Open Loop Transfer Function of a System with One Zero

The open loop transfer function of a system is a mathematical representation that describes the relationship between the input and output of the system. It is obtained by taking the Laplace transform of the system's differential equation, assuming zero initial conditions.

Definition of a Zero
In control systems, a zero refers to a value of the transfer function where the numerator becomes zero. This means that when the input of the system takes on that specific value, the output will be zero. Zeros can have different properties depending on their location in the complex plane.

Positive Real Zero
A positive real zero is a zero that lies on the real axis of the complex plane with a positive value. This means that the numerator of the transfer function becomes zero when the input to the system is a positive real number.

Non-Minimum Phase System
A non-minimum phase system is a system in which the phase of the transfer function is not monotonically increasing or decreasing with frequency. In other words, the phase response of the system has peaks and dips. This can cause the system to exhibit undesirable behavior such as overshoot, ringing, or instability.

Explanation
When a system has a transfer function with a positive real zero, it means that there is a value of the input that will cause the output to be zero. This can be seen as a "hole" in the transfer function, indicating that the system has a certain input value that results in no output.

A non-minimum phase system is characterized by having complex poles and zeros in the transfer function. When a zero is on the real axis with a positive value, it contributes to the non-minimum phase behavior of the system. This is because the phase response of the system will have peaks or dips at the frequency corresponding to the zero.

Therefore, the correct answer is option D - Non-minimum phase function. The presence of a positive real zero in the open loop transfer function indicates that the system is non-minimum phase, and its phase response will have peaks or dips at the frequency corresponding to the zero.