PWM DC Motor Control without sensors

In the past I've done a bit with arduino PWM DC motor control with various sensors, but have not played around with writing a control program without sensors. So basically I want a motor to go from "stopped" to full "forward"or "reverse" in a specific amount of time without using sensors to tell it when to start- stop etc. In the code below I'm using the PWM range, but it seems kind finicky in terms of how long the motors go either way. Is there a better strategy/easy solution anyone knows right off, or do you have to tediously adjust value ranges for motion? I've played about with the "millis" function but no joy. Don't know if anyone would be so kind as to know of a better function or way to apply a specific time range to an analogWrite. Apologies for being a syntax troglodyte. Any help greatly appreciated.

Here's the mishmash I'm rocking right now

int leftmotor = 10; //left motor
int rightmotor = 11; //right motor

void setup() {
// initialize serial communications at 9600 bps:
Serial.begin(9600);
}
void loop() {

reverse();

delay (1500);

forward();

delay (1500);

}

// BEHAVIOR FUNCTIONS

void reverse(){
for (int b = 190; b >= 127; b--){
analogWrite(leftmotor, b);
analogWrite(rightmotor, b);
Serial.println("REVERSE");

}
}

void forward(){
for (int i = 190; i <= 252; i++){
analogWrite(leftmotor, i);
analogWrite(rightmotor, i);
Serial.println("FORWARD");

}
}

void stop_forever(){
for (int i = 140; i < 150; i++){
analogWrite(leftmotor, 0);
analogWrite(rightmotor, 0);
Serial.println("STOPFOREVER");
delay(100);
}
}

I'm not sure that I understand what your problem with this code is, but I did notice that in the forward() and reverse() functions, you call analogWrite() on each pin, with no delay after writing. The loop completes very quickly, before the motors have had any time to get to or stabilize at any given speed.

Perhaps that's why the motors don't seem to have consistent behavior.

Just look at the examples of fading LED from one colour value to another, that is the sort of thing you want to do.
Like it was said above you have to add a delay between each change in speed. But you don't have to go through each value at a fixed rate, you can take the other approach and increment the value by a certain amount every n milliseconds. The 'a certain amount' then determines the ramp up speed.

Remember PWM only works with a loaded motor, with no load it free wheel spins in the off portion and so doesn't appear to change speed much.