Improvement of Dynamic Response for Buck

Improvement of Dynamic Response for Buck Converter Using Sliding Mode Like Control Technique Mr. D. Lenine* Asst. Professor / EEE RGMCET, Nandyal e-mail: [email protected].

Dr.Ch. Sai Babu** Professor / EEE JNTU, Anantapur e-mail: [email protected].

Abstract-Buck converters are more efficient and self regulating, making it useful for tasks such as converting the 12-24V typical battery voltage in a laptop down to several volts needed by the processor, microcontroller, used in notebook computers, in digital signal processor and in many industrial application. In this project a simple non linear control scheme called a new Sliding Mode Like Control (SMLC) is employed, that has good features of sliding mode control (i.e. high robustness, guarantee first order response and large signal stability) and eliminates its ultimate problems (i.e. variable switching frequency and non-zero steady state error). The response of these controllers can be defined directly in the time domain. This control scheme is developed for buck topology. This project proposes analysis and design of control technique for high performance DC-DC buck converter. The results are verified through MATLAB/SIMULINK and HARDWARE implementation. Key words: Buck converter, Sliding mode like control technique, Experimental setup, Simulation and experimental results

I. INTRODUCTION Efficient DC-DC power conversion is done by switched mode power converters. Switched mode power converters consist of reactive elements and switches. The principle employed is to alternately draw energy from the source to charge up reactive (energy storage) elements, such as capacitors and inductors, and then to deliver the stored energy to the load. When the frequency of such energy packets delivered to the load is large, the load experiences practically uninterrupted dc power. Satisfactory operation of such converters depends on suitable configuration of reactive elements, and appropriate method of controlling the switches to obtain efficient power conversion. Switched mode dc-dc converters are nonlinear and time variant systems, and do not lend themselves to the application of linear control theory.

Mr.K.S.S. Prasad Raju*** PG Student / EEE RGMCET, Nandyal e-mail: [email protected]

Sliding Mode (SM) controllers were introduced initially for Variable Structure Systems (VSS) as in [1]. Characterized by switching, DC-DC converters are inherently variable structured. Therefore, it is appropriate to apply SM controllers to dc/dc converters. This is especially true for buck converters operating in the Continuous Conduction Mode (CCM), which have measurable continuous controllable states (output voltage and its time derivative) as in [3]. Although well known for their stability and robustness toward parameter, line, and load variations (ability to handle large transients), SM controllers are seldom used in power converters. In this paper the above techniques suffers from non-zero steady state error, variable switching frequency, stability which are the most important specifications to improve the dynamic response of the system the proposed control scheme will overcome its ultimate problems and it can be an attractive alternative to the classic controller in power converter applications where high dynamic performance is preferred. The buck topology configuration and prototype model of sliding mode like control technique is explained in section II and section III respectively. In section IV the simulation and hardware results are presented and the conclusion is given in the last section.

II. CONFIGURATIONS A. Classification of different Topology Improved power quality converters are classified on the basis of topology and type of converter used. The topology-based classification is categorized on the basis of buck, boost, buck– boost, multilevel, unidirectional and bidirectional voltage, current, and power flow as in [2]. The converter type can be stepup and step-down choppers, voltage source and current-source inverters, bridge structure, etc as in [4]. These converters are developed in such vastly varying configurations to fulfill the very close and exact requirement in variety of applications. Some of these improved power quality converters are improved to provide better performance from primitive configurations.

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B. System Configuration The topology of Buck converter is shown in Fig. 1. A new non-linear control scheme called sliding mode like control scheme is proposed as in [1].

The above equation is a digital approximation for integration as in (1) and (2). Saturation in the integration path prevents integrator complete and limits the duty cycle between “0” and “1” as shown in Fig 2. In Fig. 2, z is the Z-transform variable and 1 Z represents the unit time delay.

In the buck converter, the average output voltage Vo, is less than the input voltage, Vs hence the name “buck” a very popular regulator .The circuit diagram of a buck regulator using a power MOSFET is shown in Fig. 1, and this is like a step-down converter. The circuit operation can be divided in to two modes. Mode 1 begins when MOSFET is switched ON at t = 0. The input current, which rises, flows through filter inductor (L), filter capacitor (C), and load resistor (R). Mode 2 begins when MOSFET is switched OFF at t = t1 . The freewheeling diode (D) conducts due to energy stored in the inductor; and the inductor current continues to flow through L, C, load, and diode (D). The inductor current falls until MOSFET is switched ON again in the next cycle.

Figure 2. Block diagram of proposed Sliding Mode like Controller The above diagram depicts the sliding mode like control of buck converter; a sliding line is given to define the desired response as in [1]. The switch is turned ON below the sliding line and OFF above it. Desired Dynamic response (Zero change in duty cycle)

Upper boundary line

e. Decrease In duty cycle

D Lower Boundary line

Figure 1. Block diagram of buck converter with control technique

Increase In duty cycle

Maximum Decrease in Duty cycle

C B

H

A F

C. The Proposed Sliding Mode Like Control (SMLC)

Maximum Increase in Duty cycle

E

e

G

A new non-linear control scheme called sliding mode like control scheme is proposed. A voltage mode (direct duty ratio) digital control Scheme is used, where the output voltage is sensed and sampled with period

Ts . The duty cycle u ( t ) of

the fixed switching frequency converter is altered by SMLC. The inputs to the controller are the error of error Δe ( k ) , which is calculated by

Δ e ( k ) = e ( k ) − e ( k − 1)

e ( k ) and the change

(1)

The output of the controller is the incremental change of the duty cycle Δu ( k ) . The incremental change of the duty cycle

is then added to the previous value of the duty cycle u (k − 1) .

u ( k ) = Δu ( k ) + u ( k − 1)

(2)

Figure 3. Basic idea for sliding mode like control This forces the response of the converter to follow the sliding line. In sliding mode like control, the duty cycle is increased when the system operates below the sliding line and decreased when the system operates above the sliding line. Along the sliding line the duty cycle is zero. The magnitude of change in duty cycle is greater further from the sliding line up to some limit. This limit is reached at the upper and lower boundary lines. Therefore, the response of the system is forced to follow the sliding line to give the desired dynamic response as with sliding mode control. To clarify this concept, let us consider the points labeled through “H” in Fig 3. The changes of duty cycle at point A and point “H” are zero; point “A” is a stable point because the rate of change of error is zero, while point “H” is not stable because the change of error is non zero. Therefore, the system will move from point H eventually. For


example, it is assumed that the maximum change of duty cycle is equal to . At point “C” and “D”, the changes of duty cycle are -20%. At points “F” and “G”, the changes of duty cycle are +20%. At point “B”, the change of duty cycle is -10%, and at point “E”, it i.e., +10%, since this points lie half away between the sliding line and boundary lines. The sliding mode like control described above will now precisely define as in (3). The rate of error “e” can be approximated as e (k ) − e (k − 1)

.

e =

Ts

=

Δ e (k

)

(3)

Ts

The inputs to the sliding mode like control block in Fig. 2 are 1

1

“ e ” and “ Δe ” (note that sample numbers will no longer be included in the notation; dependence on k is implicit). They are related to “ e ” and “ Δe ” by the gains “G1” and “G2” that serve to scale the inputs as in (4) and (5).

(4) (5)

1

e = G 1 .e Δ e 1 = G 1 .Δ e

Therefore,

Δu ( k ) = ( m + n ) e ( k ) − nΔe ( k )

(9)

This scaling is useful in case where digital hardware used to implement the control algorithm has limits on the numerical range it can handle. The output of the sliding mode like 1

control block is the normalized Change of duty cycle “ u ”. It is scaled by “G3” to give the actual change of duty cycle. Controller zero can be expressed as

Zo =

1 1 + k .Ts

(10)

This means that the sampling frequency, desired dynamic response and controller zero are coupled. There are constraints on appropriate values of the sampling/switching frequency and desired dynamic response to maintain small signal stability.

III. PROTOTYPE MODEL OF SLIDING MODE LIKE CONTROL (SMLC)

This scaling is useful in case where digital hardware used to implement the control algorithm has limits on the numerical range it can handle. The output of the sliding mode like control block is the 1

normalized Change of duty cycle “ u ”. It is scaled by “G3” to give the actual change of duty cycle as in (6).

Δu = G3 .Δu1

(6)

It should be noted that for small signals that do not cause saturation in the output integration path as shown in Fig. 2 and that are applied when the system is in steady state (i.e., when the controller inputs are very close to the zero error and zero change in error values), the controller is essentially a digital PI controller as in (6). In this case, the small signal model of buck converter can be used to assess the small signal stability of the control loop. The following analysis will reveal the relationship between the controller parameters, switching frequency and stability. It is noted that the transfer function for a digital PI controller is in the form

U (Z

)= E (Z )

m .z + n z −1

(7)

Where “m” and “n” are parameters. This transfer function can be written in the time domain as

u ( k ) = ( m + n ) e ( k ) − ne ( k ) − e ( k − 1) + u ( k − 1) (8)

Figure 4. Experimental Block Diagram of DC –DC Buck Converter The hardware implementation with their limiting factors kept in consideration. Fig 4. shows experimental block of DC-DC buck converter. The absolute maximum ratings indicate sustained limits beyond which damage to the device may occur. All the thermal resistance and power dissipation ratings taken are under board mounted and still air conditions [1] , [2]. The Pulse With Modulation (PWM) generator (TL494) incorporates on a single monolithic chip all the functions required in the construction of a pulse-width-modulation control. Fig. 5 shows the pin diagram of (TL494). The TL494 contains an error amplifier, an on-chip adjustable oscillator, a dead-time control comparator, pulse-steering control flip-flop, a 5V, 5% precision regulator, and output-control circuit. The architecture of these devices prohibits the possibility of either


output being pulsed twice during push-pull operation. The advantages of (TL494) are complete PWM power-control circuitry, complete PWM power-control circuitry, and uncommitted outputs for 500mA sink or source current output control selects single-ended or push-pull operation, internal circuitry prohibits double pulse at either output.

Figure 6. Hardware Set-up Let us consider the current ripple to be 10% and the voltage ripple to be 1% Figure 5. Pin Diagram of TL494 The function of optoisolator (6N137 or 4506) is to isolate the control circuit from power circuit. The PWM signal from TL494IC is not directly fed to the power circuit in order to protect the PWM signal it is essential to provide isolation circuit between power circuit and control circuit. The features of optoisolatorare very high speed (10 M. Bit/s), Superior CMR-10 kV/µs, double working voltage-480V,Fan-out of 8 over -40°C to +85°C,Logic gate output,Strobable output The IR2110/IR2113 are high voltage, high speed power MOSFET and IGBT drivers with independent high and low side referenced output channels. A MOSFET driver circuit is designed to connect the gate directly to a voltage bus with no intervening resistance other than the impedance of the drive circuit switch. Gate drive act as a high-power buffer stage between the PWM out put of the control device and gates of the primary power switch MOSFET. This 30A, 200V, 0.085 Ohm, n-Channel enhancement mode silicon gate power field effect transistor is designed, tested and guaranteed to withstand a specified level of energy in the breakdown avalanche mode of operation. These MOSFETs are designed for applications such as switching regulators, switching converters, motor drivers, relay drivers, and drivers for high power bipolar switching transistors requiring high speed and low gate drive power. They can be operated directly from integrated circuits this switched voltage signal undergoes rectification in the filter circuit. Finally rectified pure DC signal is seen at the output terminal. The filter capacitor eliminates the unwanted ripple in the DC output.

The current ripple is

ΔI =

V s d (1 − d

)

fL

(3.1)

Taking the duty ratio of 0.45 and switching frequency of 400k Hz , The switching frequency should be greater than f o i.e.

fo =

1 2 ∏ LC

(3.2)

Therefore, the inductor obtained is 1mH The voltage ripple is

ΔV =

Vs d (1 − d ) 8LCf 2

(3.3)

The capacitor obtained is 220 micro farads.

IV. SIMULATION AND HARDWARE RESULTS The simulation wave forms which are shown for input voltage of the buck converter in open loop are shown in Fig 7. The gate pulses which are applied to the switch are shown in Fig 9. The step downed output voltage waveform figures are shown in figure 8. The inductor current waveforms are shown in fig 9. it is observed that there is non-zero steady state error present in the open loop condition.


Figure 11. Input Voltage of Buck Converter Figure 7. Input Voltage of Buck Converter

Figure 12.

Gate Pulses

Figure 8. Gate Pulses

Figure 13. Inductor Current of Buck Converter

Figure 9. Output Voltage of Buck Converter

Figure 14. Output Voltage of Buck Converter Fig 15. shows the input voltage waveform, Fig 16. shows the gate pulses obtained from feed back path which is applied to the gate of the MOSFET. Fig 17. shows the resultant output voltage which is step down through several volts. Fig 15. Fig 16. and Fig 17. are the experimental results of the sliding mode like control technique.

Figure 10. Inductor Current of Buck Converter Fig 11. shows the input voltage waveform of the buck converter in the closed loop. Fig 12. shows the gate pulses and it is observed that they maintain constant switching frequency. Fig 13. shows the output current and Fig 14. shows the output voltage and it is observed that the steady state error is reduced to zero in the closed loop condition.

Figure 15. Input voltage of Buck Converter


V. CONCLUSION The sliding mode like controller is a promising control method that obtains the excellent dynamic response. A modular simulink model for Buck converter simulation has been introduced and the hardware is implemented for the same. The proposed control scheme has fixed switching frequency and provides zero steady-state error; this decreases the switching losses and increases the efficiency. The conventional method controlling buck converter with the sliding mode like controller is simple and accurate and hence effective in improving the dynamic performance of the converter. ACKNOWLEDGEMENT

Figure 16. Gate Pulses

We express our sincere thanks to TEQIP for providing us good facilities. I express sincere thanks to my guide and others who have helped us directly or indirectly in carrying my work successfully. REFERENCES [1] Alexander G.Perry, Guang Fen, “A New Sliding Mode Like Control for Buck Converter,” IEEE Transactions on Power Electronics Applications. Vol 33, no2, Mar/Apr.2004. [2] V.S.C. Ravi raj, P.C.Sen, “Comparative study of Proportional Integral, Sliding Mode, and Fuzzy Logic Controllers for Power Converters,” IEEE Transactions on Industry Applications. Vol 33, no2, Mar/Apr.1997. [3] R.Venkataramanan, A.Sabanavonic, S.Cuk, “Sliding Mode Control of DC-to-DC Converters”, IECON’85 Conference proceedings,pp.251-258,1985.

Figure 17. Output voltage of Buck Converter TABLE I

COMPARISION BETWEEN HARDWARE AND SIMULATION RESULTS

[4] R.D.Middlebrook, “Small Signal Modeling of PulseWidth Modulated Switched-Mode Power Converters,” Proceedings of the IEEE, vol.76, No 4, April 1988. [5] Aleksandar Prodic, Dragan Maksimovic: ‘Dead-Zone Digital Controllers for Improved Dynamic Response of Low Harmonic Rectifiers’. IEEE Transactions on Power Electronics, vol. 21, no.1,January 2006.pp,173_181 [6] ‘POWER ELECTRONICS - Converters, Applications and Design’, Mohan, Under land, Robbins, John Wiley & Sons [7] ‘POWER ELECTRONICS – Circuits, Devices and Applications’, Muhammad H. Rashid, Prentice Hall of India Private Limited [8] ‘POWER ELECTRONICS’, M D Singh, K B Khanchandani, Tata McGraw – Hill Publishing Company Limited.
