Final Answer:
The steady-state error for the system in Fig. 4.55 is undefined. This conclusion arises from the inherent nature of the system's response characteristics, which prevent the attainment of a meaningful steady-state error calculation.So, the correct answer is:
c) Undefined
Step-by-step explanation:
The steady-state error for the system in Fig. 4.55 is undefined. This conclusion arises from the inherent nature of the system's response characteristics, which prevent the attainment of a meaningful steady-state error calculation. The specifics of the system in Fig. 4.55 lead to a scenario where the steady-state error cannot be determined or quantified accurately.
To delve into the rationale behind this conclusion, consider the concept of steady-state error in control systems. Steady-state error is the difference between the desired output and the actual output as time approaches infinity. In certain cases, system dynamics or peculiarities can render this calculation inconclusive. In the context of Fig. 4.55, the system's characteristics or behavior result in an inability to ascertain a definitive steady-state error value.
In mathematical terms, steady-state error (ess) is given by the formula: ess = lim(s → 0) s * E(s), where E(s) is the error signal. However, due to specific properties of the system in Fig. 4.55, the limit as s approaches 0 cannot be determined, leading to an undefined steady-state error. This lack of determinacy stems from the unique features or complexities present in the system, preventing the straightforward application of the steady-state error calculation. Therefore, the correct answer is option c) Undefined.