Chapter 6, Problem 6.3E

Interpretation Introduction

(a)

Interpretation:

Show that:

$\text{Y}\left(\text{0}\right)\text{=}\frac{{\text{KMτ}}_{\text{α}}}{{\text{τ}}_{\text{1}}}$.

Concept introduction:

The magnitude of change is represented by percentage change. Or how many times one number is larger than another one.

When the initial response of the system is in the opposite direction of the final magnitude, then it is known as the Inverse response. Generally, the results of two separate effects occur at the same time but its direction and dynamics are different.

The inverse response most commonly found in the control of the boiler.

Interpretation Introduction

(b)

Interpretation:

For step input change of magnitude $\text{M}$, it should be determined that the overshoot occurs only for the condition ${\text{τ}}_{\text{α}}>{\text{τ}}_{\text{1}}$.

Concept introduction:

The magnitude of change is represented by percentage change or how many times one number is larger than another one.

When the initial response of the system is in the opposite direction of the final magnitude, then it is known as the Inverse response. Generally, the results of two separate effects occur at the same time but its direction and dynamics are different.

The inverse response most commonly found in the control of the boiler.

Interpretation Introduction

(c)

Interpretation:

For step input change of magnitude $\text{M}$, it should be determined the inverse response occurs only for condition ${\text{τ}}_{\text{α}}<0$.

Concept introduction:

The magnitude of change is represented by percentage change or how many times one number is larger than another one.

When the initial response of the system is in the opposite direction of the final magnitude, then it is known as the Inverse response. Generally, the results of two separate effects occur at the same time but its direction and dynamics are different.

The inverse response most commonly found in the control of the boiler.