fan speed control using pulse sensor in Arduino Uno

Question

Good day everyone, I have some problem regarding to my practice of fan speed control using pulse sensor in Arduino Uno. I can gather the pulse rate and rpm of the fan. However, the fan won't change its speed depending on the pulse rate. Here is my circuit on using this project

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And here is my code right now in arduino IDE:

#define USE_ARDUINO_INTERRUPTS true    // Set-up low-level interrupts for most acurate BPM math
#include <PulseSensorPlayground.h>     // Includes the PulseSensorPlayground Library

const int PulseWire = 0;       // 'S' Signal pin connected to A0
int Threshold = 550;           // Determine which Signal to "count as a beat" and which to ignore
int pulse;
const int fan_control_pin = 3;
int count = 0;
unsigned long start_time;
int rpm;

PulseSensorPlayground pulseSensor;  // Creates an object


void setup() {
  Serial.begin(9600);

    pulseSensor.analogInput(PulseWire);   
    pulseSensor.setThreshold(Threshold);  

  // Double-check the "pulseSensor" object was created and began seeing a signal
    if (pulseSensor.begin()) {
        Serial.println("PulseSensor object created!");
    }

  pinMode(fan_control_pin, OUTPUT);
  analogWrite(fan_control_pin, 0);
  Serial.begin(9600);
  attachInterrupt(digitalPinToInterrupt(2), counter, RISING);
}

void loop() {
  int pulse = (pulseSensor.getBeatsPerMinute()/2.5);
  if (pulse < 40) analogWrite(fan_control_pin, 0);
  if ((pulse >= 40) && (pulse < 70)) analogWrite(fan_control_pin, 102);
  if ((pulse >= 70) && (pulse < 85)) analogWrite(fan_control_pin, 153);
  if ((pulse >= 85) && (pulse < 100)) analogWrite(fan_control_pin, 204);
  if (pulse >= 100) analogWrite(fan_control_pin, 255);
  start_time = millis();
  count = 0;
  while((millis() - start_time) < 1000);
  rpm = count * 60/2; 


  if (pulseSensor.sawStartOfBeat()) { 
    Serial.print("The pulse is ");
    Serial.print(pulse);
    Serial.println(" bpm");
    Serial.print("The fan speed is ");
    Serial.print(rpm);
    Serial.println(" rpm");
  }
  delay(1000);
}

void counter() {
  count++;
}

The code tells me the rpm and my bpm but the fan speed is not allign with my pulse rate. I want to have a fan speed depending on the pulse rate. high pulse rate, fast fan speed, and low pulse rate, low fan speed. below minimum pulse rate, off fan.