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.

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 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.

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.