A control system uses a sensor with gain H = 0.5 (non-unity feedback) to measure a temperature output. The reference is set to R = 200°C. After the loop reaches steady state with zero error signal (E → 0), what is the actual temperature output?
A200°C — the system tracks the reference exactly in all well-designed closed-loop systems
B100°C — because with H = 0.5, the sensor reads half the actual temperature, so the system drives the actual output to 400°C to make the sensor reading match R
C400°C — the non-unity feedback gain scales up the actual temperature, so E = R − H·Y → 0 means Y = R/H = 400°C
D100°C — the sensor attenuates the signal, so the controller only corrects half the error and settles at 100°C
In non-unity feedback, the error is E = R − H·Y. At steady state, E → 0, so H·Y = R, meaning Y = R/H = 200/0.5 = 400°C. The controller drives the loop until the *sensed* output H·Y matches R — it has no way to distinguish between R and H·Y independently. This is why non-unity feedback changes steady-state behavior: the system tracks R/H, not R. Option A (200°C) assumes unity feedback. Understanding this prevents errors when designing systems with sensors that have their own gain.
Question 2 Multiple Choice
Two disturbances affect a feedback control system: D₁ enters at the plant input (before the plant, inside the feedback loop), and D₂ enters at the plant output (after the plant, outside the forward path). Which disturbance can the feedback controller attenuate, and why?
AD₂ only — output disturbances are directly subtracted from the reference in the error computation
BBoth D₁ and D₂ equally — feedback attenuates all disturbances regardless of where they enter
CD₁ only — it enters inside the feedback loop, so its effect propagates to the output and is measured; the controller corrects for it. D₂ enters after the measurement point and is not visible to the controller
DNeither — disturbance rejection requires separate feedforward controllers in both cases
A disturbance that enters *inside* the feedback loop (before or within the forward path) affects the output, which the sensor measures. The controller sees the deviation from reference and generates corrective action. A disturbance at the output (after the plant, outside the loop) adds directly to the measured signal but bypasses the correction path — the controller sees the disturbed output but cannot distinguish disturbance from true output. Worse, high feedback gain amplifies output-side disturbances like sensor noise. The topology of where disturbances enter relative to the measurement point is critical to predicting what can be rejected.
Question 3 True / False
Increasing feedback gain generally improves both tracking accuracy and system stability simultaneously.
TTrue
FFalse
Answer: False
This is a common misconception. While higher loop gain generally reduces steady-state error (improving tracking), it simultaneously reduces phase margin and can push closed-loop poles into the right half-plane, causing instability. Additionally, high gain amplifies sensor noise at the plant input. There is a fundamental tradeoff in feedback design: performance (tight tracking, fast disturbance rejection) versus robustness (stability margins). Every practical controller design must balance these — unlimited gain is not the answer.
Question 4 True / False
In non-unity feedback, the error signal is computed as the difference between the reference R(s) and the sensed output H(s)·Y(s), not the actual plant output Y(s) directly.
TTrue
FFalse
Answer: True
This is the definition of non-unity feedback. The summing junction computes E(s) = R(s) − H(s)·Y(s), where H(s) represents the sensor or feedback element dynamics. In unity feedback (H = 1), E = R − Y and the error directly reflects the tracking error. In non-unity feedback, the controller sees and responds to the *sensor's* representation of the output, which may differ from the true output in gain and phase. This affects both steady-state values and the closed-loop transfer function.
Question 5 Short Answer
Why does the location of a disturbance — before versus after the plant — determine whether the feedback controller can reject it?
Think about your answer, then reveal below.
Model answer: Feedback works by measuring the output, comparing it to the reference, and generating a corrective signal. A disturbance entering *before* the plant (at the plant input) passes through the plant before reaching the output sensor. The sensor detects the resulting deviation from the reference, the controller generates a corrective input, and the loop works to cancel the disturbance's effect. A disturbance entering *after* the plant — or equivalently, corrupting the sensor measurement — is already past the point where the controller can introduce a physical correction. The controller cannot distinguish it from a legitimate output change, so it responds by driving the plant harder, which can amplify the disturbance rather than cancel it.
This is why sensor noise is treated differently from input disturbances in control design. Sensor noise is an output-side disturbance: high loop gain makes the controller respond aggressively to noise, injecting large control signals for small measurement errors. Input disturbances (wind gusts on a drone, load changes on a motor) can be attenuated by the loop. Feedforward control is often added to handle disturbances that enter outside the feedback path and are known or measurable ahead of time.