibits an overshoot (undershoot) for the load decrease (increase), but it quickly settles around the set value of 30 V. The slight variation in the output voltage may be attributed to the drop in the inductor and the diode. The variation in inductor current is also smooth, as is evident from Fig. 10(a). A CCM to the just DCM change is made by increasing the load resistance to 95 Ω, and the corresponding output-voltage and inductorcurrent waveforms are shown in Fig. 10(b). Similar to the transients in CCM to CCM operation, there is a jump in the output voltage, but the output voltage soon settles at the set value of 30 V. The load resistance is further increased to 220 Ω to change the converter operation from the just DCM to the perfect DCM. The corresponding output-voltage and inductor-current transients are shown in Fig. 10(c). It is observed that the transition in inductor current and output voltage is very smooth under the disturbance during the DCM operation. The experimental results show that the converter operation in CCM and DCM is robust under load variations. While the converter is working with a load of 45 Ω (CCM operation), a step change in the input voltage from the nominal V and back is applied. The change in the input voltage and the corresponding output-voltage waveforms are shown in Fig. 11(a). It is observed that the output voltage remains constant, and the transients in output voltage are well within limits. The effect of the change in the input voltage in the DCM operation (load resistance: R = 220 Ω) is also studied by gradually varying the input voltage above and below the rated value of 15 V. This also reveals that the output voltage remains constant and does not go through any undesirable

8 SREEKUMAR AND AGARWAL: CONTROL ALGORITHM FOR VOLTAGE REGULATION IN DC DC BOOST CONVERTER 2537 Fig. 9. (a) Steady-state inductor current and switching pulses for the CCM operation (R =20Ω)(scale X-axis: 25 µs/div; Y -axis: CH1: 5 V/div and CH2: 1 V/div = 1A/div). (b) Output voltage corresponding to (a) (scale X-axis: 25 µs/div; Y -axis: 10 V/div). (c) Inductor current and switching pulses for the just DCM operation (R =95Ω)(scale X-axis: 25 µs/div; Y -axis: CH1: 5 V/div and CH2: 1 V/div =1A/div). (d) Output voltage corresponding to (c) (scale X-axis: 25 µs/div; Y -axis: 10 V/div). (e) Inductor current and switching pulses for the DCM operation (R = 220 Ω) (scale X-axis: 25 µs/div; Y -axis: CH1: 5 V/div and CH2: 1 V/div =1A/div). (f) Output voltage corresponding to (e) (scale X-axis: 25 µs/div; Y -axis: 10 V/div). Fig. 10. Waveforms during transient conditions. (a) Output voltage and inductor current when the load is changed from R =20Ω(CCM operation) to R =45Ω (CCM operation) and back (scale X-axis: 500 ms/div; Y -axis: CH1: 10 V/div and CH2: 1 V/div =1A/div). (b) Change in the output voltage and the inductor current for a load change from R =45Ω(CCM operation) to R =95Ω(just DCM operation) and back (scale X-axis: 500 ms/div; Y -axis: CH3: 10 V/div and CH2: 1 V/div =1A/div). (c) Change in output voltage and inductor current for a load change from R =95Ω(just DCM operation) to R = 220 Ω (DCM operation) and back (scale X-axis: 500 ms/div; Y -axis: CH3: 10 V/div and CH2: 1 V/div =1A/div). Upward arrows indicate the load-changing points. Fig. 11. Output voltage during input-voltage disturbances. (a) Sudden input-voltage change from 15 to 20 V and back to 15 V when R =45Ω(CCM operation) (scale X-axis: 500 ms/div; Y -axis: CH1: 5 V/div and CH2: 10 V/div). (b) Input voltage changed from 15 to 21 V and back to 13 V when R = 220 Ω (DCM operation) (scale X-axis: 500 ms/div; Y -axis:ch1:5v/divandch2:10v/div).

9 2538 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 6, JUNE 2008 characteristics [Fig. 11(b)]. The results shown in Fig. 11 validate the effectiveness of the proposed hybrid control scheme to handle perturbations in the input voltage. VI. CONCLUSION A new technique for the hybrid control of a boost-type dc dc power converter has been proposed. In this approach, the control problem is simplified as a guard-selection problem in a hybrid-automaton representation to obtain the required voltage regulation. The whole system, which is modeled in a hybrid perspective, is simulated in MATLAB/SIMULINK using the state flow chart feature. The algorithm is implemented by using a laboratory prototype. The simulation and experimental results establish the effectiveness of the control scheme. The salient features of the proposed scheme are the following. 1) Computations involved in the algorithm are minimal, making it a good choice for real-time control. 2) The complete operating range of the converter (CCM and DCM) is covered by the proposed control scheme. 3) The approach is generic in that similar control schemes can be implemented for other second-order converter topologies. 4) The control scheme in CCM results in a hysteresis like switching, although the control computation is entirely different. The error voltage or the control voltage is not calculated, and the PWM type of control is not used. The proposed scheme has a variable switching frequency with a maximum allowable output voltage ripple in the CCM operation. The operation in DCM is very smooth, even under disturbances. Both in the CCM and DCM operations, as the guard conditions depend on the load value, an accurate load current sensor is required. 5) The control scheme is demonstrated with an example with output filter-capacitor value as 10 µf. A higher value of filter capacitor will improve the transient response, although it may need a fine tuning of trap frequency in the DCM operation. In addition, in our experiments, the load is varied by using toggle switches. Hence, the dynamics of the switch also play a role in the transient response of the system. 6) The parasitic elements are not considered in the analysis to reduce the computational complexity. Nevertheless, it is proved through practical experiments that the proposed scheme gives good regulation characteristics over a wide range of load and line disturbances. REFERENCES [1] R. D. Middlebrook and S. Cuk, A general unified approach to modeling switching Converter power stages, in Proc. IEEE PESC, 1976, pp [2] W. M. Polivka, P. R. K. 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