Design and Simulation Analysis of Sliding Mode Controller for DC-DC Cuk Converter

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International Journal of Modern Research in Engineering & Management (IJMREM) ||Volume|| 1||Issue|| 10 ||Pages|| 01-07 || November 2018|| ISSN: 2581-4540

Design and Simulation Analysis of Sliding Mode Controller for DC-DC Cuk Converter 1,

Amir Muhammad, 2, Dr. Anwar Ali Sahito, 3, Prof. Dr. Abdul Sattar Larik, 4, Faisal Nawab 1,

Student M.E. (Electrical Power) IICT, Mehran UET Jamshoro; Associate Professor, Electrical Engg. Mehran UET, Jamshoro; 3, Professor, Electrical Engg, Mehran UET, Jamshoro; 4, Student (Renewable Energy) USPCAS in Energy, UET Peshawar; 2,

-----------------------------------------------------ABSTRACT----------------------------------------------------Due to compact size and fast dynamic response DC-DC converters are used to a great extent. DC-DC Cuk converter has switching transients which leads to switching losses and harmonics generation. With a linear controller like Proportional integral derivative (PID), the transients and oscillations under supply and load variations cannot be controlled. So, it becomes necessary to use a nonlinear controller to make transient performance of the converter stable increase its efficiency. A great advantage of this controller includes, it’s based on large signal model of DC to DC converters hence its stability is not bounded by the size of the interpretations around the working point. In this research work, simulation model of cuk converter with sliding mode controller is developed and tested using MATLAB SIMULINK. Effectiveness of proposed sliding mode controller for cuk converter is proved from simulation results. INDEX TERMS: Cuk converter, Sliding mode control, DC-DC converter. --------------------------------------------------------------------------------------------------------------------------------------Date of Submission: Date, 07 November 2018 Date of Accepted: 13 November 2018 ---------------------------------------------------------------------------------------------------------------------------------------

I.

INTRODUCTION

Power electronic converters are now a days invariably used in mostly all fields of today’s control systems because of numerous advantages like economics, robustness, flexibility and compact size. The conversion of direct current (DC) is required due to the demand of variable direct current (DC) on industrial site. This conversion can be done by DC-DC converters which directly convert from DC to DC [1]. DC-DC converters are commonly used in forklift truck, mine haulers, machine tools, distributed power supply systems, telecommunication equipment, ships, space stations and airplanes. The better results can be obtained by increased efficiency, smooth acceleration control and quick dynamic response during operation [1]. Different controllers are used for stabilizing performance of Cuk converter. Linear PID and nonlinear controllers like Generalized Proportional Integral and Sliding Mode Controller results in sturdiness response as compared to linear controllers like PID. Hence power electronic devices can use nonlinear controller rather than linear controller [3]. The common type of nonlinear controller being used in modern control system is a sliding mode controller because of its robustness, compact size and potentiality to cope with supply and load variations [4]. To analyze the performance of any model computer-based simulation software’s are intensely helpful. MATLAB / SIMULINK is among such software which provides different built in models of variety of power electronic converters. The switching transients and harmonics in the DC-DC converters adversely affect the power quality of the converters and the power system network to which it is connected [5]. The problems associated with the DC to DC cuk converter have been illustrated in this paper. The sliding mode controller technique for the converter were analyzed and it was concluded that for better results of the cuk converter both SMC and PI technique should be used. Different control techniques for DC-to-DC cuk converter have been observed using SIMULINK.

II.

CUK CONVERTER

Cuk converter is a DC-to-DC converter, whose output is inverted and either greater or lower than the voltage at the input side, hence it can either step up or step down the input voltage depend on the desired condition. Fig. 1 shows basic circuit diagram of Cuk converter [1]. Major advantage of cuk converter over other converters is that the cuk converter uses capacitor for storing charge. Cuk converters having the ability to either operate in step up mode or in step down mode so largely functional in DC power supplies [2]. Employment, topology, performance, control and dynamics are research topics for cuk converters.

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Design and Simulation Analysis of Sliding Mode‌

Fig.1 Cuk Converter There are two modes of operation of cuk converter i.e. CCM (Continuous conduction mode) in which the current through the inductor does not falls to zero and DCM (Discontinuous conduction mode) in which at some instance the current through the inductor may fall to zero.

III.

STATE SPACE ANALYSIS OF CUK CONVERTER

When we turn ON the switch, the state equations for the cuk converter will be đ??żđ?‘– đ??żđ?‘œ đ??śđ?‘–

đ?‘‘đ?‘–đ??żđ?‘–

= ��

đ?‘‘đ?‘Ą đ?‘‘đ?‘–đ??żđ?‘œ đ?‘‘đ?‘Ą đ?‘‘đ?‘Łđ??śđ?‘–

đ?‘‘đ?‘Ą đ?‘‘đ?‘Łđ??śđ?‘œ

đ??śđ?‘œ

đ?‘‘đ?‘Ą

− − − −− → (i)

= đ?‘‰đ?‘?đ?‘– − đ?‘‰đ?‘?đ?‘œ

− − − −− → (ii)

= −đ?‘–đ??żđ?‘œ

− − − −− → (iii)

= đ?‘–đ??żđ?‘œ −

đ?‘‰đ?‘?đ?‘œ

− − − −− → (iv)

đ?‘…

When the switch is turned OFF, then the state equations for cuk converter will be in the form đ??żđ?‘– đ??żđ?‘œ đ??śđ?‘–

đ?‘‘đ?‘–đ??żđ?‘–

= đ?‘‰đ?‘– − đ?‘‰đ?‘?đ?‘–

đ?‘‘đ?‘Ą đ?‘‘đ?‘–đ??żđ?‘œ

= −đ?‘‰đ?‘?đ?‘œ

đ?‘‘đ?‘Ą đ?‘‘đ?‘Łđ??śđ?‘–

đ??śđ?‘œ

đ?‘‘đ?‘Ą đ?‘‘đ?‘Łđ??śđ?‘œ đ?‘‘đ?‘Ą

− − − −− → (˅) − − − −− → (vi)

= đ?‘–đ??żđ?‘–

− − − −− → (˅ii)

= đ?‘–đ??żđ?‘œ −

đ?‘‰đ?‘?đ?‘œ

− − − −− → (˅iii)

đ?‘…

Now by combining the two sets of equations (ON and OFF) with the control unit U , the final state equations for the cuk converter are shown below in equation (ix),(x),(xi),(xii) Solving equation (i) and (v) we get đ?‘‘đ?‘–đ??żđ?‘– đ?‘‰ đ?‘‰đ?‘? = đ?‘– − (1 − đ?‘ˆ) đ?‘–

− − − −− → (ix)

Solving equation (ii) and (vi) we get đ?‘‘đ?‘–đ??żđ?‘œ đ?‘‰đ?‘? đ?‘‰đ?‘? = (đ?‘ˆ) đ?‘– − đ?‘œ

− − − −− → (x)

Solving equation (iii) and (vii) we get đ?‘‘đ?‘Łđ??śđ?‘– đ?‘–đ??ż đ?‘–đ??ż = (1 − đ?‘ˆ) đ?‘– − (đ?‘ˆ) đ?‘œ

− − − −− → (xi)

Solving equation (iv) and (viii) we get đ?‘‘đ?‘Łđ??śđ?‘œ đ?‘–đ??ż đ?‘‰đ?‘? = đ?‘œâˆ’ đ?‘œ

− − − −− → (xii)

đ?‘‘đ?‘Ą

đ??żđ?‘–

đ?‘‘đ?‘Ą

đ??żđ?‘œ

đ?‘‘đ?‘Ą

đ?‘‘đ?‘Ą

đ??żđ?‘–

đ??żđ?‘œ

đ??śđ?‘–

đ??śđ?‘œ

đ?‘…đ?‘?đ?‘œ

đ??śđ?‘–

By using the above state equations (ix, x, xi, xii) the block diagram of Cuk converter is constructed below

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Design and Simulation Analysis of Sliding Mode‌

Fig.2 Block diagram of cuk converter The main objective of all the controllers is to enhance the overall system efficiency, fast dynamic response and at the same time keeping the system less sensitive to the disturbances. During the variation in supply and load the oscillations are generated. Harmonics will arise and conduction losses will be increased. Therefore, the efficiency of cuk converter and overall efficiency of the system will be effected.

IV.

CONTROLLERS FOR CUK CONVERTER

In order to maintain equilibrium of systems, the feedback control system is momentous to use. The output of the system will be taken into consideration with the help of which the performance of system is adjusted to meet once desired response at the output. Researchers have either proposed or developed different control techniques in order to control the dynamic behavior of DC-DC cuk converter. Conventional technique including pulse width modulation (PWM) which is based on the averaging techniques have been initially used in order to control the dynamics of converter. This technique can only be used under specific operating conditions. [5]. Some linear controllers Proportional (P), Proportional plus Integral (PI) and PID were being used to upgrade the interpretation of such type converters. These converters also failed to perform during large variations in the load and supply. Derivative action sensitive to higher frequency unwanted distortions available with input. By eliminating the derivative action will lead the worst response of controller to such type of signals. Hence PI controller is better competent under noisy data input which led the system more stable in the steady state conditions. [8]. Linear controller (PID) and nonlinear controllers Generalized Integral Proportional (GPI) and Sliding mode controller (SMC) being compared for power electronic converters. The results of both linear and nonlinear controllers have been compared in terms of peak time, settling time and peak overshoot. The results concluded that nonlinear controllers GPI and SMC have robust performance as compared to linear controller PID [7]. Using Mode order reduction method, the controller was designed for DC-DC cuk converter operating under continuous conduction mode. State space averaging method is employed to linearize the model. To design such a compensator for Cuk converter has been found very complex [15]. Converter dynamics toolbox in MATLAB is used to design PI controller for DC-DC cuk converter. Under step change in the input voltage and load variations, the performance or the controller were simulated [1]. PI and SMC were being designed and compared on the basis of controlling the output voltage of DC-DC cuk converter. Both the controllers were found similar during the steady state, but in transient region SMC has shown lower overshoot in voltage and current both. Under the step change in line and load the SMC was found robust [13].

V.

SLIDING MODE CONTROLLER

Linear controllers like PID were failed to resolve the dynamics of nonlinear converters. Therefore, it became necessary to shift towards nonlinear controllers. While comparing nonlinear converters SMC has an edge over the rest nonlinear controllers due to easy from installation point of view and shown higher degree of flexibility during design. SMC is a type of controller (nonlinear) that was been initially designed for the controlling purpose of variable structure systems (VSS). Technically it is composed of time variant state feedback discontinuous control law which switches according to the existing position of state variables from one structure to another. The main objective of such controller is to force the dynamics of system under control flow in the same manner as desired.

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Design and Simulation Analysis of Sliding Mode‌ Basic principle of the sliding mode controller is to retain a certain sliding surface namely reference path such that trajectory of controlled system is converge towards the specified equilibrium point. Zengshi Chen have provided analytical solution of DC-DC cuk converter under PI and SMC. Using equivalent control technique a fourth order nonlinear ordinary differential equation has been obtained and linearized. Transients in the load voltage that arise during the parametric variation are found to be predictable. High accuracy of the controller has been obtained by using a validation circuit for chasing the reference voltage and swift transient response. Y. He and F. L. Luo analyzed the performance of designed SMC for DC-DC converters (Buck and Luo). The controller is based on the large signal model of the converters due to which the variations around the operating point cannot affect the stability of the system. The controller has been successfully employed on Buck and Luo converter, while simulation results under different operating conditions have been presented.Anwar Ali Sahito et.al, to control the dynamics of nonlinear system it is necessary to design a nonlinear controller as linear controller failed during supply and load variations. SMC has found to be robust, quick responsive and ease to implement while designed for Buck converter. They also proposed a new scheme of SMC to control the dynamics of DC-DC converters. H. Guldemir have controlled the dynamics of Buck Boost converter using SMC technique. The robustness of the SMC under load variations and supply variations have been analyzed. During validations of results it has been concluded that better dynamic result and robust operation can still be achievable even for considerable changes in supply voltage and the load. Sanjevi Kumar Padmaban, developed a SMC for modified Boost Cuk converter. SMC based technique have been proposed to get robust performance. Additional current controller was merged with the controller to achieve better results and it found to be very difficult task to develop and measure all states for a third order modified Cuk converter. Fiaz Ahmed et.al, used Sim Power System toolbox to predict the performance of Cuk converter being controlled by PI (for voltage control) and SMC (for current control) purpose. The simulation results still shown some transients at inductor current waveform and voltage output waveform. Gerardo D. Guerrero-Cabarcas et.al, designed feedback controllers including sliding mode controller for Cuk converter being connected with a PV system. But still there were some transients found in output voltage. Efin A. Aksenov et.al, singular perturbation on Sliding Mode Control are summarized to get a cascade control system technique to control the dynamic behavior of DC-DC Cuk converter. The proposed technique includes one inner loop to control inductor current and an outer loop for the output voltage control purpose. Still some transients exist during implementation.

VI.

SLIDING MODE CONTROLLER DESIGN

The sliding mode will be operating according to the control unit operating conditions as shown below in equation (A) 1 đ?‘“đ?‘œđ?‘&#x; đ?‘† > 0 U={ } -----------> (A) đ?‘œ đ?‘“đ?‘œđ?‘&#x; đ?‘† < 0 The value of operator U can be found by using the mathematical expression given below, U 1 = (1 − đ?‘ đ?‘–đ?‘”đ?‘›(đ?‘ )) -----------> (B) 2 The sign function in the equation (B) shows weather the coming signal is positive or negative, it is defined as shown below +1 đ?‘–đ?‘“ đ?‘?đ?‘œđ?‘ đ?‘–đ?‘Ąđ?‘–đ?‘Łđ?‘’ Sign(s) = { } -----------> (C) −1 đ?‘–đ?‘“ đ?‘›đ?‘’đ?‘”đ?‘Žđ?‘Ąđ?‘–đ?‘Łđ?‘’

VII.

RESULT DISCUSSION

Fig.3 Open loop model of cuk converter

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Design and Simulation Analysis of Sliding Mode‌

Fig.4 SIMULINK model for SMC controlled cuk converter During the performance analysis of the sliding mode controlled cuk converter small transients arise. Robustness of the SMC has been proved by small transients while small settling time shows the quick response of the controller. Overshoot and settling time for voltage and current for initial transient, supply and load variation are shown in the table below. Simulations results of initial transient voltage and under supply and load variations has shown in figure (a, b, c, d, e and f). S. No Initial transient Supply variation (14v - 10v) Load variation (0 - 0.5)

Overshoot 0v 1.1v 1.05 v

Settling time 23 milliseconds 25 milliseconds 10 milliseconds

S. No Initial transient Supply variation (14v - 10v) Load variation (0 - 0.5)

Overshoot 0.3 amp 0.8 amp 0 amp

Settling time 23 milliseconds 25 milliseconds 10 milliseconds

(a)

(b)

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Design and Simulation Analysis of Sliding Mode…

(c)

(d)

(e)

(f)

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Design and Simulation Analysis of Sliding Mode… VIII.

CONCLUSION

Cuk converter is a variable structure system and produce switching transients. Transients increase during variation in supply and load. Linear controllers like Proportional integral (PI) cannot cope with these problems. SMC being nonlinear controller handle such behavior in a better way. SMC is preferred because of robustness, easy implementation and rapid dynamic response. The transients found predictable under supply and load variations. In this research work, simulation model of cuk converter with sliding mode controller is developed and tested using MATLAB SIMULINK. Simulation analysis show small settling time and overshoot for initial transient, supply and load variations. Effectiveness of proposed sliding mode controller for cuk converter is proved from simulation results.

IX.

ACKNOWLEDGEMNTS

Authors are thankful to Mehran University of Engineering & Technology Jamshoro for providing necessary resources for carrying this research work.

REFERENCES [1] [2] [3]

[4] [5]

[6] [7]

[8] [9] [10] [11] [12] [13] [14]

Farzin Asadi et.al. “Designing PI controller for cuk converter using converter dynamics toolbox for MATLAB.” International journal of Advanced and Applied Sciences, vol. 4 (6). Pages 175-180. 2017. Gerardo, D.G.; Eduardo, I.O.; Rachid, D.; and Jesus, G. “Nonlinear Analysis of Cuk Converter Connected with a PV System.” Journal of IEEE ANDESCON, INSPEC Accession Number 16650405. 2016. Aksenov, E.A.; and Yurkevich, D.V, “Control System Design Based on Sliding Mode Control and Singular Perturbation Technique for a Cuk Converter,” Proceedings of 13th International Scientific-Technical Conference, Automation Department, Novosibirsk State Technical University, Novosibirsk, Russia, V.1, pp 77-82. 2016. Fiaz Ahmed et.al. “Design of a robust cascaded controller for cuk converter” control and automation engineering, Istanbul technical university, 978-1-5090-1798-0/16 2016 IEEE. 2016. Sahito, A.A.; Uqaili, M.A.; Larik, A.S.; and Mahar, M. (2014) “NON LINEAR CONTROLLER DESIGN FOR BUCK CONVERTER TO MINIMIZE TRANSIENT DISTURBANCES.” Journal of Sci.Int (Lahore), 26(3), pp 1033-1037. 2014. H. Guldemir, “Sliding mode control of DC-DC converters,” Journal of Applied Sciences, vol.5, no.3, pp.558–592. 2005. Mahesvari, L.; Vadivoo, R.S.; and Vijayalakshmi, S. “COMPARISON OF LINEAR AND NON-LINEAR CONTROLLERS.” International Journal of Innovative Science, Engineering and Technology, V.1, ISSN 2348-7968. 2014. A.SAHITO et.al. “Transient response improvement of Buck converter through Sliding Mode Controller.’’ Sindh University Research Journal (science Series), vol. 47(4) pages 659-662. 2015. Sarvi, M.; Soltani, I.; Namazypour, N.; and Rabbani, N. “A New Sliding Mode Controller for DC/DC Converters in Photovoltaic Systems.” Journal of Energy V, 2013, Article ID 871025. 2013. Chen, Z.; “PI and Sliding Mode Control of a Cuk Converter.” Journal of IEEE Transactions on Power Electronics, V.27, NO 8, pp 3695-3707. 2012. Kordkheli, R.A.; and Yazdani-Asrami, M, M. “Making DC-DC Converters Easy to Understand for Undergraduate Students.” IEEE Conference on Open Systems, Malaysia, pp 28-33. 2010. H.guldemir “Modelling and Sliding Mode Control of DC-DC Buck-Boost converter.’’ Proceedings of 6th International Advanced Technologies Symposium (IATS’11), 16-18 may Elazig Turkey. 2011. R.Sriranjani et.al. “Dynamic characteristics of cuk converter based on Sliding Mode Control.” Research journal of Applied Sciences, Engineering and Technology. Vol 5(22) pages 5148-5153. 2013. He, Y.; and Luo, F.L. “Study of Sliding-Mode Control for DC-DC Converters.” Proceedings of International conference on Power System Technology POWERCON, Singapore, pp 1964-1974. 2004.

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