SME
Process Dynamics & Control · Problem type
Static feedforward gain
Use this for “A feed-flow disturbance has gain Kd = 1.5 and the process Kₚ = 3. What feedforward gain cancels it?”
Diagram
Kff
=
−
Kd
Kₚ
=
−
1.5
3
=
−0.5.
Through the process the feedforward adds KffKₚ = −1.5 to Y, cancelling the disturbance’s Kd = 1.5.
This is an example. Type your own values to start a new problem.
Kff
=
−
Kd
÷
Kₚ
Formulas
Kff
=
−
Kd
Kₚ
−0.5
=
−
1.5
3
Assumptions
•
Steady-state gains only: the feedforward ignores the dynamics of each path.
•
The disturbance is measured, and the feedforward output adds to the process input.
•
Ideal valve and sensor (gain 1); deviation variables.
Step-by-step
WE KNOW
Kd = +1.5, Kₚ = +3
FIND
feedforward gain (Kff)
Step 1 · Find feedforward gain (Kff)
Use Kff = −Kd ÷ Kₚ
Through the process the feedforward adds KffKₚ to the output; that must cancel Kd.
Kff
=
−
1.5
3
Kff = −0.5
Check
Put the numbers back in. Both sides should match.
−0.5
=
−
1.5
3
✓
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Feedback, feedforward, cascade or ratio
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