Fuzzy Sliding Mode Control of DC-DC Boost Converter

—A sliding mode fuzzy control method which combines sliding mode and fuzzy logic control for DC-DC boost converter is designed to achieve robustness and better performance. A fuzzy sliding mode controller in which sliding surface whose reference is obtained from the output of the outer voltage loop is used to control the inductor current. A linear PI controller is used for the outer voltage loop. The control system is simulated using Matlab/Simulink. The simulation results are presented for input voltage and load variations. Simulated results are given to show the effectiveness of the control system.


INTRODUCTION
Voltage-mode control and current-mode control are two methods used to control DC-DC converters [1].The voltagemode control is robust to disturbances, but slow.Current-mode control has a fast transient response but is more complex than voltage mode control.Classical PI and hysteretic controllers are the most used controllers for DC-DC converters.The linearized converter model around an operating point obtained from the state space average model [2] is used for conventional linear controllers.The classical controllers are simple to implement but the effect of variation of system parameters cannot be avoided, due to the dependence of linearized model parameters on the converter's operating point [3].The controller for DC-DC converters must account the nonlinearity and parameter variations.It should maintain stability and provide fast response in any operating condition.Classical control methods for DC-DC converters are not much efficient in achieving the desired performance [4][5].A nonlinear control technique developed in [6] derived from variable structure control theory is called sliding mode control (SMC) has advantages of simple implementation, robustness and fast transient response [7].SMC is used to maintain the output voltage of the converter to be independent of parameters, input and load variations [8].It provides invariant system dynamics to uncertainties when controlled in the sliding mode [9].SMC has a problem of chattering.Chattering is undesirable oscillations having finite amplitude and frequency due to the presence of unmodeled dynamics or discrete time implementation [10].Some methods such as equivalent control and boundary layer approach are used to reduce the chattering.Equivalent control based methods cannot be used to reduce chattering because of their finite number of output values.The boundary layer approach has a problem of reaching sliding mode due to the replacement of the discontinuous control action with a continuous saturation function [10].Fuzzy sliding mode control (FSMC) is another method used to avoid the chattering problem [11].Fuzzy logic control is a nonconventional and robust control technique which is suitable for nonlinear systems characterized by parametric fluctuation or uncertainties [12][13].FSMC has the advantage of not being directly related to the mathematical model of the controlled systems as the SMC.FSMC combines fuzzy logic and SMC to control the DC-DC converter to achieve better performance.In FSMC, the fuzzy system is used to estimate the upper bound of the uncertain disturbances to reduce the chattering.Fuzzy logic controller (FLC) has an increased level of efficiency regarding nonlinear converters.In this method, the control action is generated by linguistic rules which do not require an accurate mathematical model of the system, hence the complexity of the nonlinear model is decreased [14][15].FLC overcomes the deficiency resulting from using linearized small signal models and improves the dynamic behavior.

II. DC-DC BOOST CONVERTER MATHEMATICAL MODEL
The output voltage of a boost type DC-DC converter is higher than the input source voltage.This is achieved by periodically opening and closing the switching element in the converter circuit.The DC-DC boost converter is shown in Figure 1.The switching period is T. The switch is kept open for time (1-D)T and is kept closed for time DT.The analysis is done by examining voltage across and current through the capacitor for both times, when the switch is open and when the switch is closed.Continuous conduction mode (CCM) will be assumed in which the inductor current will have a nonzero value due to load variations.When the switch is closed, the diode in the circuit is reverse biased and becomes open circuit as shown in Figure 2(a).Then the voltage across the inductor is: and the current through the capacitor is: ol input and f discontinuous (10) such that the , (11) disturbances.(12) states to reach the control str inequality mu (13) rantees the sy me [17].f the inputs w ction of outpu re is presente buck-boost con oller was also ons.It is foun and robust to ances [16].The performa st tested for the  rter is oltage and current waveforms are shown in Figure 10 for a step change in the desired reference voltage from 30V to 40V at time t=0.5s.Load variation is applied to the FSM controlled boost converter to test its robustness under load variation.Figure 11 shows the voltage and current waveforms when the load resistance is changed from R=200 to R=100 at time t=0.5s.30 V output voltage is maintained during the load change.Test for the input voltage change is also made to see the effects of the input voltage variations on the output voltage.A step change in input voltage is made when the converter is at steady state with a 30V output voltage.The performance of the controlled system is shown in Figure 12 and Figure 13 when a change in input voltage from 20V to 15V and 20V to 25V occurs at the time t=5s.In Figure 12, a decrease in input voltage occurs and in Figure 13, an increase in input voltage occurs at t=0.5s.Figures 10-13 prove the robustness of the FSM control against changes in the load and input voltage.The recovering feature of the FSM controlled boost converter can be clearly seen.

VIII. CONCLUSIONS
A sliding mode fuzzy controller designed and simulated for a DC-DC boost converter to improve the performance and achieve robustness.The error obtained from the load current and the reference current which is the sliding surface and its derivative are used as inputs to the fuzzy controller which controls the duty ratio of the signal driving the switch in the converter circuit.Matlab/Simulink programming environment is used for the simulations.The obtained results show that the controlled system is robust against load and input voltage variations.A good dynamic performance is also achieved.
Fig. 2. Boost Rearranging uations by tak rrent through ), (3) and (2), lues 0 and 1 osed when u=1 = 1 = 1 u Taking x 1 =i Fig. 3 Input data ar embership fun d the linguistic d then control ed to convert k) which is easured curren he output of th , which is Fig VI.

Fig. 10 .
Fig. 10.Output voltage and output and input current waveforms for step change in reference voltage.

Fig. 11 .
Fig. 11.Output voltage and output and input current waveforms for step load variations.

Fig. 12 .
Fig. 12.Output voltage and output and input current waveforms when input voltage decreased from 20V to 15V.

Fig. 13 .
Fig. 13.Output voltage and output and input current waveforms when input voltage increased from 20V to 25V.