PI Controller (Proportional Integral) Controller in Control System

How does PI Controller Work?

The control mode of PI Controller has a one-to-one correspondence of the proportional mode as well as the integral mode which eliminates that inherent offset. This controller is mostly used in areas where the speed of the system is not an issue. Since proportional controller can not provide new nominal controller’s output in case of new load condition, but in this new configuration necessity of fixed (offset) error has been replaced by the accumulation of error term i.e integral term. Mathematically, this can be represented as,

Where,

  • P = PI controller’s output
  • KP = Proportional Gain
  • ­KI= Integral Gain
  • ep (t)= Desired Value of controlled variable – Measured Value
  • I(0) = Integral term initial value

Form PI controller’s equation we can say that when an error is zero, but the controlled variable is oscillating about desired value, then integral action tries to eliminate error and reaches desired value.

When an error is not zero and only accumulated error is not sufficient for resulting in the quick ramp up, in that case, the proportional controller reduces rise time and tries to achieve optimal controller’s output at new load conditions.

Applications of PI Controller

Flow control of any liquid is a dynamic process, improper prediction of error might result in control value saturation or extended flow of liquid which usually happens when we apply derivative controller to such a system.

In this case, the Proportional controller gives proper ramp up to achieve desired value quickly as well as the occurrence of offset error or steady state error about desired value has been eliminated by the integral term.

Advantages

  1. Desired value can be achieved accurately.
  2. Ease to apply for fast response processes as well as processes in which load change is large and frequent.
  3. Removes steady state error.

Disadvantages

  1. The speed of response of system becomes sluggish due to the addition of integral term.
  2. During start-up of a batch process, the integral action causes an overshoot.
  3. Since PI controller doesn’t have the ability to predict the future errors of the system, therefore it cannot eliminate steady state oscillations and reduces settling time. Hence, overall stability system is comparatively low.

Video

Please watch below video for more understanding on PI Controller. In this video, they have explained how we can eliminate steady state error using PI Controller.

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Derivative Controller in Control System

How does Derivative Controller work?

With an integral controller, we can calculate accumulated error, but with the derivative control, we can calculate the ratio of error change per unit time, hence act as a predictor. Derivative controller action responds to the rate at which the difference between desired value and the measured value is changing that is derivative of the error.  Mathematically represented as below,

Where,

  • KD­ = Derivative gain
  • The derivative controller is also known as Rate action controller or anticipatory controller.
  • ep (t)= Desired Value of controlled variable – Measured Value

Applications

The derivative controller is not used alone because it provides no output when the error is constant.

Advantages

  1. Effect of transportation lag occurred due to the remote allocation of the sensor can be minimized.
  2. Accumulation of error which will go to affect on actuator saturation can be minimized.
  3. Peak errors are minimized.

Disadvantages

  1. Cannot be used when an error is constant. (Derivative of constant value is zero).
  2. A small change in error will affect largely on controller’s output. The high derivative gain will result in heavy overshoots and overall system’s stability.