# How PID Controller Works

Time is most precious thing human can ever have since we do not have the ability to reutilize it. Being human we always want work to be done automatically, accurately and timely, to do so we need an optimal control strategy which should have command over all tenses of time i.e. Present + Past + Future. One of such control strategy is PID Controller.

### How PID Controller Works?

This mode of the controller is a complex combination of proportional-integral-derivative control modes.Â  PID control mode possesses zero steady state error, oscillations, and high stability. By the addition of the derivative term to PI control mode helps to reduce overshoot, reduce settling time as well as becomes capable of handling sluggish and fast dynamics higher order processes. In this mode, integral terms try to stabilize the lightly damped system, usually, only PD control mode can not do it easily.

Mathematically this isÂ represented as,

Where,

• P = PD controllerâs output
• KP = Proportional Gain
• KI = Integral Gain (=1/Integral Time (Ti))
• Ki = KP / Ti
• Â­KD= Derivative Gain (=Derivative Time (Td))
• Kd = KP x Td
• ep (t)= Desired Value of controlled variable â Measured Value
• PÂ­I(0) = Integral term initial value

Since, PID control mode can be utilized in many different ways as shown in above equation, which actually helps to define tunable parameters of PID controller.

### Applications

PID controller has many industrial as well as domestic applications.
The example we are going to consider here is âmaintaining the position of booster rocket at the time of taking offâ. To replicate this problem in simplified terms, letâs consider launch pad as a cart and rocket as an inverted pendulum. Now, this a classic example of runaway process, i.e. pinch to the pendulum in normal condition will result in instability of the overall system. Such a system either only PI or only PD controller can not stabilize since one can not handle sudden disturbance and another can not handle initial instability. PID controller maintains itâs position by eliminating steady-state error and predicting error trend.

### Advantages:Â Why PID controller is used?

2. Improves overall stability of system
3. Ability to handle nonlinear higher order unstable system such as CSTR runaway processes
4. Accurate and quick desired value tracking