Control Engineering Basics
In PID control, which of the following prevents the manipulated variable from jumping sharply at the instant the setpoint is changed as a step (derivative kick)?
- AApplying the derivative only to the controlled variable (the measured value), not to the error
- BIncreasing the integral gain to bring the error back to zero quickly
- CShortening the sampling period so that the difference used for the derivative is calculated more finely
Show answer and explanation
Answer: A. Applying the derivative only to the controlled variable (the measured value), not to the error
When the setpoint changes as a step, the error also changes discontinuously and its derivative is in theory infinite, so the derivative term produces a very large manipulated variable. The controlled variable changes only smoothly because of the lag of the plant, so applying the derivative only to the controlled variable y (derivative on measurement, PI-D control) prevents the jump. On the same idea, I-PD control also applies the proportional action only to the controlled variable. While the setpoint is constant, the derivative of the error and that of the controlled variable differ only in sign, so the response to disturbances does not change.
- A. Correct. Setpoint changes no longer pass through the derivative term.
- B. Raising the integral gain does not remove the jump in the derivative term.
- C. A digital derivative (e[k] − e[k − 1])/Ts actually becomes larger when Ts is shortened.