Response of the Controller

The closed control-loop that we discuss before have a time response that we need to define. This response is actually the response of the controller. In order to define the response of the controller we must found suitable parameters. In that way, we should ask a question what result will be expected from the controller in a closed control loop if, for instance, a new setpoint is applied? How many time will need the controller to achieve this new setpoint level of the process variable, and during this time, the transient mode, how much the process variable deviates far from the setpoint? The time diagram of the response of the controller is shown on the Picture 1. We are observing the process from time moment (t0) when the setpoint changes from S1 to S2.

Picture 1: The response of the controller

Depending on the control requirements, we can define the size of the band around the setpoint (+/- Δx), so when the process value lay within this band we say it's stabilized to a steady value. The time needed for the process value to stabilize within this band is called a settling time (Ta).

During the transient mode when controller, or better said the process value moves from the setpoint S1 to the setpoint S2, it is possible for the process value to results in overshoot. In this case, the maximum difference between the process value and the new setpoint is known as the overshoot (Xmax). From the other side, the time taken for the process value to reach the new setpoint for the first time is called the approach time (Tap).

So, at this point we can note that the performance of the control loop will be better if the values for settling time (Ta) and overshoot (Xmax) are smaller. In other words, the control loop is better when it takes less time for the process value to reach the steady state on new setpoint, and during this change there is not a big overshoot. These two parameters are somehow connected between themself, because the big overshoot means more time for the process value to stabilize to a steady value.