Understanding Open Loop Transfer Function in Closed Loop Systems

The question asks for the definition of the open loop transfer function within the context of a closed loop control system. To understand this, let's first define some key signals in a standard closed loop system:

• Actuating signal: This is the signal that drives the forward path of the system. In a typical negative feedback system, this is the error signal, which is the difference between the reference input and the feedback signal.
• Output signal: This is the main output of the system, usually denoted as C(s).
• Feedback signal: This is the signal from the output that is sent back through the feedback path, usually denoted as B(s). It is compared with the reference input to generate the actuating signal.

A standard closed loop control system typically consists of a forward path with a transfer function, say \( G(s) \), and a feedback path with a transfer function, say \( H(s) \). The input to the forward path is the actuating signal, and the output of the forward path is the system's output.

The transfer function of the forward path, \( G(s) \), is defined as the ratio of the output signal to the actuating signal, assuming the loop is operational:

\[ G(s) = \frac{\text{Output}}{\text{Actuating signal}} \]

The open loop transfer function of the closed loop system is generally defined as the transfer function from the input of the forward path (actuating signal) around the loop back to the feedback signal input point (before the summing junction). This is obtained by multiplying the forward path transfer function \( G(s) \) and the feedback path transfer function \( H(s) \):

\[ \text{Open Loop Transfer Function} = G(s)H(s) = \frac{\text{Output}}{\text{Actuating signal}} \times \frac{\text{Feedback signal}}{\text{Output}} = \frac{\text{Feedback signal}}{\text{Actuating signal}} \]

However, the options provided are specific signal ratios. Let's evaluate the given options:

1. Actuating signal / feedback signal: This would be \( \frac{1}{G(s)H(s)} \).
2. Output / feedback signal: This would be \( \frac{1}{H(s)} \).
3. Output / actuating signal: This is the definition of the forward path transfer function \( G(s) \).
4. Feedback signal / actuating signal: This is the standard definition of the open loop transfer function \( G(s)H(s) \).

Based on the provided correct answer which states "Output / actuating signal", the question appears to define the 'open loop transfer function' in this context as the transfer function of the forward path \( G(s) \). While the more common definition of the open loop transfer function of a closed loop system is \( G(s)H(s) \), the option that matches the provided answer is the ratio of the Output signal to the Actuating signal.

Therefore, interpreting the question in line with the given options and correct answer:

The open loop transfer function is considered as the transfer function of the forward path, which relates the output to the signal entering the forward path (the actuating signal).

\[ \text{Forward Path Transfer Function} = \frac{\text{Output}}{\text{Actuating signal}} \]

This corresponds to the provided correct option.