Control Systems

4.

Time-Domain Analysis

4.1.

System Response Characteristics

4.1.1.

Transient Response

4.1.2.

Steady-State Response

4.1.3.

Natural Response

4.1.4.

Forced Response

4.2.

Standard Test Inputs

4.2.1.

4.2.1.1.

Unit Step Function

4.2.1.2.

Step Response Analysis

4.2.2.

4.2.2.1.

Unit Ramp Function

4.2.2.2.

Ramp Response Analysis

4.2.3.

Parabolic Input

4.2.3.1.

Parabolic Function

4.2.3.2.

Parabolic Response Analysis

4.2.4.

4.2.4.1.

Unit Impulse Function

4.2.4.2.

Impulse Response Analysis

4.2.5.

Sinusoidal Input

4.2.5.1.

Sinusoidal Response

4.2.5.2.

Frequency Response

4.3.

First-Order Systems

4.3.1.

4.3.2.

4.3.3.

Response to Standard Inputs

4.3.3.1.

4.3.3.2.

4.3.3.3.

Impulse Response

4.3.4.

Physical Examples

4.4.

Second-Order Systems

4.4.1.

4.4.2.

Natural Frequency

4.4.3.

4.4.4.

System Classification

4.4.4.1.

Undamped Systems

4.4.4.2.

Underdamped Systems

4.4.4.3.

Critically Damped Systems

4.4.4.4.

Overdamped Systems

4.4.5.

Step Response Analysis

4.4.5.1.

Response Equations

4.4.5.2.

Response Characteristics

4.4.6.

Physical Examples

4.5.

Higher-Order Systems

4.5.1.

Dominant Pole Concept

4.5.2.

Approximation Methods

4.5.3.

Response Characteristics

4.6.

Performance Specifications

4.6.1.

Time-Domain Specifications

4.6.1.1.

4.6.1.2.

4.6.1.3.

Maximum Overshoot

4.6.1.4.

4.6.1.5.

4.6.2.

Steady-State Error

4.6.2.1.

Error Definition

4.6.2.2.

Error Constants

4.6.2.2.1.

Position Error Constant

4.6.2.2.2.

Velocity Error Constant

4.6.2.2.3.

Acceleration Error Constant

4.6.2.3.

4.6.2.3.1.

4.6.2.3.2.

4.6.2.3.3.

4.6.2.4.

Error Analysis for Different Inputs

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