Performance Evaluation of Voltage and Current Control Mode Controller for SEPIC Converter in CubeSats Application K.D. Mananga Bayimissa, A. K. Raji, and M. Adonis Cape Peninsula University of Technology, Bellville Campus, South Africa
Abstract— Front-end power converters for satellite application demand better performance in terms of accurate reference tracking because of the wide-range input voltage of the solar panels. The very tight output voltage requirements demand for robust, reliable, and higher efficiency. The control of such converter is very complex and time consuming to design. Two commonly used control modes are current and voltage control. The design and implementation of a voltage controller for power converter is simpler but not do provide for overcurrent protection compared to current mode controller. Single-ended primary inductance converter is selected in this research work because of its ability to buck or boost the input voltage coupled with the ability to provide non-inverting polarity with respect to the input voltage. Parameter values for the studied converter is used to analyse and design both current and voltage mode controllers for performance evaluation. Output voltage reference tracking with step and ramp changes in input voltage is evaluated in terms of the time taken to reach steady-state after the injected disturbances and the overshoot or undershoot of the output voltage reference. Changes in the output voltage reference to load changes are also studied considering the two controllers. The modelling and simulation work was done on PSIM simulation platform. The controllers design and implementation was carried out using the Smart-Control added module on the PSIM simulation platform. Results show that the current mode controller performed better than the voltage mode controller in terms of the reference tracking and disturbance rejection. Index Terms—SEPIC converter, solar panels, satellite, PSIM, Smart-Control module
1
INTRODUCTION
In the past 20 years the DC-DC power converter has matured into a ubiquitous technology, which is present in the wide variety range of applications, such as DC power supplies, DC motor drives and space power system [1]. DC-DC power converters are complex to control due to their switching behaviour, such as hybrid system and switching linear. Currently there is an excessive amount of control techniques has been proposed to overcome the solutions. These control schemes range from linear schemes, such as proportional integral (PI) controllers based on average models to fuzzy logic; from the
K.D. Mananga Bayimissa, Cape Peninsula University of Technology, P O Box 1906, Bellville 7535, South Africa (e-mail:
[email protected]). A. K. Raji, Cape Peninsula University of Technology, P O Box 1906, Bellville 7535, South Africa (e-mail:
[email protected]). M. Adonis, Cape Peninsula University of Technology, P O Box 1906, Bellville 7535, South Africa (e-mail:
[email protected]).
nonlinear schemes, sliding mode to feed-forward control and H∞ methods [2]. All existing control system approaches for power converters have been illustrated to be reasonably effective, several challenges have not been fully appointed yet, such as ease of controller design and tuning, as well as the robust of the load parameter variations [1]. The main goal in this paper will be focus on stabilisation of the output voltage signal to a specific value which going to able to charged batteries while taking its input from the solar panels by taking into considering the impact of space environment weather change [3]. The voltage and current mode controller used here, it’s accurately design using PSIM software and its add-on Smart-Control to predicted the plant behaviour when operation in continuous conduction mode (CCM) as well as discontinuous conduction mode (DCM). Although as a result, the formulated controllers are applied to the whole operating system regime, not rather to the partial operating point; the robust of the controllers ensured even when the DC-DC power converter operates above or under nominal condition [4]. 2
THEORY OF SINGLE ENDED PRIMARY CONVERTER (SEPIC)
The single ended primary inductor (SEPIC) is a DCDC converter topology which provides a positive output voltage regulated from the wide range of input voltage that varies from below to above the nominal output voltage [5]. The switch of the SEPIC is controlled by changing the duty cycle; the uses of a series capacitor couple the energy from input stage to the output stage. The SEPIC converter response rapidly to a short circuit state condition and when the switch is turned off its act in a true shutdown mode; its output drops to 0V by following a hefty transient dump of charge [6]. Fig 1 illustrated the completed SEPIC converter circuit as well as the turn on and off state of it (Fig 2 and Fig 3).
in frequency increase. That is the main criterion or design goal for loop stability of any DC-DC power converter, either a current mode control or voltage mode control [8]. The plant transfer function of the current mode control differs to the one of a voltage mode control; however, both result to the shape of G(s) x H(s), and intended to be at the slope of -1. When the load and line variation occur, G(s) can be change and quite in one control method compared to the other [8].
Fig. 1. SEPIC converter topology
3.1
Fig. 2. SEPIC converter state, during on-time of the MOSFET
Voltage mode control In a voltage mode control, the DC-DC converter output voltage is fed back to a pulse width modulation controller correspondingly to the adjustment of the duty cycle. Fig 4 shows a DC-DC converter voltage mode control set-up voltage mode control has a single control loop. Stability design of a control loop design depends on a small transfer function of a DC- DC converter power stage, the measure voltage and the gain of the PWM comparator has to be taken in consideration. The control loop is stabilized by adding a compensation network [9]. Van Rhyn (2006) the advantages and disadvantage of a voltage mode control are listed below. Advantages of voltage mode control The analysis of the feedback loop is easy, which simplifier the design of the compensation network. Large amplitude ramp waveform to ensure the good quality of noise immunity.
Fig. 3. SEPIC converter, during Off-state of the MOSFET
The SEPIC is used in applications where the input voltage could be lower or higher of the regulated intended output voltage. Its transfer energy between the capacitors and inductors during the switching operation, this process is done in order to convert a voltage from one to another. The quantity of energy is controlled by the switch, which employ transistor such as an IGBT, MOSFET. MOSFET offer wide range of advantage such as high input impedance which makes it to require simple drive circuit, low voltage stress, as well as do not required any biasing resistors. In addition, MOSFET switching can be controlled in voltage mode rather than a current mode [7]. 3
CHALLENGES OBJECTIVES
OF
CONTROL
LOOP
Disadvantages of voltage mode control Slow response of the control loop to changes in the load current and line voltage, these changes causes indirect sensed as a change in the output voltage. Decreased of the input voltage range causes during a small signal transfer function of the DC-DC converter power stage. Voltage mode control does not allow the control of the current in the system; however it used a current limiting to protect the system under fault conditions.
AND
The main goal of loop stability consists of two principal tasks; first is to know the type of plant transfer function needed to be used, such as: gain-phase Bode plot with all the characteristic of poles and zeros. The second is to design a feedback compensator correspondingly, such that its zeros and poles are properly located with respect to the plant. Clearly, the transfer function is the product of G(s) and H(s). By calculating G(s), the design of H(s) such that the combined gain is closely to a straight line of slope which fall ten times in gain every ten times
Fig. 4. DC-DC converter Voltage mode control [10] 3.2
Current mode control A current mode control is a double loop control system (see Fig 5). The inner loop control the inductor current of the DC-DC converter. It provided the simplicity of the outer voltage control loop design for better dynamic and improves the performance of a DC-
DC converter [10]. The current mode control has several method of implementation such as: peak current mode control, average current mode control, hysteretic current mode control. However in this paper will consider hysteretic current mode control scheme because of its dynamic response over the converter.
Fig. 6. Hysteretic current mode control with slop compensation DC-DC SEPIC power converter Fig. 5. DC-DC converter current mode control [10] Advantages of current mode control The DC-DC converter will response instantaneously to the changes of an input voltage, knowing that the inductor current increases with a slope of ,
the input voltage change will reflected into inductor current measured waveform. The delay problem experience in voltage mode control due to the input voltage changes has been eliminated by current mode control. Minimizes the effect of the output filter inductor and decreases a transfer function of the output filter and single pole by using an error amplifier. Sharing the load current if multiple DC-DC converters are used. The use of an extra comparator sense the current, the system is stable at the highest duty cycle (>50%) and no slop compensation is needed. Average current mode tracks the current to a high degree of accuracy.
Disadvantages of current mode control Instability of the system at above 50% duty cycle, therefore the needed of a slope compensation. Poor noise immunity of the system. Complexity analysis of the system due to the extra feedback loop added. 3.3
Hysteretic current mode control The hysteretic current mode control is the method where a switch mode DC-DC converter has two or more inductors need to be control, the operation of a switch mode DC-DC converter will be based on the theory of sliding mode control [12]. Fig 6 depicted a circuit diagram of a hysteretic current mode control with slope compensation using a DC-DC single ended primary inductor converter [4].
Considered a DC-DC SEPIC converter, the output voltage is the last target when it acts as a DC-DC buck (step-down) or a boost (step-up) converter, however it is not possible for a closed loop system to reach the stability motion of the switching function whether the output voltage has been chosen to be a direct control target. The sum of inductor current is selected plus slope compensation as a direct control target which may lead to a stability of switching operation; Equation (1) shown the switching function selected [11]. 0
(1)
Equation 1 ensures a stability operation of the hysteretic current mode control as the switching function is defined and minimise the current error as well as follow the control law [11].
Fig. 7. Control signal waveform of the hysteretic current mode control DC-DC SEPIC power converter The switching current control law is: U
1; S 0; S
0 0
(2)
Where sigma is a positive constant known as the width of hysteresis use to limit the switching frequency; the sum of inductor currents operates on the surface as depicted in Fig 8. The average state-space equations of the inductor currents and the capacitor voltage in terms of the control law are given in the Equation (3) below [11].
,
,
,
, ,
(3)
(8) ,
3.4
On the switching function; S
ı
ı
0
(4)
The equivalent control on the switching function is calculated using Equation (3) and Equation (5),
Stability analysis of hysteretic current mode control The stability of the DC-DC SEPIC converter using hysteretic current mode control can be analysed by creating a Jacobian matrix, which can be derive from Equation (7). The Jacobian evaluated at the equilibrium point is shown as:
(5) (9) Equilibrium point are calculated by substituting ,
(6)
0
,
,
,
,
The equilibrium point of the eigenvalues is calculated from;
Solving Equation (6), results 4
2
,
0
2
(10)
4
(7)
2 4 2
With the standard function for switching, the fourthorder system is reduced to a third-order system. The dynamic equations stability analysis for the system in third-order is depicted by Equation (8); 0 J Xe
1
0
1 0
Increasing the values of the reference current (Table 1), the stability of the system is determines by the eigenvalues for each value of the reference current (from 5A to 15A). The hysteretic current mode control system operates at a stable state up to the reference current is equal to 14A. Fig 8 and Fig 9 have shown how the eigenvalues increased for each value of the reference current, the real part decreases negatively; however, at the critical reference current (15A) the real part goes to zero and the operating point becomes unstable [12].
(11) 1
Table 1: Eigenvalues for different values of reference current Iref Eigenvalues Results 5 -8469, -678 ± 21649i stable 6 -8582, -602 ± 2164i stable 7 -8675, -524 ± 21635i stable 10 -8880, -296 ± 2161i stable 12 -8982, -149 ± 21588i stable 14 -9066, -892 ± 21569i stable 15 -9103, 61 ± 21557i unstable
be used to improve the stability of DC-DC SEPIC power converter. These compensation circuits work by inserting poles and zeros into the closed loop system response of a DC-DC SEPIC power converter; its decreases or increased the phase and the gain of the closed loop system response. The phase boost is required at the crossover frequency in order to obtain a usable phase margin [13]. The type of compensation network circuit (Fig 10) discussed in this paper is the PI control, because of its dynamic response, simple implementation and load variation; the optimization stability of DC-DC SEPIC power converter knowing the right working condition at any stage, the PI control is a more feasible approach a good alternative control of DC-DC SEPIC power converter [3].
Fig. 8. Eigenvalues real part complex
Fig. 10. Compensation network circuit
Fig. 9. Eigenvalues when Iref increased, loci complex
4
POWER CONVERTER DESIGN AND CONTROLLER The main parameters of propose DC-DC SEPIC power converter is depicted on the Table 2 (components value).
Table 2: SEPIC components values Parameter Input voltage Power of the converter Switching frequency Output voltage Inductors Capacitors Load resistance Range of duty ratio
Symbol Vin P Fsw Vout L1,L2 C1,C2 Rload D
Value 3V - 20V 8W 250 kHz 10V 8.7uH 10uF,27uF 12Ω 0.334 to 077
The stability of DC-DC SEPIC power converter requires the compensation network circuit for improvement, such as to provide a control closed loop system with a right phase margin at the selected crossover frequency point and a high DC gain. There are many way to implement the compensation network circuit that may
PSIM software with its add-on Smart-Control is used to overcome the problem of PI controller. The principal purpose is to select the nominal input voltage value and tune a controller in such a way to obtain the loop transfer function of DC-DC SEPIC power converter plan. Adjusting the loop transfer function to the ideal gain vs. Frequency, the crossover frequency has to be selected in the range of 10% to 20% of the switching frequency of the DC-DC SEPIC converter. And the select phase margin between 450 to 600 to obtain better response, and stability margin; by running the AC-Sweep analysis of the DC-DC SEPIC power converter on PSIM software, the transfer function of the current mode and voltage mode control are derived with respect to their implementation. The loop gain and phase of the DC-DC SEPIC power converter for the voltage mode control and current mode control are depicted in Fig 11 and Fig 12, the transfer function file obtained is then exported to Smart-Control platform. Once a transfer function file has been exported, the implementation of the current mode control and voltage mode control feedback can simply be performs. The step applies selected a single loop sensor type, which in the case of this paper a voltage divider and the regulator type is a PI controller. Fig 13 shows the stability of the design.
5
SIMULATION RESULTS
In order to verify the proposed topology of the performance evaluation of DC-DC SEPIC power converter for CubeSats application, the simulation results have been analyzed by using the components values listed in Table 1, the use of PSIM software under the following conditions: Current mode control Voltage mode control 5.1
Fig. 11. Bode-plot, gain vs. frequency for current mode scheme
Fig. 12. Bode-plot, gain vs. frequency for voltage mode scheme According to this controls design, the phases and gain margin limitations depicted in Fig 11 and Fig 12. As well as the proportional and integral gain are summarized in the Table 3 below.
DC-DC SEPIC power converter current mode control simulation model The circuit diagram of the current mode control DCDC SEPIC power converter is illustrated below in Fig 14. This model has been implemented, in terms of PI controller components values, the values had been obtain while using PSIM Smart-Control Bode-plot technique explained above in section 4.
Fig. 14. DC-DC SEPIC power converter current mode control scheme, hysteretic model
Fig. 13. Nyquist plot Table 3: Control Limitations values Current control Name PhM(o) G(dB) Kp Kint
Min
o
45 0.81 dB 2.801 34.954 u
Max
o
60 7 dB 15.485 77.514 u
Voltage Control Min
o
45 6.02 dB 0.236 35.38 u
Max 60o 11.05 dB 0.428 45.54 u
Fig. 15. Current mode control, output voltage response with a step change input voltage The current mode control in Fig 15 illustrated output voltage when a step change is applied to the input voltage. It can be seen that the output voltage was obtained
throughout the step change, however, there is a 1V overshoot at the 0.3 seconds. Performing the load changes for current mode control scheme, the scale of output currents and output voltages Figures was changed to 30X1 (the actual value multiply by 30) for better readings of data, as well as the voltage mode control which is late discussed. The depicted of Fig 16 below, shown that when the load resistor decreases the output current increases which result the current mode control to stabilized the output voltage at the desire value (10V); according to Fig 16 this phenomena happened at the times of 0.05s-0.2s,0.3s-0.4s, and 0.5s-0.6s.
Fig. 18. Current mode control, output voltage response and step change output current with 20V input voltage 5.2
DC-DC SEPIC power converter voltage mode control simulation model Fig 19 shows the circuit diagram of the voltage mode control DC-DC SEPIC power converter. This scheme has been verify by using PSIM simulation. Once again the components value of PI controller is obtained while using Smart-control technique explained above in section 4.
Fig. 16. Current mode control, output voltage response and step change output current with 3V fixed input voltage
Fig. 19. DC-DC SEPIC power converter voltage mode control scheme Fig. 17. Current mode control, output voltage response and step change output current with 11.5V nominal input voltage Since the controller has been design with the nominal voltage value, Fig 17 above shows the stability of the output voltage (10V) over the load current step change when using a fixed nominal input voltage. At the maximum input voltage (20V), the output voltage produced the uninformed noise when increasing the output load current in the range of 0.05s to 0.2s as depicted in Fig 18; however the average output voltage value remained 10V.
It is shown that the output voltage response of Fig 20 has an overshoot of 30V at the time of 0.3s before going back to a steady state value desired (10V). Depicted Fig 21 below had illustrated the output voltage response with a step change output current at 3V fixed input voltage; it shows that at the higher output current, the output voltage has a inform noise between 0.05s to 0.2s, 0.3s to 0.4s, and 0.5s to 0.6s; then fallen back to steady state value desire.
the range of 0.08s to 0.2s due to the high step change of the output current. Depicted Fig 23 had shown that, the output voltage response to a step change output current at the maximum input voltage (20). It can be seen that in the range of 0.1s to 0.2s the output voltage produced the uninformed noise at the maximum output current. The summarized comparison of the voltage and current mode control are depicted on Table 3 below Table 4: Summarized comparison of voltage and current mode control characteristics Loop stability Overshoot Response time
Fig. 20. Voltage mode control, output voltage response with a step change input voltage
Fig. 21. Voltage mode control, output voltage response and step change output current with 3V fixed input voltage
Voltage mode control Good High Slow
Current mode control Excellent Low Rapid
Fig. 23. Voltage mode control, output voltage response and step change output current with 20V input voltage 6
CONCLUSION
Different control methods (voltage and current mode) have been performed and evaluated for DC-DC power converter used in CubeSats application, based on single ended primary inductor (SEPIC) topology. A comparison study has been done by studying the effect of the load changes on DC-DC SEPIC power converter response in terms of the output voltage. It is believed that the classification and studied carried out of the control techniques presented in this paper would be useful for DC-DC SEPIC power converter for CubeSats application. However the current mode control scheme will be more reliable than the voltage mode control due to its abilities of controlling the amount current and voltage distributed in the CubeSats. Fig. 22. Voltage mode control, output voltage response and step change output current with 11.5V nominal input voltage At the nominal input voltage (11.5V), the output voltage response of a voltage mode control has a noise in
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Khader D Mananga Bayimissa. He received the B.Tech Electrical Engineering from Cape Peninsula University of Technology (CPUT) in 2013. He is currently working toward the MastersTechnology of electrical Engineering (MTech) at Cape Peninsula University of Technology (CPUT) in South Africa. He is an active student of French South Africa Institute of Technology and center of Distributed Power and Electronics Systems at CPUT. Mr. Mananga research interests include control of power converters, model predictive for space applications. Raji K Atanda. He is senior Lecturer and Researcher in the Department of Electrical Electronic and Computer Engineering and an active member of Centre for Distributed Power and Electronic Systems. His current research areas include waste-to-energy, embedded system, renewable systems development. Marco Adonis. He is senior Lecturer and Researcher in the Department of Electrical Electronic and Computer Engineering and an active member of Centre for Distributed Power and Electronic Systems. His current research areas include waste-to-energy, embedded system, renewable systems development. Presenting author: The paper is presented by K.D. Mananga Bayimissa
