The steer the car in the correct direction.

The need of
feedback loop is the main concept. It continuously calculates the error i.e.
the difference between the output and the desired setpoint. This error is
feedback into the controller or the system itself depending on the situation as
a correction. Using feedback on its own, the system only takes cares of the
uncertainty which is one of the major advantage of the using a feedback loop in
a system.

The sensors
on the car detect the lane using marking on the road. This can be a center
broken white line to mark the center of the road or two separate line to divide
between the lanes. The desired path is the center of the lane which is
processed by the computer using the images from the camera mounted to the
dashboard of the car. The computer should ideally process how far is the car
from this desired point with what direction, left or right. This correction
will now be fed into the feedback system. The output to the system will involve
several actuators or a motor attached to the steering wheel to steer the car in
the correct direction. If we are to the left of the desired line, vehicle will
turn right and if we are to right, the vehicle will turn to the left but how
much do we turn and if we the steering wheel turn with the fixed amount of
turning to either side, the vehicle will never reach the desired set point,
instead will oscillate about that set point. This will be very uncomfortable
for the passengers. 

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To steer
the vehicle in either direction with varying angle rather than with the fixed
amount of left or right turn, we will implement the proportional controller to
the feedback loop implemented to the system. The figure of the correction is
now better and efficient. The correction is bigger if the vehicle is farther
from the desired setpoint i.e. the vehicle will steer harder if it’s further
away from the center line. The value of gain will remarkably affect the
performance of the system. It gets better with the higher value of gain, but
too high value for the gain can set the vehicle to rotate out of control if
away from the center line. Hence a moderate value is chosen. We cannot use
proportional gain on its own, as it doesn’t work very well because it has some
drawbacks. It will introduce overshoot and oscillations in the system which
again is not very comfortable for the passengers on the vehicle. Also because
of the oscillation, the vehicle will repeatedly overshoot the actual desired
setpoint and will not settle down.

To fix this
we will need to add another set of correction measurement to the system. We
will implement the integral controller. An integral action does something
really clever. It looks at what has happened before, it goes back a bit in time
because it is keeping a track in time where the vehicle has been, it will fix
the overshoot or the constant steady state error introduced in the system. If
the value of the integral gain is too large the system will go unstable. Again
we cannot use the integral controller on its own because it’s too slow for
correction and an attempt to make it fast using the high gain value will make
the system unstable. Integral action plays a very important role in case of
external factors on the system. This can be any environmental factors, such as
weather or road conditions. These offsets are also cured with the
implementation of the integral controller.

Now the
derivative controller is implemented with the two of the above controller. You
can think of it as the resistance to the motion created by the above two controllers.
This help vehicle opposes the fast trajectory and hence stable movement. This
act is also known as damping and hence remove any oscillation in the system. If
the value of gain is low the system will be known to be underdamped and result
in the slow killing of the oscillations, which means it will still oscillate.
If the value is too high, the system will be known to be overdamped and will
now take a long time to corrects any offsets. A moderate value of gain is also
chosen here where the vehicle is quick with zero offsets. Now the system will
be called critically damped.

combination of the controller working together and reflection of feedback
system makes a successful lane-keeping control.

We have
supposed the speed of the car is constant for this scenario to make the
understanding of feedback loop and PID controller easier as this will be dealt
in a separate control loop.