When the period of the observation is large, the type of the error wil...
Answer: b
Explanation: The error will be the steady state error if the period of observation is large as the time if large then the final value theorem can be directly applied.
View all questions of this test
When the period of the observation is large, the type of the error wil...
Introduction:
When observing a system, it is important to consider the period of observation. The period of observation refers to the length of time over which the system's behavior is analyzed. In control systems, the type of error that occurs during the observation period depends on the length of that period.
Steady State Error:
Steady state error is the difference between the desired output and the actual output of a system when the system has reached a stable condition. It occurs when the system has settled into a steady state and the output remains constant over time. Steady state error can be caused by various factors such as disturbances, noise, or inaccuracies in the system.
Transient Error:
Transient error, on the other hand, occurs during the transient response of a system. The transient response is the behavior of the system immediately after a change in input or disturbance. It is characterized by a temporary deviation from the desired output before the system settles into a steady state. Transient errors are typically short-lived and diminish over time.
Effect of Observation Period:
When the period of observation is large, it implies that the system is being observed for an extended period of time. During this time, the system has ample time to settle into a steady state and any transient error that may have initially occurred would have diminished significantly. Therefore, the primary type of error that would be observed in this case is steady state error.
Reasoning:
The reason behind this is that steady state error is a result of factors that persist over time, such as disturbances or inaccuracies in the system. These factors can cause a constant deviation between the desired and actual output of the system. When the observation period is large, the system has enough time to reach a stable condition and any transient error would have already diminished. Thus, the primary type of error that remains is the steady state error.
Conclusion:
In summary, when the period of observation is large, the type of error that is primarily observed is steady state error. This is because transient errors diminish over time and the system settles into a stable condition. Understanding the type of error that occurs during a given observation period is crucial for analyzing and improving the performance of control systems.