Features of PID controllers

Summary: PID control

Proportional control, is the simplest to implement, but not always sufficient for stabilization.

Derivative control, helps achieve stability, improves time response, i.e., more control over pole locations.

PD control gives arbitrary pole placement (only valid for second order response); in general though, we still have control over two dominant poles.

Derivative control cannot be implemented directly, so need approximate implementation; D-control also amplifies noise.

Integral control, is essential for perfect steady-state tracking of constant reference and rejection of constant disturbance.

What is the role of P, I and D in a PID controller?

Understanding the roles is important while tuning.

Proportional (P) parameter

The P-action is proportional to the error or the PV. The error (or PV) is multiplied with the proportional gain and added to the controller output. The P-action gives the output a ‘kick’ in the right direction.

If the error value is zero, then the P action is zero. This implies that a controller with only P action needs a non-zero error to have a non-zero output. Accurate tracking is therefore not possible with only P control.

Integral (I) parameter

Consider a plot of the error between PV and SP over time. In mathematics, the “integral” of the error can be interpreted as the surface between the curve and the x-axis and between the y-axis and the current time instant.  Every time step, the plot extends a bit to the right. If the error is zero at that time, the surface does not increase and the integral remains constant.

If your error is positive the surface below the error curve will increase, resulting in a higher controller output. The I action will decrease when the error becomes negative.

Typically the I-action will act much slower compared to the proportional action. However, it will bring the error to zero eventually, which the proportional action can’t do. So basically, the integral action looks at the past and checks if the error is getting to the setpoint. If not, it’s acting on the output. It is going to steer the wheel until you are heading in the intended direction.

Derivative (D) parameter

The integral doesn’t have the possibility to predict the behavior of error. The derivative action addresses this problem by anticipating the future behavior of the error.

So, the derivative action is the change of the error. It adds a contribution to the output according to how the error changes. When the error is positive, but is starting to decline the D action, it will reduce the output of the controller. It’s the brake that tries to avoid overshoot. It reduces the oscillations induced by the other two actions. It can speed up the controller to the setpoint that we want to achieve.

It reduces the oscillations induced by the other two actions. It can speed up the controller to the setpoint that you want to achieve. However, the derivative action is not often used in PID tuning. The problem is that it can amplify noise. If the error signal is very noisy, the controller output tends to oscillate a lot. This can negatively affect the lifetime of the equipment like pumps and valves.