Performance analysis of different methods for optimal sliding mode control of DC/DC buck converter

ABSTRACT


INTRODUCTION
Buck converter has an essential role in powering electrical and electronic circuits.Though, an important concern regarding stability, regulation of voltage, and current always needs to be addressed.Due to the non-linear behavior of the components of disturb buck converter, such as capacitor and inductor, circuit control plays vital role in converter dynamic performance [1]- [5].In order to adhere to its intrinsic nonlinearity during abrupt load and input voltage changes as well as ensuring stability with rapid transient response, the DC/DC converters should be designed to work with a relevant control method [6]- [8].One of the most relevant ways to control converter disturbance is via utilization of sliding mode control (SMC) which is well known by simplicity, stability, and robustness [9]- [15].The non-linearity of SMC force the dynamics behavior of a non-linear systems to slide in the implementation of a control action that inherent the variable structure of DC/DC converter.The instantaneous values of the state variables reflect the functionality of the converter switches, making trajectory of the system in a proper selected surface called the sliding surface [14], [16]- [19].
Numerous studies propose various methods to design and implement SMC.According to Komurcugil et al. [20] an indirect SMC for single-ended primary-inductor converters (SEPIC) was implemented by applying a function of a sliding surface according to the error of input current only.A sliding surface function simplifies and reduces the cost of implementation.A proportional-integral (PI) regulator was used to generate the input current reference.A laboratory prototype of SMC buck and boost converters were used to investigate the validity of the proposed method.The investigation was carried out with simulation to verify the regulation of output voltage regulation during a sudden variation of the input voltage and load resistance as well.Research by Qaisi et al. [21] an investigation of a DC/DC buck converter with the SMC by a frequency response method, was implemented.The MATLAB program was used to obtain the graphic presentation of root locus, Polar, Nyquist, and bode plots to assess the performance of the controller of pulse width modulation (PWM) with proportional integral-derivative sliding mode voltage controller (PID SMVC).The controller was designed to obtain the appropriate control parameters and the result showed that the dynamic response of the PID SMVC is fast and efficient for different variety of applications.Research by Das et al. [22] an algorithm of integral sliding mode control (ISMC) was implemented for closed loop control of a DC-DC buck converter.The ISMC aimed to tackle the variable switching frequency issue, using PWM scheme using MATLAB/Simulink.The result of the comparative assessment of the ISMC indicate that, with different operating conditions, the frequency has very little fluctuation.According to Nhan et al. [23] a SMC method was adopted to manage the position and speed of a slotless self-bearing motor.The simplicity and effectiveness in reaching the reference value was evaluated analytically by using MATLAB/Simulink software.According to Ningappa et al. [24] a chattering was suppressed and steady state error was reduced with fast speed in a step down converter by implementing robust reaching law for SMC.
This paper is organized as follow: section 1 included the introduction.Hereinafter, section 2 illustrate the state space modeling and mathematical formula of DC/DC buck converter with CSMC methodology.Also the design of the ISMC and system modeling is included.Section 3 present the simulation outcomes and brief discussion.Finally, in section 4, the conclusions are drawn.

TOPOLOGIES AND MODES OF OPERATION
The basic structure of the DC/DC converter is illustrated in Figure 1(a).The state space method for Figures 1(b) and (c) is represented in ( 1) and ( 2): where  1 is the inductor current and  2 is the capacitor voltage.

Principle of operation of the sliding mode controller
The fundamental operation of SMC is to create a sliding surface, guiding the trajectory of the state variables on the way to a desirable source.The sliding surface  is calculated as in ( 3) and ( 4) [1]: where  is the coefficients of a sliding surface.
Performance analysis of different methods for optimal sliding mode control of … (Amer A. Chlaihawi) 119

Types of slide mode of operation
In this paper, beside type I: the conventional PWM, there are three types of SMC to be tested.These modes will be examined and discussed based on the number of state variables.Type II: SMC with two variables   and   .In this type, two state variables are sensed, the current and voltage of the capacitor as shown in Figure 2.

Figure 2. SMC with two variables vo and ic
Type III: SMC with two variables   and   [25].In this type, the current of the inductor and the output voltage are sensed, as it is illustrated in Figure 3.
where ,  are the coefficients of a sliding surface correspond to   and   respectively.ISMC for DC/DC converter is based on PWM scheme.PWM compares the control signal to a saw-tooth waveform to generate gate pulses with the same frequency as the desired switching frequency.ISMC has three parameters,  1 ,  2 , and  3 , where  1 is a load voltage error,  2 is a voltage error' rate of change, and  3 is an integration of voltage error.The parameters are described in its state space as in (10) [22]: The sliding surface for ISMC is expressed as in (11): Where  1 ,  2 , and  3 are sliding coefficients.The condition,  • < 0, () =  2 /2, has been defined.On the basis of this, the following inequality must be satisfied as in ( 12) [20]: Using the values from (10) and (11) to obtain (13): 0 < ( By setting the derivative of the sliding surface to zero  • = 0, equivalent control,   can be determined as in (14): Changing (13) to the equivalent control action results in (15): where (  −   ) +

RESULTS AND DISCUSSION
The DC/DC buck converter is aimed for a ripple of output voltage less than 0.3% and operates at frequency about 20 kHz.The parameter set strategies are =24 V, =1.776mH, =86 uF, and =10 Ω.The performance of DC/DC buck converter using the CSMC and ISMC, they have been examined and their validity to be tested by analyzing and representing maximum overshoot, peak, rise, and steady state times.Figure 5 represent the simulation of time response waveform of the system when using the DC/DC buck converter (type I), conventional SMC (type II), low pass filter (LPF) with SMC (type III), and ISMC (type IV) as illustrated in Table 1.

Bulletin of Electr Eng & Inf
ISSN: 2302-9285  Performance analysis of different methods for optimal sliding mode control of … (Amer A. Chlaihawi) The results demonstrate that, the DC/DC buck converter without SMC (type I) has an overshoot of 40.14%, undershoot of 9.793%, a  of 527 usec, a tp of 1.24 msec, and a  of 4.848 msec.Whereas, introducing converter based on conventional SMC with two variables,   and Vout, (type II) has demonstrated better performance as the figure change to an overshoot of 24.375%, an undershoot of 7.32%, a  of 496 usec, and a ts of 4.694 msec.Moreover, introducing converter based on CSMC with two variables,   and Vout, (type III) has demonstrated much better performance than the previous method, as the response change to an undershoot of 3.64%, a  of 3.253 msec, and a ts of 19.277 msec.Finally, presenting converter based on ISMC (type IV) which has demonstrated the best performance among the previous methods, as the figure change to demonstrate an undershoot of 1.991%, a  of 1.39 ms, and a ts of 1.85 msec.It is interesting to notice there is no overshoot when using conventional slide mode with two variables ( and Vout) and ISMC.Figures 5(a) and (b) illustrates output voltage and inductor current in ISMC respectively.It is noticeable that both the voltage and current has a lower ts and faster response than other compared methods to reach the steady state with a lowest ripple value.Dynamic performance and robustness of the four types have been checked in regard to load variation.The simulation results for the four topologies with sudden changes of load on steps 5 Ω, 10 Ω, and 15 Ω at interval of 12.5 msec have been examined.The simulation results demonstrate that the type I (fixed frequency PWM) and type II CSMC are vulnerable to high effect of output voltage during load resistance changing as shown in Figures 7(a) and (b).While, the type III LPFSMC has a stable output voltage and it is not affected by change of the load resistance.However, the system still has a considerable chattering in its voltage as detailed in Figure 7(c).Finally, type IV is presenting ISMC, which has demonstrated the best performance among the other methods in terms of smooth output voltage with no overshoot as shown in Figure 7(d).

CONCLUSION
In this paper, the basic PWM and three different types of SMC controllers for DC/DC buck converter have been examined by investigating the transient and steady state responses of the output voltages, inductor, and capacitor current.The results of analysis and simulation of proposed methods are compared by different parameters and operating conditions.It is found that the ISMC control strategy has the best dynamic performance over the other tested methods, by minimizing the settling time and chattering of the output voltage.The simulation result demonstrates that the voltage regulation of ISMC has a stable response under rapid changes of the load variation.Also, it is proven that, the ISMC is less sensitive to disturbances caused by power supply variations.For future development, inorder to get better performance, a double ISMC will be adopted in a DC to DC buck boost converter.

Figure 1 .
Figure 1.Buck converter; (a) basic circuit, (b) equivalent circuit at on-state, and (c) equivalent circuit at off-state

Figure 3 .Figure 4 .
Figure 3. SMC with two variables vo and iL

Figure 5 .
Figure 5.Time response of the compared four types of control to (a) output voltage and (b) inductor current

Figure 6 .Figure 7 .
Figure 6.Time responses of output voltage, corresponding to input voltages from 18 V to 30 V for DC/DC buck converter with (a) PWM-type I, (b) CSMC-type II, (c) LPFSMC-type III, and (d) ISMC-type IV

Table 1 .
The performance of different types of SMC and PWM for DC/DC converter