The line marked as X is the closed loop response of: 

Explanation:

Single Acting Steam Engine

Definition: A single acting steam engine is a type of steam engine where the steam acts on only one side of the piston during its operation, producing one working stroke per revolution of the crankshaft. This configuration contrasts with double-acting steam engines, where the steam alternately acts on both sides of the piston.

Working Principle: In a single acting steam engine, steam is introduced into the cylinder on one side of the piston. The pressure of the steam pushes the piston, converting thermal energy into mechanical work. After the steam has expanded, it is exhausted, and the piston is returned to its original position by a flywheel or another mechanism, ready for the next cycle.

Advantages:

• Simplicity in design and construction, making it easier to manufacture and maintain.
• Less mechanical complexity compared to double-acting engines, resulting in fewer parts and potential points of failure.

Disadvantages:

• Lower efficiency as only one side of the piston is used for performing work.
• Requires a more substantial flywheel to maintain smooth operation due to the intermittent power delivery.

Applications: Single acting steam engines are commonly used in smaller applications where simplicity and cost are critical factors, such as in some types of pumps and small locomotives.

Correct Option Analysis:

The correct option is:

Option 3: a PI controller

This option correctly describes the closed loop response of a PI controller. A Proportional-Integral (PI) controller is used in control systems to improve the performance of the system by considering both the present and the past errors. The Proportional (P) part addresses the current error, while the Integral (I) part addresses the accumulation of past errors, which helps eliminate the steady-state error.

In the given context, the closed loop response marked as X is likely indicative of the characteristics of a PI controller, such as improved steady-state performance and reduced oscillations compared to other types of controllers.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: a P controller

A Proportional (P) controller responds to the current error but does not consider the accumulation of past errors. This often results in a faster response but can leave a steady-state error. The closed loop response of a P controller would typically be more oscillatory and less stable compared to a PI controller.

Option 2: a PD controller

A Proportional-Derivative (PD) controller uses the present error and the rate of change of the error (derivative). This can provide a faster response and reduce overshoot, but it does not eliminate the steady-state error as effectively as a PI controller. The closed loop response of a PD controller would show quicker damping but would not address steady-state errors as well as a PI controller.

Option 4: an I controller

An Integral (I) controller considers the accumulation of past errors, which helps eliminate steady-state errors but can lead to slower responses and potential instability if not properly tuned. The closed loop response of an I controller would typically be slower and more prone to oscillations.

Conclusion:

Understanding the different types of controllers and their impact on the closed loop response is crucial in control systems. The PI controller combines the advantages of both Proportional and Integral actions, leading to improved steady-state performance and stability. This makes it suitable for a wide range of applications where both quick response and minimal steady-state error are desired.