Beard, McLain, Peterson, “Introduction to Feedback Control,” Chapter 1: Slide 1

Chapter 1

Introduction

Beard, McLain, Peterson, “Introduction to Feedback Control,” Chapter 1: Slide 2

Course Overview

Physical System

Simulation Model

Transfer Function Design Model

State Space Design Model

Observer Based Control

Euler-Lagrange Equations

Linearization, Model Reduction, Simplification, etc.

Test in Simulation

Implement on Physical System

PID Control

Loopshaping Control

Beard, McLain, Peterson, “Introduction to Feedback Control,” Chapter 1: Slide 3

Course content

I Brief Intro to Simulation ModelsII Design Models

• Equilibria and Linearization

• Transfer Function Models

• State Space Models

III PID Control Design• Pole Placement for Second Order Systems • Design Strategies for Second Order Systems

• System Type and Integrators

• Digital Implementation of PID Controllers

IV Root-locus-based Control Design• Root-locus Analysis, Stability, Performance• Dynamic Compensation

V Loopshaping Control Design• Frequency Response of LTI Systems• Frequency Domain Specifications• Stability and Robustness Margins• Compensator Design

VI Observer-Based Control Design • Full-State Feedback• Integrator with Full State Feedback• Observers

Beard, McLain, Peterson, “Introduction to Feedback Control,” Chapter 1: Slide 4

Design Study A: Single Link Robot Arm

Beard, McLain, Peterson, “Introduction to Feedback Control,” Chapter 1: Slide 5

Design Study B: Pendulum on a Cart

Beard, McLain, Peterson, “Introduction to Feedback Control,” Chapter 1: Slide 6

Design Study C: Satellite Attitude Control

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Beard, McLain, Peterson, “Introduction to Feedback Control,” Chapter 1: Slide 7

Design Study D: Mass Spring Damper

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Beard, McLain, Peterson, “Introduction to Feedback Control,” Chapter 1: Slide 8

Design Study E: Ball on Beam

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Beard, McLain, Peterson, “Introduction to Feedback Control,” Chapter 1: Slide 9

Design Study F: Planar VTOL

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Beard, McLain, Peterson, “Introduction to Feedback Control,” Chapter 1: Slide 10

What can feedback do for you?

• Reduce your system’s sensitivity to disturbances• Reduce your system’s sensitivity to changes in its dynamics• Change the dynamics of your system

• Can move the eigenvalues (aka poles, characteristic roots) to desirable locations in the s-plane

• Improve stability properties• Improve system performance (e.g., speed of response, steady-state error,

etc.)• Other stuff too!

Beard, McLain, Peterson, “Introduction to Feedback Control,” Chapter 1: Slide 11

Our big goal

Learn how to use feedback control to bring about desired behaviors in dynamic systems

• Analysis• Design