Control engineering – Match control action to a typical real-world application List I (Control action) A. On–off control B. Proportional control C. Cascade control (nested loops) D. Digital (discrete-step) control List II (Application) Steam kettle with selectable power settings Elevator speed/position system Robot positioning servo Domestic refrigerator thermostat Choose the correct mapping from List I to List II.

Introduction / Context:
This matching problem connects four classic control strategies with representative applications. Recognizing the “signature” use cases of on–off, proportional, cascade, and digital control helps you pick the right controller architecture in practical systems ranging from household appliances to industrial servos.

Given Data / Assumptions:

• A: On–off control is a two-state (bang–bang) action with hysteresis.
• B: Proportional (P) control output is proportional to error.
• C: Cascade control means an outer loop drives a setpoint for an inner loop.
• D: Digital (discrete-step) control here implies selectable discrete settings (not continuous).
• Applications listed: domestic refrigerator, elevator, robot servo, and multi-setting kettle.

Concept / Approach:

Map each control strategy to the most characteristic application: On–off control is ubiquitous in thermostatic systems (refrigerators). Proportional control is a basic building block in motion control, such as elevators. Cascade control is widely used in multi-loop precision systems like robots (inner velocity/current loop, outer position loop). Digital step control suits devices offering discrete power levels like a multi-setting kettle.

Step-by-Step Solution:

Verification / Alternative check:

Compare with standard control texts: thermostats are canonical on–off; elevators commonly use proportional (often augmented to PID); robotics frequently employs cascaded loops; household devices with “level 1–5” power are discrete/digital in nature.

Why Other Options Are Wrong:

Pairing on–off with elevators or robots ignores the need for smooth motion; assigning cascade to kettles provides no benefit; mapping proportional to refrigerators would cause excessive cycling without hysteresis.

Common Pitfalls:

Confusing “digital control” (discrete-time algorithms) with “digital steps.” Here, “digital” clearly refers to discrete selectable power levels. Also, cascade implies a nested inner/outer loop, not just two separate controllers.

Final Answer:

A-4, B-2, C-3, D-1.