Benutzerhandbuch für National Instruments 370753C-01

Inhaltsverzeichnis

• Xmath Control Design Module

  1
• Important Information

  3
  • Warranty

    3
  • Copyright

    3
  • Trademarks

    3
  • Patents

    3
  • WARNING REGARDING USE OF NATIONAL INSTRUMENTS PRODUCTS

    3
• Conventions

  4
• Contents

  5
• Chapter 1 Introduction

  9
  • Using This Manual

    9
    • Document Organization

      9
    • Bibliographic References

      10
    • Commonly Used Nomenclature

      10
    • Related Publications

      11
    • MATRIXx Help

      11
  • Control Design Tutorial

    12
    • Helicopter Hover Problem: An Ad Hoc Approach

      12
      • Figure 1-1. Block Diagram of Helicopter System H(s) with Compensators K1(s) and K2(s) in the Feedforward Path

        14
      • Figure 1-2. Locus of all Open-Loop and Closed-Loop Roots of Gs

        16
      • Figure 1-3. Helicopter Velocity Response to a Step Input at the Rotor

        17
      • Figure 1-4. Block Diagram of the Closed-Loop Controller

        18
      • Figure 1-5. Helicopter Velocity Tracking Step Input at the Rotor

        20
      • Figure 1-6. Closed-Loop System Bode Plot

        21
    • Helicopter Hover Problem: State Feedback and Observer Design

      21
      • Figure 1-7. Full-State Feedback Regulator

        22
      • Figure 1-8. Complete Controller and Estimator

        22
      • Figure 1-9. Step Response for Observer-Based Design

        24
      • Figure 1-10. Multiple Plots Showing Time Needed for States to be Correctly Tracked by Estimator, Given Incorrect Initial Values

        26
    • Helicopter Hover Problem: Discrete Formulation

      26
      • Figure 1-11. Frequency Response of ssys and Its Discrete Equivalent ssysd

        27
      • Figure 1-12. Step Response of a Discrete System Using Discretized Observer-Based Controller

        28
    • Inverted Wedge-Balancing Problem: LQG Control

      28
      • Figure 1-13. Response of Full-State Feedback Controller to a Unit Step Disturbance

        31
      • Figure 1-14. Response of Observer-Based Controller to a Unit Step Disturbance

        32
• Chapter 2 Linear System Representation

  33
  • Linear Systems Represented in Xmath

    33
    • Table 2-1. Summary of Linear Systems

      33
  • Transfer Function System Models

    34
  • State-Space System Models

    37
    • Basic System Building Functions

      38
    • system( )

      38
    • abcd( )

      40
    • numden( )

      42
    • period( )

      42
    • names( )

      43
  • Size and Indexing of Dynamic Systems

    44
  • Using check( ) with System Objects

    44
  • Discretizing a System

    45
    • discretize( )

      45
      • Numerical Integration Methods: forward, backward, tustins

        46
      • Table 2-2. Mapping Methods for discretize( )

        46
      • Pole-Zero Matching: polezero

        47
      • Z-Transform: ztransform

        47
      • Hold Equivalence Methods: exponential and firstorder

        47
      • Figure 2-1. Comparison of Different Frequency Response Techniques

        49
    • makecontinuous( )

      49
      • Table 2-3. Mapping Methods for makecontinuous( )

        50
• Chapter 3 Building System Connections

  52
  • Linear System Interconnection Operators

    52
    • Table 3-1. Summary of Interconnection Operators

      52
  • Linear System Interconnection Functions

    55
    • afeedback( )

      55
      • Figure 3-1. afeedback System Configuration

        55
      • Algorithm

        56
    • append( )

      57
      • Figure 3-2. Output of a Dynamic System

        58
    • connect( )

      59
      • Figure 3-3. Parameters Used with the connect Command

        59
      • Algorithm

        61
    • feedback( )

      62
      • Figure 3-4. Feedback System Configuration

        62
      • Algorithm

        63
• Chapter 4 System Analysis

  65
  • Time-Domain Solution of System Equations

    65
  • System Stability: Poles and Zeros

    66
    • poles( )

      67
    • zeros( )

      67
      • Algorithm

        69
  • Partial Fraction Expansion

    69
    • Figure 4-1. Constructing the Closed-Loop System Gcl (s) from the Open-Loop System G(s), with Input U(s) and Output Y(s)

      70
    • Figure 4-2. Transient Response of the Closed-Loop System as a Function of Time

      72
    • residue( )

      72
    • combinepf( )

      73
  • General Time-Domain Simulation

    74
    • Figure 4-3. System Time Response to a Series of Step Signals

      76
  • Impulse Response of a System

    77
    • impulse( )

      77
      • Figure 4-4. 15-Second Impulse Response

        79
    • deftimerange( )

      79
  • System Response to Initial Conditions

    80
    • initial( )

      80
      • Figure 4-5. 15-Second System Response to Unity Nonzero Conditions at Each of the States

        81
  • Step Response

    82
    • step( )

      82
      • Figure 4-6. 15-Second Step Response, Showing Performance Measures

        83
• Chapter 5 Classical Feedback Analysis

  85
  • Feedback Control of a Plant Model

    85
    • Figure 5-1. Feedback Control System Block Diagram

      85
  • Root Locus

    86
    • rlocus( )

      87
      • Figure 5-2. Root Locus of H for Gain K = 0.07

        88
  • Frequency Response and Dynamic Response

    89
    • freq( )

      89
      • Algorithm

        90
      • Figure 5-3. Representation of the Open-Loop System

        91
  • Bode Frequency Analysis

    91
    • bode( )

      94
      • Figure 5-4. Bode Plot Showing System Gain and Phase Margins

        95
    • margin( )

      96
    • nichols( )

      98
      • Figure 5-5. nichols( ) Gain-Phase Plot

        99
  • Nyquist Stability Analysis

    99
    • Figure 5-6. Closed-Loop System Containing a Variable Gain K

      100
    • nyquist( )

      100
      • Figure 5-7. Nyquist Plot of the Open-Loop System for Frequencies from 0.01 Hz to 10 Hz

        102
      • Figure 5-8. Nyquist Plot of the Open-Loop System for Frequencies from 0.5 Hz to 5 Hz

        102
      • Figure 5-9. Nyquist Contour Formed by Drawing the System’s Nyquist Plot for All Positive Frequencies

        103
  • Linear Systems and Power Spectral Density

    104
    • psd( )

      104
• Chapter 6 State-Space Design

  106
  • Controllability

    106
    • Figure 6-1. Full-State Feedback Being Used to Relocate the Eigenvalues of a Controllable System Based on the Value of the Gain K

      108
    • controllable( )

      108
  • Observability and Estimation

    109
    • Figure 6-2. General Observer Block Diagram

      111
    • observable( )

      111
  • Minimal Realizations

    112
    • minimal( )

      113
    • stair( )

      114
  • Duality and Pole Placement

    115
    • poleplace( )

      115
  • Linear Quadratic Regulator

    117
    • Figure 6-3. Continuous-Time Regulator

      117
    • regulator( )

      119
      • Figure 6-4. Diagram of Plant for the Inverted Pendulum Problem

        120
  • Linear Quadratic Estimator

    121
    • Figure 6-5. Diagram of the Estimator Representation

      122
    • estimator( )

      125
  • Linear Quadratic Gaussian Compensation

    126
    • Figure 6-6. Linear Quadratic Gaussian Compensator (in the Bold Rectangle)

      127
    • lqgcomp( )

      128
      • Figure 6-7. f and x as a Function of Time, Starting from Zero, as a Result of a Sinusoidal Force Applied to the System Input

        130
  • Riccati Equation

    130
    • riccati( )

      131
  • Steady-State System Response Using Lyapunov Equations

    133
    • lyapunov( )

      135
      • Algorithm

        135
    • rms( )

      137
  • Balancing a Linear System

    138
    • balance( )

      140
  • Modal Form of a System

    142
    • modal( )

      142
    • mreduce( )

      143
      • Figure 6-8. Modal System and Reduced Modal System

        147
• Appendix A Technical References

  148
• Appendix B Technical Support and Professional Services

  150
• Index

  152
  • A-D

    152
  • E-H

    153
  • I-N

    154
  • O-R

    155
  • S

    156
  • T-Z

    157