Questions: Control System Structure and Configuration

Question 1

A basic toaster runs for a preset time regardless of actual bread color. A smart toaster measures surface temperature and adjusts cooking time in real time. Which structural concept explains the smart toaster's superior consistency?

• A. The smart toaster uses a more powerful heating element to reach target temperature faster
• B. The smart toaster uses closed-loop feedback — it measures the actual output and computes an error signal that drives corrective action, compensating for disturbances like bread thickness or starting temperature
• C. The smart toaster uses feedforward control, computing in advance how long each bread type will take
• D. The smart toaster uses open-loop control but with a higher-precision timer

Answer: (B)

The basic toaster is open-loop: it runs for a fixed time with no measurement of actual output. It is vulnerable to disturbances (bread moisture, initial temperature, thickness) that open-loop control cannot correct because it never observes the result. The smart toaster is closed-loop: it measures actual browning (or temperature as a proxy), forms an error signal (actual vs. desired), and adjusts dynamically. This measurement-correction loop is what makes feedback robust to real-world variation. Option C (feedforward) would compute commands in advance based on bread type — possible, but requires a model of each bread, not the same as measuring actual output.

Question 2

In a closed-loop control system, why can negative feedback cause system instability?

• A. Negative feedback always reduces loop gain below one, causing the system to stop responding
• B. If the controller amplifies errors at frequencies where the loop introduces enough phase lag that the feedback effectively becomes positive, the error can grow rather than diminish — potentially causing sustained oscillation
• C. Negative feedback cancels both disturbances and the reference signal, driving output to zero
• D. Instability occurs because the sensor always adds a 180° phase shift that cannot be compensated

Answer: (B)

This is the fundamental tradeoff in feedback control. At low frequencies, negative feedback works as intended — the correction opposes the error. But at high frequencies, every physical component (sensors, actuators, the plant itself) introduces phase lag. If the cumulative phase shift around the loop reaches 180° at a frequency where the loop gain is still ≥1, then what was designed as negative feedback has become positive feedback at that frequency — small disturbances at that frequency are amplified each cycle. The Bode stability criterion and gain/phase margins are tools for ensuring this never happens. Open-loop systems don't face this risk because there is no feedback path for errors to circulate through.

Question 3

Open-loop control is typically inferior to closed-loop feedback control because it can seldom correct for disturbances or model errors.

• T. True
• F. False

Answer: False

Open-loop control is appropriate — and often preferable — when disturbances are negligible and the process model is accurate. A toaster timer, a microwave's set cooking time, a stepper motor in a 3D printer, or a simple irrigation timer all operate open-loop successfully for their intended purpose. The advantages are simplicity (no sensor, no feedback-driven instability risk, lower cost). The trade-off is that any mismatch between model and reality accumulates as permanent error. Neither structure is universally superior; the choice depends on disturbance levels, required precision, stability concerns, and available sensors.

Question 4

In cascade control, an inner loop controlling a fast inner variable (such as motor current) is nested inside an outer loop controlling a slower process variable (such as shaft speed), so that the inner loop can reject fast disturbances before they propagate to the outer loop.

• T. True
• F. False

Answer: True

Cascade control is precisely this nested structure. The inner loop operates at a faster timescale — for example, a current controller (milliseconds) inside a speed controller (hundreds of milliseconds). A disturbance affecting the fast inner variable (like a supply voltage fluctuation causing current deviation) is corrected by the inner loop entirely within one outer-loop cycle — the outer speed controller never even 'sees' the disturbance. This separation of timescales is what makes cascade control effective: each loop only needs to handle disturbances at its own bandwidth, keeping both loops stable and well-tuned.

Question 5

Explain why closed-loop feedback can cause instability in a control system, and why an open-loop system with the same plant and controller never faces this problem.

Model answer: Closed-loop feedback becomes unstable when the loop introduces enough phase shift at a frequency where the loop gain is still large. Every physical component adds phase lag at high frequencies — sensors have response delays, actuators have inertia, and the plant itself integrates or filters signals. If the total phase shift around the loop reaches 180° at a gain ≥ 1, then the intended negative feedback has become positive feedback at that frequency: disturbances at that frequency are amplified each pass around the loop rather than attenuated, producing growing oscillations or instability. Open-loop control has no feedback path. The controller generates commands based only on the reference input, and the output of the plant never returns to influence those commands. Without a loop, there is no mechanism for errors to circulate and amplify — the system is always stable (though potentially inaccurate, since there is nothing to correct errors).