Chapter 7: Compensation

The following sections are included:

• Compensation—An Introduction

• The Attenuator

• Phase-Lag Compensation

• Phase-Lead Compensation

• Lag-lead Compensation

• The PID Controller

• An Extended Example

  • The Attenuator

  • The Phase-Lag Compensator

  • The Phase-Lead Compensator

  • The Lag-Lead Compensator

  • The PD Controller

  • A Comparison of the Step Responses

• The Ziegler-Nichols Rules

  • Introduction

  • The Assumption

  • Characterizing the Plant

  • A Partial Verification

  • Estimating the System’s Phase Margin

  • Estimating the System’s Gain Margin

  • Estimating the System’s Settling Time

  • Using the Python Programming Language to Examine the Ziegler-Nichols Rules

• Bode’s Sensitivity Integrals

  • Introduction

  • The Sensitivity Function

  • Bode’s Sensitivity Integrals

  • Case I

  • Case II

  • Case III

  • Case IV

  • Available Bandwidth

  • Open-Loop Unstable Systems with Limited Available Bandwidth

• Exercises