Question 4 1AE01 - First Assistant Engineer

The Correct Answer is A ### Explanation for Option A (Correct) Closed-loop control systems (feedback systems) are designed to make the output of a system track a desired input (setpoint) or reject disturbances (load changes). When evaluating the performance of a controller, three primary objectives related to the system's transient and steady-state response are critical, assuming stability is already achieved: 1. **Minimize the maximum value of the error (Overshoot/Maximum Deviation):** This ensures the system does not deviate too far from the desired value during the transient phase. 2. **Minimize the settling time:** Settling time is the time required for the system output to settle within a specified tolerance band (e.g., $\pm 2\%$ or $\pm 5\%$) of the final steady-state value. Minimizing this time means the system reaches the desired performance quickly. 3. **Minimize the residual error (Steady-State Error):** Residual error is the difference between the setpoint and the actual process variable after the transient phase is complete and the system has settled. Minimizing this error ensures high accuracy in the long run. Therefore, the two additional objectives, alongside minimizing maximum error, are minimizing settling time and minimizing residual (steady-state) error. --- ### Explanation of Incorrect Options **B) The closed-loop control system should minimize the settling time and maximize the residual error.** While minimizing settling time is correct, maximizing the residual (steady-state) error means the final output value is highly inaccurate, which defeats the purpose of precise control. **C) The closed-loop control system should maximize the settling time and minimize the residual error.** Maximizing the settling time means the system takes an unnecessarily long time to reach its target performance, resulting in a sluggish and slow response. Control systems generally aim for a fast response. **D) The closed-loop control system should maximize the settling time and maximize the residual error.** This option combines the worst outcomes for both performance metrics: the system is both slow (long settling time) and inaccurate (large residual error). This is never a control objective.