Open Loop and Closed Loop

In your own words, explain what an open-loop control system and a closed-loop control system are, and give an everyday example of each other than a thermostat.

Define what the setpoint (reference value) of a control system is, and state the typical setpoint for each of these three systems: home heating, a car's cruise control, and a refrigerator.

Explain what the comparator in a closed-loop system is: what two values it receives and what output it delivers to the controller.

Classify these systems as open-loop or closed-loop and justify each answer: (a) timed bread toaster, (b) air conditioning, (c) fixed-time traffic light, (d) car cruise control, (e) garden watering system with a timer.

True or false, justifying your answer with an example: "An open-loop system automatically corrects the errors it makes."

An electric heater has three power settings and no sensors. Explain why it operates in an open loop and describe two changes that would convert it into a closed loop.

The figure shows the block diagram of a closed-loop system, but the name of the signal returning from the sensor to the summing junction (marked with "?") is missing.

1. a) State the name of that signal.
2. b) Explain what information it carries and what it is used for.

Match each term with its definition: (a) setpoint, (b) error, (c) feedback, (d) output. Definitions: (1) value to be maintained; (2) difference between the desired value and the actual value; (3) information about the actual state that returns to the input; (4) quantity controlled by the system.

A clay oven is heated by a fixed-power heating element and takes no measurements. State which components it lacks to operate in a closed loop and explain what each component would do.

A thermostat is set to a setpoint of $22\ ^\circ\text{C}$ and the room is at $19\ ^\circ\text{C}$. Calculate the error measured by the comparator and describe what the system does until the error becomes zero.

In a tank, a float connected to a valve shuts off the water inlet upon reaching the desired level. Identify the setpoint, sensor, comparator, actuator, and controlled variable in this system.

The figure shows the control loop for a car's cruise control, with the setpoint and actual speed shown. Calculate the missing error value, identify which physical component acts as the sensor and which as the actuator, and explain what command the controller will give.

Create a comparison table between a ceiling fan (open loop) and an air conditioner (closed loop), listing two advantages and two disadvantages for each, considering precision, cost, and electricity consumption.

A timed irrigation system waters every night whether it rains or not; another system measures soil moisture first. State which loop each system uses and explain two problems of the first system that the second avoids.

A dishwasher always runs the same cycle whether full or half empty; a modern washing machine weighs the laundry and adjusts the water and time. Classify the loop type for each appliance and explain the advantages of taking measurements.

Explain what a disturbance is in a control system and identify the main disturbance in these closed loops: (a) a thermostat with an open window in winter, (b) cruise control on an uphill slope, (c) filling a tank with the drain open.

Look at the level control mechanism in the figure. It is desired for the water to stabilize at a higher level than the current one without replacing any parts.

1. a) Analyze the role of the pivoting lever (marked with "?"): justify how it physically performs the function of a comparator between the setpoint and the actual measurement.
2. b) Design and justify two possible mechanical adjustments in the mechanism (on the rod, the float, or the pivot point) to raise the desired filling level.
3. c) Predict what will happen to the water level if the tank suffers a constant leak through the bottom that is smaller than the maximum inflow rate (disturbance): will it empty, reach the desired level exactly, or stabilize slightly below it? Justify your answer in terms of error and feedback.

A vehicle drives with cruise control set at $100\ \text{km/h}$. When starting to climb a steep slope, its speed drops to $92\ \text{km/h}$, takes $5\ \text{s}$ to return to $100\ \text{km/h}$, and even momentarily reaches $102\ \text{km/h}$ before stabilizing. A driver states: "The system does not work properly; if it were an effective closed loop, the speed would never have dropped below $100\ \text{km/h}$ nor would it have overshot later."

1. a) Refute the driver's statement by explaining why it is physically impossible for the correction to a disturbance to be instantaneous, identifying the limitations of the actuator and the process.
2. b) Analyze the evolution of the error ($e = v_{\text{setpoint}} - v_{\text{actual}}$): indicate its sign and how it varies at the three key moments (during the drop to $92\ \text{km/h}$, when crossing $100\ \text{km/h}$, and during the peak of $102\ \text{km/h}$).
3. c) Justify what causes this overshoot of $102\ \text{km/h}$ in terms of the vehicle's inertia and the loop's response time.

You are tasked with automating the filling of a swimming pool so that the water stays between two marks: a minimum level of $1.40\ \text{m}$ and a maximum level of $1.50\ \text{m}$.

1. a) Justify why a design with a single level sensor that activates the electric pump as soon as the water drops below $1.50\ \text{m}$ would cause premature motor breakdowns due to waves caused by wind or swimmers.
2. b) Design the appropriate control loop: specify what type of sensors you would use (on/off type with hysteresis or two independent sensors), what the actuator is, and develop the logic rule or decision table that the controller must follow to turn the pump on and off.
3. c) Analyze two external disturbances of opposite sign (one that increases the level and another that reduces it) and describe how the system will react to each to protect the facility.

The temperature graph of the inside of a refrigerator (setpoint set to $4.0\ ^\circ\text{C}$) shows that, after the door was left ajar at 23:00, the temperature rises progressively from $4.0\ ^\circ\text{C}$ until stabilizing at $15.0\ ^\circ\text{C}$ at 03:00, remaining at that constant value all night. A novice technician concludes: "Since the temperature no longer changes after 03:00, the sensor has broken down and the loop has stopped acting."

1. a) Refute the technician's conclusion: justify why the temperature plateaus at $15.0\ ^\circ\text{C}$ even though the compressor (actuator) is running at $100\ \%$ of its capacity (thermal equilibrium between losses and cooling capacity).
2. b) Determine the value of the steady-state error ($e = T_{\text{setpoint}} - T_{\text{actual}}$) starting from 03:00 and explain what control signal the comparator continues to send to the actuator.
3. c) Design an improvement for the refrigerator's control system to prevent the compressor from running indefinitely in this failure condition and protect the food.

In the telemetry of a car equipped with cruise control, two events are recorded on a horizontal highway section:

• Event 1: At $t = 20\ \text{s}$, the actuator suddenly increases fuel injection; the speed smoothly goes from $90\ \text{km/h}$ to $120\ \text{km/h}$.

• Event 2: At $t = 80\ \text{s}$, the speed suddenly drops from $120\ \text{km/h}$ to $111\ \text{km/h}$; a fraction of a second later, the engine accelerates to bring the speed back to $120\ \text{km/h}$.

1. a) Reasonably identify which of the two events corresponds to an external disturbance (such as a wind gust or a change in gradient) and which to a modification of the setpoint by the driver.
2. b) Explain at which point of the block diagram the causing signal enters in each case and how the error evolves ($e = v_{\text{setpoint}} - v_{\text{actual}}$) at the initial instant of each event.
3. c) Predict what would have happened to the vehicle's speed in both events if the car did not have cruise control (operating in open loop with the throttle in a fixed position).

A Technology student categorically states: "Any machine or household appliance works better if it is designed in closed loop; open loop is an obsolete and flawed design."

1. a) Refute their stance by analyzing two everyday devices: a bread toaster with a timer and a fixed-cycle traffic light at an intersection. Explain what sensors and actuators each would need to become closed-loop, and what technical or reliability issues would arise when trying to do so.
2. b) Justify, using at least three objective engineering criteria (economic cost, complexity, and robustness against sensor failures), why open loop remains the optimal and preferable solution in many industrial and domestic applications.

The autopilot of a sailboat is programmed to maintain a constant heading of $090^\circ$ (East). During a voyage with strong lateral wind from the North, two situations are analyzed:

• Situation 1: The boat sails steadily but showing an actual heading of $094^\circ$, never finishing correcting those $4^\circ$ of deviation even though the digital compass measures with complete accuracy.

• Situation 2: After replacing the rudder servomotor during a stopover, the mechanic accidentally reverses the actuator connection cables (when ordered to turn to starboard, the rudder turns to port).

1. a) Draw or describe the system's block diagram, identifying each element (setpoint, comparator, controller, actuator, process, and sensor), and indicate exactly which block the lateral wind affects.
2. b) Analyze Situation 1: why can a simple control loop exhibit this steady-state error in the presence of a constant disturbance? What would the controller have to do with the rudder to eliminate it?
3. c) Reasonably predict what will happen to the boat's trajectory in Situation 2 as soon as a small wave deviates the heading by $1^\circ$, justifying your answer using the concepts of positive feedback, negative feedback, and stability.

You can draw the diagram on paper and attach a photograph.

To fire clay pieces without them cracking due to thermal stress, an electric kiln must raise the temperature at a constant rate of $150\ ^\circ\text{C/h}$ until reaching $1,000\ ^\circ\text{C}$, maintain that value for $2\ \text{h}$, and then cool down at $100\ ^\circ\text{C/h}$.

1. a) Draw or describe the qualitative temperature-time graph of the setpoint and explain how this setpoint differs conceptually from that of a domestic heating thermostat.
2. b) If the kiln's actuator were a simple on/off relay (which only connects or disconnects the heating elements at maximum power), predict what technical difficulties the system would have in accurately tracking the progressive temperature rise and fall phases.
3. c) During the holding phase at $1,000\ ^\circ\text{C}$, the kiln door is opened for $20\ \text{s}$ to inspect a piece. Explain the temporal sequence of the loop's response (sensor evolution, sign of the error, and actuator response) from the moment the disturbance occurs until equilibrium is restored.