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Closed loop Control of DC to DC boost converter



DC-DC boost converter boosts the DC input voltage to higher DC voltages  according to the duty cycle of  PWM  applied to the mosfet used to charge the inductor.While the mosfet state is on the inductor gets charged, than when the mosfet turns off the voltage stored in inductor and input voltage gets added and appears in the output. But if only these components are used output Voltage will be pulsating and have a frequency similar to that of mosfet switching. So we need to put a capacitor in output in order to oscillating output to smoother output. Still the stored voltage in capacitor will backflow through the mosfet when it is on, So we need to place a diode in between mosfet and capacitor in order to prevent backflow of stored charge in capacitor.After these circuit requirements are completed the boost converter will be boost low voltage DC input to higher DC voltages.The circuit should look like as shown below:-

Boost Converter Circuit

Output Voltage calculation

The output voltage of boost converter will be as follows

Vout  = vin /(1-Duty_cycle)

PWM output signal is in scale of (0-255) in atmega 328 due to 8 bit output register so to calculate duty cycle PWM output needs to be mapped from (0-155 to 0-100) that can be done in Arduino by the function
Duty_cycle = map(PWM,0,255,0,100) 

Running Converter to maintain constant output voltage with varying load

as the load increases the load will discharge inductor to much lower levels thereby increasing time required by inductor to charge itself to a suitable required voltage so by the increase in the load of converter the duty cycle of the signal firing the mosfet will increase if  the converter is operated in closed loop trying to maintain constant output voltage. Similarly duty cycle will decrease if the load connected to the output of converter decreases.

Running Converter to maintain constant output voltage with varying input voltage

as the input voltage increases the inductor will charge at faster rates reducing the time required by inductor to charge upto required output voltage there by reducing duty cycle of mosfet firing signal. if the voltage decreases the time required to charge the inductor to required voltage level increases thereby increasing the duty cycle of the mosfet firing signal.

Relation between inductor size and mosfet firing frequency 

Inductor rating required is inversely proportional to firing frequency of mosfet. Because larger the inductor size longer time it will take to charge and discharge hence once charged boost converter with larger inductor size will be able to hold the output voltage level steady longer than boost converter with lower inductor size in equal loads. so converter with lower inductor size will need to charge more frequently than higher inductor sized converter. so switching frequency and inductor size are inversely proportional. By using higher switching frequency we can reduce the inductor size used in the converter, reducing both cost and size of converter. 



Simulation
MATLAB Simulation circuit

Tuned PID response in MATLAB


Hardware 



three inductors were connected in series in order to achieve total inductor size of 2200 uH, one capacitor of 470 uf and 220V, irf540 mosfet is used along with heat sink I was able to get maximum stable output voltage of 97V With the load of 270 ohm connected in output. that is 34.84 Watt at 97 volts.

following Arduino code was used to stabilize output voltage

int voltage  = 0;
int Pwm = 100;
void setup()
{
pinMode(9,OUTPUT);
pinMode(A0,INPUT);
}

void loop()
  voltage = analogRead(A0);
  voltage = map(voltage, 0, 1023, 0, 250);
 
  if (Bus_voltage  <= 97)
  {
    Pwm = Pwm + 1;
  }
  else if (Bus_voltage >= 97 )
  {
    Pwm = Pwm - 1;
  }
  
// too high duty cycle can heat the mosfet too much and damage it so limiting the PWM output
  if (Pwm >= 200)
  {
    Pwm = 200;
  }
analogWrite(9,Pwm);
delay(10);
}

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