Exercises: Open loop and closed loop

Explain what an automatic system is and name its four basic elements (input or reference, controller, actuator and output or process), stating what each one does in a specific example.

Explain what an open-loop control system is and give two examples of everyday devices that operate this way (a toaster, a fan without a thermostat, timed irrigation...), justifying why they are considered open loop.

Explain what a closed-loop control system is and what it means to have "feedback". Give an everyday example (for instance, heating with a thermostat) and identify the sensor and the variable that is fed back.

Explain what the setpoint or reference value of a control system is and give two examples: one for a home thermostat and another for a car's cruise control.

What is a disturbance in an automatic system? Describe two specific disturbances: one for a home heating system (for example, opening a window) and another for a car's cruise control (driving uphill).

State which sensor you would use to measure each quantity in an automatic system and what signal it sends to the controller: the temperature of a room, the ambient light of a street, and the open or closed position of a door.

In a closed loop, the "error" is the difference between the reference and the sensor measurement. Explain what the controller tries to do with this error and what happens when the error reaches zero.

Classify these systems as open loop or closed loop, justifying your decision: (a) a dishwasher that executes its program by timer, and (b) an air conditioner that maintains the room temperature.

Classify these systems as open loop or closed loop, justifying each decision: (a) a traffic light that changes at fixed intervals, (b) cruise control in a car, (c) a garden irrigation system programmed by time, and (d) a fridge compressor, which switches on and off automatically.

The diagram compares the two types of loop: above, the block diagram without feedback; below, the block diagram with feedback, where an element in the feedback path is covered by a question mark, as shown in the diagram.

State which element is missing from the feedback path in the second diagram, explain what it measures and what the comparator (the circle with + and −) does with its signal, and reason what advantage this loop has over the first one.

A car with cruise control starts driving up a hill. Explain step by step how the closed-loop system reacts (what it detects, what it compares, what it commands) and describe what would happen instead to a hypothetical open-loop system that kept the accelerator pedal position fixed.

A ceiling fan is switched on and its speed is adjusted using a manual control. Describe its block diagram, reason whether it is open loop or closed loop, and explain what elements would need to be added to convert it into a closed loop that maintains the room temperature.

In control systems, feedback is negative: the measurement is subtracted from the reference. Explain what would happen if it were added instead of subtracted (positive feedback), reasoning how the output would grow uncontrollably, and give an everyday example of positive feedback (acoustic feedback between a microphone and a loudspeaker).

A refrigerator regulates using bang-bang (on-off) control: the compressor turns on or off, with no intermediate power levels. Explain why the internal temperature oscillates slightly around the setpoint and what hysteresis or deadband is (the margin between the turn-on and turn-off temperatures), indicating its purpose (to prevent continuous starting and stopping of the compressor).

An open-loop garden irrigation system operates on a timer and it rained today. Analyse what has conceptually failed (the system does not know the actual state of the process) and explain how a soil moisture sensor would close the loop: what it would measure, what the controller would compare it to, and what it would command the solenoid valve to do.

When taking a shower, you adjust the tap by hand until the water is to your liking. Identify in this "system" the reference (the desired temperature), the sensor (your skin), the comparator and controller (you), the actuator (the mixer tap), and a possible disturbance (someone opens another tap in the house). Reason why it is a true closed loop even though there is no electronics involved.

In a house with boiler heating and a digital thermostat set to a setpoint of $21.0\ ^\circ\text{C}$, it is recorded during a winter afternoon that the actual room temperature rises continuously until reaching $27.5\ ^\circ\text{C}$ while the boiler remains on at full power. On the thermostat screen, however, a fixed and frozen reading of $12.0\ ^\circ\text{C}$ is observed.

1. a) Identify the elements of the control loop (reference signal, comparator, error signal, controller, actuator, process, and feedback sensor) and analytically interpret why the boiler does not turn off despite the excessive heat.
2. b) Justify whether, given this failure, the system has started behaving as an open loop or if it remains a closed loop operating abnormally. Predict what will happen to the system if a user does not intervene.

You need to design the automated climate control system for a greenhouse so that the interior temperature remains within the optimal range of $[18.0\ ^\circ\text{C},\ 24.0\ ^\circ\text{C}]$. You have a temperature probe, an electric heater, and a motorized roof window opening system coupled with an exhaust fan.

1. a) Draw the detailed block diagram of the closed-loop system, explicitly identifying: setpoint signal, comparator, controller, actuators, plant or process, external disturbances (such as solar radiation or cold wind), and feedback variable.
2. b) Design the control logic by defining three operating bands (low, adequate, and excessive temperature). Justify why it is essential to provide a deadband between turning off the heating and opening the windows to avoid actuator wear and energy waste.

A technical team proposes replacing the time programmer of the sprinklers in a municipal park and the electromechanical timer of a domestic toaster with closed-loop systems equipped with continuous moisture and surface temperature sensors. Their justification is: "Any closed-loop system is intrinsically superior to an open-loop one, so it is always worth implementing."

1. a) Refute this argument by analyzing what technical, economic, and reliability criteria (probability of sensor failure in harsh environments, calibration complexity, maintenance cost versus process tolerance) advise against closed loop in these cases.
2. b) Propose a severe external disturbance for each of the two cases that would indeed technically justify making the leap to feedback control.

In an industrial water tank with a capacity of $10\ \text{m}^3$, the volume must be continuously maintained at $8.0\ \text{m}^3$. Water enters driven by a variable-flow pump and empties randomly due to the demand of a production line (disturbance).

1. a) Draw the closed-loop block diagram, identifying with precision: setpoint, error signal, comparator, controller, actuator, process, disturbance, controlled variable, and sensor.
2. b) During an inspection, it is detected that the level sensor has become mechanically stuck, transmitting a fixed equivalent signal of $2.0\ \text{m}^3$. Analytically deduce the sign of the error calculated by the comparator and predict the system's response and the physical consequences on the facility.
3. c) Design a redundant safety solution (active or passive) to protect the facility against this specific failure mode without stopping the production process.

A passenger car is driving on a highway at $120.0\ \text{km/h}$ with adaptive cruise control (ACC) activated. Upon catching up with a truck traveling at $90.0\ \text{km/h}$, the system automatically brakes and positions itself behind it at the programmed safety distance ($50.0\ \text{m}$). Minutes later, the truck changes lanes and leaves the road completely clear.

1. a) Model the system's operation using a diagram that integrates the two coupled control loops (the speed loop and the safety distance loop). Identify which signal acts as a hierarchical constraint when they conflict, and justify why they cannot operate as independent decoupled loops.
2. b) Analyze the actuator transition (throttle/brake) the moment the truck clears the lane: predict the time evolution of the speed error, the controller response, and evaluate what comfort or grip problem could arise if the closed-loop gain were excessively high.

An underfloor heating system exhibits noticeable transport delay and thermal inertia: heat takes about $45$ minutes to diffuse through the slab into the room. In a home regulated by a conventional on/off thermostat set at $20.0\ ^\circ\text{C}$, it is observed that when the temperature drops to $19.5\ ^\circ\text{C}$ the boiler turns on, but the room continues cooling down to $18.0\ ^\circ\text{C}$; then, after reaching $20.0\ ^\circ\text{C}$ again and the boiler turning off, the room continues heating up due to inertia until reaching $23.5\ ^\circ\text{C}$.

1. a) Draw a qualitative temperature-time graph showing this behavior, identifying the setpoint, overshoot, and delay. Explain physically why high inertia causes these continuous oscillations in on/off control.
2. b) Justify and describe two technical control solutions (such as modulating control with weather compensation via an outdoor sensor or algorithms with inertia calculation) that stabilize the temperature without causing excessive oscillations.

The analog signal sent by a PT100 RTD installed next to a variable-frequency drive suffers from high-frequency electromagnetic interference. The system controller, configured with a setpoint of $60.0\ ^\circ\text{C}$, receives a sequence of consecutive readings taken every second: $59.2\ ^\circ\text{C}$, $60.5\ ^\circ\text{C}$, $58.7\ ^\circ\text{C}$, $61.1\ ^\circ\text{C}$, $59.4\ ^\circ\text{C}$, $60.8\ ^\circ\text{C}$, even though the actual fluid temperature remains stable at $59.9\ ^\circ\text{C}$.

1. a) Deduce the behavior that an on/off actuator (a relay controlling a cooling solenoid valve) connected to a direct comparator without signal conditioning will experience. Justify the electromechanical effects and the impact on component service life.
2. b) Design and justify two complementary technical modifications to solve the problem: one at the software/signal conditioning level for the sensor signal, and another at the comparator logic level (implementation of hysteresis or deadband), determining the width you would give to that band.

A municipality is considering replacing fixed-timer traffic lights with sensor-based traffic lights (induction loops under the road surface). Evaluate the decision: elements of the new system (sensors, controller, communications), advantages (fewer delays when there is no traffic), costs, and what backup operating mode it should have if a sensor fails (reverting to fixed timings).