Process control – comparing controllers by maximum deviation Which controller structure generally yields the least maximum deviation (minimum peak error/overshoot) for comparable tuning on the same process?

Introduction / Context:
In feedback control, the choice of controller form affects both transient and steady-state performance. Maximum deviation (the largest excursion of the controlled variable from setpoint after a disturbance or setpoint change) is a practical metric related to overshoot and peak error.

Given Data / Assumptions:

• Same process (e.g., first-order plus dead time), similar tuning effort across controllers.
• Maximum deviation refers to the peak magnitude of error after an upset.
• We compare P, PI, PD, and PID structures.

Concept / Approach:
Each controller term contributes differently. Proportional (P) reduces error but leaves offset. Integral (I) removes offset but can worsen overshoot if aggressive. Derivative (D) provides predictive action that damps the response, reducing peak error. Combining P, I, and D allows steady-state error elimination while damping the transient, typically achieving the least peak deviation when properly tuned.

Step-by-Step Solution:

Verification / Alternative check:
Standard tuning correlations (e.g., Ziegler–Nichols, Cohen–Coon, IMC) and step-response comparisons show that PID typically yields lower peak error than P, PI, or PD alone for many common process classes.

Why Other Options Are Wrong:

• P: Leaves offset and often larger peak deviation.
• PI: Eliminates offset but may overshoot more without derivative action.
• PD: Damps transients but cannot eliminate steady-state error, and peak may not be minimal for load disturbances.

Common Pitfalls:
Assuming any PID will always be best regardless of tuning. Poor PID tuning can still yield large peaks; the statement presumes competent tuning for each structure.

Final Answer:
P-I-D controller