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.

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.

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."

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.

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.

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.

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.

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).