PID Velocity Control in Python

A self-driving car company has requested a speed controller for their new model of electric autonomous vehicles. Unlike standard cruise control systems, this speed controller must manage transitions between all velocities ranging from 0 to 25 m/s (56 mph or 90 km/hr).

The speed controller changes a gas pedal (%) input that adjusts electrical current to the motor, creates a torque on the drive train, applies forward thrust from wheel contact on the road, and changes the velocity of the vehicle. Regenerative braking is part of this application by allowing the gas pedal to go from -50% to 100%. Decreases in velocity are also due to resistive forces. Negative velocities (backwards driving) is highly undesirable.

Design a controller that will achieve satisfactory performance in set point tracking over the range of requested driving velocities. Use physics-based modeling to create a suitable dynamic representation of the relationship between gas pedal position (%) and vehicle velocity. Create simulated step tests to fit to a first-order plus dead-time (FOPDT) model. Use the FOPDT model parameters to design a PID controller. Test the controller over a range of set point changes that may be encountered in typical driving conditions. Show plots of the velocity and gas pedal position as the car achieves the desired velocity set points. Discuss how disturbances such as wind or a hill would affect the velocity and how the controller would respond. See http://apmonitor.com/pdc/index.php/Main/SpeedControl