A PID controller uses proportional, integral and derivative terms to minimize error over time between a measured process variable and desired setpoint. It continuously calculates an error value as the difference between the process variable and setpoint, and applies a correction based on proportional, integral and derivative terms for the error. The proportional term responds to current error, the integral term responds to accumulated historical error, and the derivative term responds to the rate of change of error. PID controllers are commonly used to control temperature, pressure, flow and other process variables due to their robustness and ability to achieve zero steady-state error.

1. PID CONTROLLER
PID controller stands for Proportional-Integral-Derivative controller. It allows measurement
to be controlled at a desired set point by continuously adjusting a control output .Control
parameters act on the error or deviation between set point and variable .These kind of
controllers are expected to compensate automatically due to frequent changes in the set point,
the amount of energy available or the mass to be controlled.PID controllers are used for more
precise and accurate control of various parameters.
Figure 1: PID Controller block diagram
Where,
u(t) -controller output
Kp -Proportional Gain
Ki -Integral Gain
Kd -Derivative Gain
e(t) -Error
t -time or instantaneous time (the present)
τ - variable of integration (takes on values from time 0 to the present ).

2. There are three main terms in this controller:
 Proportional term
It is proportional to the current value of the SP-PV error e (t) that is depends on present
error and gives a faster reaction .If the error is large and positive, the control output will
be proportionately large and positive. This reduces the rise time but never eliminate the
steady state error. Proportional term reduces maximum overshoot to disturbances.
 Integral term
It accounts for past values of the SP − PV error and integrates them over time to produce
the I term. Relatively slow responding and fine tune your results .This have the effect of
eliminating the steady state error ,but it may make the transient response slower and also
accelerates movement of process towards set point
 Derivative Term
It is a best estimate of the future trend of the SP − PV error, based on its current rate of
change. This has an effect of eliminating oscillations, reduces overshoot, improve the
transient response. Typically make the system more damped and stable.
Figure 2: Effect of increasing parameters independently
Advantages:
 Simple and efficient.
 Effective and robust.
 Fast response.
 Zero steady state error.
 Less overshoot.
Disadvantages:
 Difficulties in the presence of non linearities.
 Do not react to changing process behaviour.

3.  Lag in responding to large disturbances.
 Proper tuning is difficult.
 May trade off regulation versus response time.
Applications:
 Particularly useful for controlling slow variables like pH, temperature etc.
 Chemical reactors.
 Self balancing robot.
 Line following bot.
 Auto balancing of a multi rotor flying machine.
 Auto driving vehicles for road.