A car whose PID controller is going to act to try to stabilize its speed to the given setpoint.

Code:

car := pidctl.Controller{
    P:        big.NewRat(1, 5),
    I:        big.NewRat(1, 100),
    D:        big.NewRat(1, 15),
    Min:      big.NewRat(-1, 2), // min acceleration rate: 0.5 mps
    Max:      big.NewRat(10, 2), // max acceleration rate: 5 mps
    Setpoint: big.NewRat(60, 1), // target speed: 60 mph
}
speed := float64(20) // the car starts in motion. 20mph
const travel = 15 * time.Second
for i := time.Second; i <= travel; i += time.Second {
    desiredThrottle := car.Accumulate(new(big.Rat).SetFloat64(speed), time.Second)
    actualThrottle, _ := desiredThrottle.Float64()
    actualThrottle = math.Ceil(actualThrottle)
    fmt.Printf("%s speed: %.2f throttle: %.2f (desired: %s)\n", i, speed, actualThrottle, desiredThrottle.FloatString(2))
    speed += actualThrottle
    switch i % 5 {
    case 0:
        // head wind starts strong: 2mps
        speed -= 2
    case 1:
        // head wind ends weak: 1mps
        speed -= 1
    }
}

Output:

1s speed: 20.00 throttle: 5.00 (desired: 5.00)
2s speed: 23.00 throttle: 5.00 (desired: 5.00)
3s speed: 26.00 throttle: 5.00 (desired: 5.00)
4s speed: 29.00 throttle: 5.00 (desired: 5.00)
5s speed: 32.00 throttle: 5.00 (desired: 5.00)
6s speed: 35.00 throttle: 5.00 (desired: 5.00)
7s speed: 38.00 throttle: 5.00 (desired: 5.00)
8s speed: 41.00 throttle: 5.00 (desired: 5.00)
9s speed: 44.00 throttle: 5.00 (desired: 5.00)
10s speed: 47.00 throttle: 5.00 (desired: 5.00)
11s speed: 50.00 throttle: 5.00 (desired: 4.55)
12s speed: 53.00 throttle: 5.00 (desired: 4.02)
13s speed: 56.00 throttle: 4.00 (desired: 3.46)
14s speed: 58.00 throttle: 4.00 (desired: 3.15)
15s speed: 60.00 throttle: 3.00 (desired: 2.75)