Digital Control of DC – DC Buck Converter

Digital Control of DC – DC Buck Converter

Smruthi M Krishnan

Department of Electrical and Electronics Engineering

R V College of Engineering, Bangalore, Karnataka, India

Prof. Vasudeva Banninthaya K

Associate Professor, Department of Electrical and Electronics Engineering

R V College of Engineering, Bangalore, Karnataka, India

Abstract

The paper describes the design and implementation of a digital controller for DC DC Buck Converter. Digital controllers are increasingly replacing their analog counterparts due to its improved flexibility, easier integration, programmability, reduced design time, size, cost and improved reliability. Switching devices are selected based on the power handling capability and high frequency switching. Voltage mode control is used in order to get faster response. Proposed DC DC Buck Converters are controlled using PD controller and Full State Feedback Controller designed using Pole Placement technique. The PD controller has been implemented on an

Power input

Switching converter

Control input

Controller

Feedforward Feedback

Reference

Power output

Atmega32 – 8 bit Microcontroller. The Full State Feedback controller has been simulated in MATLAB/SIMULINK.

1. Introduction

   The field of power electronics is concerned with the processing of electrical power using electronic devices. The key element is the switching converter. In general, a switching converter contains a power input, control input and a power output port as shown in fig 1. The raw input power is processed as specified by the control input, yielding the conditioned output power. In a dcdc converter, the dc input voltage is converted to a dc output voltage having a larger or smaller magnitude.

   Figure 1. A General Switching Converter with Controller

   A Digital controller implementation has the following advantages: improved flexibility, reduced design time, programmability, elimination of discrete tuning components, improved system reliability, easier system integration, and possibility to include various performance enhancements.

2. Converter Topology and Operation

   The converter topology selected is buck converter. The input voltage is 12V and output voltage has to be regulated to 5V. The load current is 1-2A range. The switching frequency of fs = 62kHz is selected. It is desired to maintain a tight voltage regulation.

   In buck converter the average output voltage is lesser than the dc input voltage[2][3][4]. The output voltage is controlled by controlling the switching duty cycle. The switching buck converter is also called as step down converter is shown in fig 2.

   The ratio of output to input is given by

   v0 D vi

   Iin

   I0

   The term D is the duty ratio and defined as the ratio of the ON time of the switch to the total switching period.

   analysis does not include any parasitic resistances (all ideal case).

   Iin

   Vi

   Switch s

   L

   iL I0

   Duty Ratio D v0

   vi

   2.3 Inductor

   0.416

   C

   D

   DC R

   Figure 2. Buck Converter Circuit

   From Fig 2 we can derive a simplified differential equation based on the assumption that the voltage across the load, and thereby across the capacitor, is fairly constant. The differential equation in terms of the current through the inductor, when the switch is closed, may now be written as

   Using Kirchoffs voltage and Kirchoffs current laws, the dynamics is described by the following set of

   L vi

   v0 D / f s I ripple

   equations

   When switch u=1

   L di v v

   The current ripple will be limited to 30% of maximum load.

   dt

   C dv

   0 i

   i vo

   I ripple

   0.3I 0

   L 78 H

   0.6 A

   When switch u=0

   dt R

   L di v

   dt 0

   dv v

   2.4. Transformer core selection

   The size of a power transformer is determined by Area product, and is given by the product of the core cross section (Ac) and the window area (Aw)

   Area product (Ap) = Cross section area (Ac) x Window area (Aw)

   C i o

   dt R

   By comparing the above equations we get

   di

   An appropriate core will be selected which must have area product greater than the calculated Ap [4]. Area product is calculated before selecting the suitable core by using below formula.

   L dt v0 uvi

   dv v

   Ap ( D Pout (1 1 )) /(kw fs B J 10 6 )

   C i o

   dt R

   2.1. Design Specification Input voltage vs = 12V Output voltage v0 = 5V Load current I0 = 2A

   Switching frequency fs = 62KHz Time period Ts= 0.016 ms

   2.2 Duty cycle

   For calculation of the duty ratio we will first of all assume that the converter is in steady state. The switches are treated as being ideal, and the losses in the inductive and the capacitive elements are neglected. Also it is important to point out that the following

   = 382.70mm4

   Where,

   kw = 0.5 B=0.3T J = 6A/mm2

   Kw=Window Utilization Factor; J=Current Density; B=Flux Density; Pout=Output Power;

   Fs=Switching Frequency; D=Maximum Duty Cycle =Efficiency

   1. Core selection

      Core part number : T106-26

      Material : Iron Powder Inductor factor AL : 93nH/T2

   2. Number of turns

      Inductance L is given by L = AL * N2 AL : inductor factor

      N = 30 Turns

   3. Selection of wire guage

   Wire gauge is selected based on the RMS current in each winding. RMS current for each winding can be calculated as

   Irms I0 D 2 0.416 1.29A

   The output voltage of the switch-mode DC-DC converters are regulated to be within a specified range in response to changes in the input voltage and the load current. There are two control methods for DC-DC converters: voltage mode control and current mode control. There are three main problems that can be examined in the study of systems in the controls: system dynamics, system identification or modelling, and system control. In system control, the system is known, and the input to the system that produces a desired output must be determined.

   In the last section we saw that the steady-state output of a dc-dc converter, usually the output voltage, is controlled by the duty ratio. To account for changes in load current, input voltage, losses, and non idealities in

   Area of conductor =

   Irms J

   0.215mm2

   the converter, feedback based control is required. The sensed output voltage is multiplied by a feedback gain before being compared with a reference value. The

   The AC resistance increased due to Skin depth and calculated as follows

   s 2

   conductivity 2 fs

   Permeability(µ) = 1.4 10 7 turns/A2

   Therefore selected wire should have a diameter less than 0.897mm(or 2* s).

   2.5 Capacitor

   The output capacitor is assumed to be so large as to yield v0 (t) =V. However, the ripple in the output voltage with a practical value of capacitance can be calculated. Assuming that all of the ripple component in iL flows through the capacitor and its average component flows through the load resistor. Effective series resistance (ESR) is used to dominate the voltage ripple and when ESR requirement is met, the capacitors capacitance is usually adequate. The ripple voltage is limited to 10% of maximum load.

   error is fed to an appropriate error compensator that generates a control voltage, which is converted to duty ratio d by the PWM block[1][6].

   The proposed digital controller is shown in fig 3. The output voltage is sensed and compared with a refernce voltage. The error signal is given as the input to the PD regulator. The output of PD regulator is given as the input to the pulse width modulator. The duty cycle is adjusted based on the error signal to make the output voltage follow the reference value.

   Switching Converter

   V

   Pulse width modulation

   A/D converter

   Controller

   Figure 3. Block Diagram of Digital Controller

   dv 0.1 v0

   Iripple 1

   C fs

   0.5V

   20 F

   A controller has to be designed to regulate the output voltage of a buck converter to a constant value. The specifications and parameters are input voltage is 12v

   dv (Iripple * esr)

   and output voltage is regulated to 5v. The load current is 1-2A range. The switching frequency of fs = 62 KHz is selected

   The transfer function of system is given by

3. Controller Design

   v0

   vi LCs 2

   rcCs

   (rc

   1

   rl )Cs 1

   Plant

   1. PD Controller

      A digital PID controller and its variants can be designed using a variety of methods available in literature [4,5,6]. A PD controller is a simple two term controller. The transfer function of the most basic form of PD controller is given by

      u B +

      dx/dt

      X

      y

      C

      –

      A

      c(s) kp kd s -k

      Where kp proportional gain kd derivative gain

      _	e	Controller C(s)	u	Plant G(s)	y

      R

      +

      Figure 5. Full State Feedback Regulator

      c

      A

      1

      Ackermanns formula may be used with single-input, single-output (SISO) systems. Ackermanns formula is

      K [0

      0……. 1]M 1 ( An

      n 1 ….

      n 1 A

      n I )

      Figure 4. PD Controller Block Diagram

      Figure 4 shows the PD controller in a closed loop unity feedback system. The variable e denotes the tracking error, which is sent to the PD controller. The control signal u from the controller to the plant is equal to the proportional gain (kp) times the magnitude of the error plus the derivative gain (kd) times the derivative of the error. Four major characteristics of the closed-loop step response are rise time, overshoot, steady state error, settling time. The controller gains were determined experimentally. The following figure shows the simulation result of PD controller applied to Buck Converter

   2. Controller Design using Pole Placement

   3.2.1 State Space Model

   Modeling using state space averaging is well known method since many years. The state space averaged model of the converter can be expressed as

   x Ax Bu

   y cx

   The state variables are the output voltage and inductor current

   o

   x v i t y v

   The matrices of the system are written as follows

   1

   Technique

   For a system that is completely controllable and where all the states are accessible, feedback of all of the states through a gain matrix can be used to place the poles at any desired location in the complex plane [5]. The control law used for state feedback is

   0

   A 1

   C

   vd

   L B L

   1 0

   RC

   C 0 1

   u kx

   which uses the matrix K to place the poles of the system at desired locations. This type of compensator is said to employ full state feedback (FSFB). A FSFB regulator is shown in fig 5

   The main advantage of state space controllers is pole placement. This method allows placing poles of the system to obtain desired outputs. The above system is completely controllable and observable. In this case we choose the damping factor and time of regulation tr.

   tr 3

   n

   Plant

   r

   -k1

   dx/dt

   u

   X

   y

   B C

   –

   + + +

   + +

   A

   -k

   Figure 6. Full State Feedback Controller

   Let, r = system input when state variable feedback is employed

   = feedback signal obtained from state variables u= plant input

   The feedback signal is obtained from state feedback and it is related to the state variables by the equation

   kx

   Therefore plant input is given by the control law

   u = r kx

   By comparing between the characteristic polynomial of system with the desired polynomial gives the design equations of the feedback coefficients.

4. Simulation Results

   The controller was simulated in MATLAB/SIMULINK to verify the properties of proposed controller. The parameters of

   converter used in simulations are L=80 H,, C=22 F, R=100. Damping factor and time of regulation for voltage loop =0.016, tr=0.004s.

   Figure 7. Simulation of PD Controlled Buck Converter

   Figure 8. Simulation of Full State Feedback Controller using

   Pole Placement Technique

5. Hardware Setup

   Digital control of buck converter is done using ATmega32 controller.

   Switch : Power MOSFET IRF540N 100v 33A. With these ratings, the same power MOSFET was being used in the main switch

   Inductor: The inductance value chosen was 80uH.

   Capacitor: The value selected was 22uF

   The inductor and capacitor values were calculated using the following

   Duty cycle : d = v0/vin

   Maximum ripple current: di = 0.3*I0 Inductor value : L = ((vin-v0)*(d/fs))/di Maximum ripple voltage : dv = (0.1*v0)

   Capacitor value : C = (di*(1/fs))/(dv-(di*esr))

   Hardware implementation of buck converter is shown in Fig 9 and PWM input to the MOSFET and regulated output voltage is shown in Fig 10.

   Figure 9. Buck Converter Circuit

   Figure 10. PWM Input to the Mosfet (Green) and Regulated

   Output Voltage (Yellow)

   New Age International (P) Limited, 2009, first edition, ISBN 10: 8122403395 / ISBN 13: 9788122403398.

   1. Hebertt Sira-Ram´rez, Ram´on Silva-Ortigoza, control design techniques in power electronic devices, Springer-Verlag London Limited 2006,

      ISBN-13: 978-1-84628-458-8

   2. B. Arbetter and D. Maksimovic, Control Method for Low- Voltage DC Power Supply in Battery Powered Systems With Power Management, IEEE Power Electronics Specialists Conference, St. Louis, Missouri, 1997.

6. Conclusion

   Digital controller implementation allows potentially much greater flexibility and better utilization of switching power converters. In this paper, design and implementation of a digital controller for an experimental low-power Buck Converter has been explained. A buck converter circuit was realized with appropriate Inductors and Capacitors. Control of buck converter is done using PD controller and Pole Placement technique. The proposed controller structure is simulated in MATLAB/SIMULINK and is also implemented using Atmega controller.

7. References

1. Yousefzadeh, Proximate Time-Optimal Digital Control for DC-DC Converters Power Electronics Specialists Conference, 2007. PESC 2007. IEEE

2. L Wuidart, Topologies for Switched Mode Power Supply Application Note, STMicroelectronics, 1999.

3. Abraham I Pressman, Keith Billings, Taylor Morey Switching Power Supply Design, McGraw-Hill Prof Med/Tech, 26-Mar-2009, 3rd edition, ISBN 13: 9780071482721 ISBN 10: 0071482725.

4. Ned Mohan, Tore M Undeland and William P Robbins, Power electronics, Converters, applications and design 3rd edition, 2006 by John Wiley & sons.

5. L Umanand, S R Bhatt, Design of Magnetic Components for Switched Mode Power Converters,