Based on the given para, answer the following question.

Sensitivity considerations often are important in the design of Control Systems. Because all physical elements have properties that change with environment and age, we cannot always consider the parameters of the Control System to be completely stationary over the entire operating life of the system. For instance, the winding resistance of an electric motor changes as the temperature of the motor rises during operation. Control systems with electric components may not operate normally when first turned on because of the still-changing system parameters during warmup. This phenomenon is sometimes called “morning sickness”. Most duplicating machines have a warmup period during which time operation is blocked out when first turn on.

For an open-loop control system, sensitivity of overall transfer function M(s) with respect to forward path transfer function G(s) will be:

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Concept:

Consider the open-loop control system shown in Figure, where u(t) represents the input control action of the system and y(t) points to the system output response.

The overall transfer function of the system in Figure is given as follows:

\(T = \frac{Y}{U} = G\)

\(\therefore \;\frac{T}{G} = 1,\;and\;\frac{{dT}}{{dG}} = 1\)

The sensitivity with respect to G can be obtained as:

\(\therefore S = \frac{{\frac{{dT}}{{dG}}}}{{\frac{T}{G}}} = 1\)

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