Integral Time (Ti)

Automation DCS
1

:stopwatch::control_knobs: INTEGRAL TIME (Ti): How Quickly the Integral Action Acts! :gear:

In a PID controller, Integral Time (Ti) is a key tuning parameter that determines the strength of the integral action.

It tells us how quickly the integral term responds to a persistent error.

:small_blue_diamond: What is Integral Time?

Integral Time (Ti), also called Reset Time, is the time required for the integral action to produce an output change equal to the proportional action for a constant error, under the standard ISA form of the PID equation.

The integral contribution can be represented as:

image
image578×153 4.47 KB

Where:

  • Ti = Integral Time
  • Kc = Controller gain
  • e(t) = Error = SP − PV
  • uI = Integral contribution

INTEGRAL TIME
INTEGRAL TIME1024×1280 549 KB

:fire: The Most Important Relationship

Smaller Ti → Stronger/Faster Integral Action

Larger Ti → Weaker/Slower Integral Action

Think of it like this:

:stopwatch: Ti = 2 min
:right_arrow: Integral action is relatively strong
:right_arrow: Persistent error is corrected faster

:stopwatch: Ti = 10 min
:right_arrow: Integral action is weaker
:right_arrow: Correction occurs more slowly

:factory: Example

Suppose a flow controller has:

:bullseye: SP = 100 m³/h
:chart_decreasing: PV = 90 m³/h

There is a persistent error of:

10 m³/h

The proportional action responds immediately.

The integral action keeps accumulating this error over time and continues adjusting the controller output until the steady-state error is eliminated.

If Ti is reduced, the integral action becomes more aggressive.

If Ti is increased, the integral action becomes less aggressive.

:warning: What Happens if Ti is Too Small?

The integral action becomes very aggressive.

This can cause:

:cross_mark: Overshoot
:cross_mark: Oscillation
:cross_mark: Poor stability
:cross_mark: Integral windup problems when the output saturates

:warning: What Happens if Ti is Too Large?

The integral action becomes too slow.

You may see:

:cross_mark: Slow elimination of offset
:cross_mark: Sluggish response to disturbances
:cross_mark: Longer time to reach the setpoint

:bullseye: Integral Time vs Integral Gain

These are often confused.

Integral Gain (Ki):
Higher Ki → stronger integral action.

Integral Time (Ti):
Smaller Ti → stronger integral action.

For the common ISA/ideal PID form:

Ki = Kc / Ti

So they are inversely related.

:light_bulb: Easy Way to Remember

:one_o_clock: Ti = Reset Time

Small Ti = Fast Reset :high_voltage:

Large Ti = Slow Reset :turtle:

And remember:

:bullseye: Integral action eliminates steady-state error, while Integral Time determines how aggressively it does so.

#IntegralTime #ResetTime #PID #PIDControl #ControlSystems #ProcessControl #Instrumentation dcs #PLC Automation #ControlEngineering #IndustrialAutomation #InstrumentationEngineer :gear::factory::control_knobs: