National Instruments 370753C-01 - Manual

National Instruments 370753C-01

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Table of Contents:

  • Page 2 – Support; Worldwide Technical Support and Product Information; Technical Support and Professional Services
  • Page 3 – Important Information; Warranty; WARNING REGARDING USE OF NATIONAL INSTRUMENTS PRODUCTS
  • Page 4 – Conventions; response; File»Page Setup»Options; italic; monospace
  • Page 5 – Contents
  • Page 8 – Index
  • Page 9 – Introduction; Using This Manual; Xmath Help; Document Organization; This manual includes the following chapters:
  • Page 10 – Building System Connections; Bibliographic References; Technical References; Commonly Used Nomenclature
  • Page 11 – Related Publications
  • Page 12 – Control Design Tutorial; Helicopter Hover Problem: An Ad Hoc Approach; letting the state variables
  • Page 13 – Use
  • Page 14 – Input Names; in the feedforward path.; Block Diagram of Helicopter System
  • Page 15 – Note; Gs; Feedback Loop Gain
  • Page 16 – Locus of all Open-Loop and Closed-Loop Roots of Gs; . To close the interactive root locus dialog; File»Exit
  • Page 17 – Close the loop using the single-input syntax of; Helicopter Velocity Response to a Step Input at the Rotor; Instead, you now place
  • Page 18 – Block Diagram of the Closed-Loop Controller; DC; G s
  • Page 19 – Because; The system has 1 uncontrollable state
  • Page 20 – Helicopter Velocity Tracking Step Input at the Rotor; You also can look at the gain and phase margins of the system.; There are no 0 dB gain crossings.; The bode plot of the closed-loop system is shown in Figure 1-6.
  • Page 21 – Closed-Loop System Bode Plot; Helicopter Hover Problem: State Feedback and Observer Design; The approach taken in the
  • Page 22 – Full-State Feedback Regulator
  • Page 23 – est
  • Page 24 – by the desired scaling factor.; Step Response for Observer-Based Design; The
  • Page 25 – When you create the estimator system
  • Page 26 – by Estimator, Given Incorrect Initial Values; Helicopter Hover Problem: Discrete Formulation; Helicopter Hover Problem: State; ssys
  • Page 27 – You can use the default exponential discretization method with; dt
  • Page 28 – Step Response of a Discrete System Using Discretized; The resulting response is shown in Figure 1-12.; Inverted Wedge-Balancing Problem: LQG Control
  • Page 29 – is the angle (in radians) the wedge makes with the vertical axis,
  • Page 30 – You then can verify that the regulator gain; Kr; can be used with full-state; NULL; and feeding back the states:
  • Page 31 – The following steps generate the plot shown in Figure 1-14:
  • Page 32 – Response of Observer-Based Controller to a Unit Step Disturbance
  • Page 33 – Linear System Representation; Xmath provides a structure for system representation called a; Linear Systems Represented in Xmath; Summary of Linear Systems; System Type; Transfer function
  • Page 34 – Transfer Function System Models; Minimal Realizations
  • Page 35 – State-Space System Models
  • Page 37 – and
  • Page 38 – Basic System Building Functions
  • Page 39 – Discretizing a System
  • Page 40 – Using system( ) to Change the Attributes of an Existing System
  • Page 41 – Sys; itself remains unchanged. The transfer function must be proper.
  • Page 42 – num
  • Page 43 – Using period( ) to Extract the Sampling Period; Xmath Commands
  • Page 44 – Size and Indexing of Dynamic Systems; convert; y q
  • Page 45 – initial delay outputs
  • Page 46 – Method of Approximation; forward; d t
  • Page 47 – ztransform; z d t
  • Page 48 – exponential
  • Page 49 – Comparison of Different Frequency Response Techniques
  • Page 50 – Hold Equivalence; Verifying a Discretization Using makecontinuous( ); s d t
  • Page 51 – Now convert back to the continuous form:
  • Page 52 – overloaded; Linear System Interconnection Operators; Diagram
  • Page 53 – Summary of Interconnection Operators (Continued)
  • Page 54 – General
  • Page 55 – Linear System Interconnection Functions
  • Page 56 – Using afeedback( ) to Connect Two Systems; Algorithm
  • Page 57 – eps; MATRIXx Help
  • Page 58 – Output of a Dynamic System
  • Page 60 – Both systems must have the same sample rate.
  • Page 61 – KD; rcond
  • Page 62 – Feedback System Configuration; Implementing Unity Gain Feedback Using feedback( ); # negative unity gain feedback
  • Page 63 – The system used for the feedback loop,
  • Page 65 – System Analysis; Time-Domain Solution of System Equations
  • Page 66 – System Stability: Poles and Zeros; stability
  • Page 67 – zeros; Using poles( ) with a System in Transfer Function Form
  • Page 68 – normal rank
  • Page 69 – QZ; Partial Fraction Expansion; residue
  • Page 70 – Dynamic Response through Partial Fraction Expansion; Constructing the Closed-Loop System; Calculate the closed-loop transfer function.; initial integrator outputs
  • Page 71 – You can examine the stability of; ) by representing it as a sum of partial; G t
  • Page 72 – Transient Response of the Closed-Loop System as a Function of Time
  • Page 73 – pls; Verifying a; Rp
  • Page 74 – General Time-Domain Simulation; y s
  • Page 76 – System Time Response to a Series of Step Signals; General Time-Domain Simulation for a MIMO System
  • Page 77 – Impulse Response of a System
  • Page 78 – 5-second Impulse Response of a Stable State-Space System
  • Page 79 – 5-Second Impulse Response; computes a regular time vector (in units of seconds); tvec; time
  • Page 80 – System Response to Initial Conditions
  • Page 81 – Using initial( ) to Determine the Sensitivity of the States; 5-Second System Response to Unity Nonzero Conditions
  • Page 82 – Step Response; Performance Measurements for a Step Response
  • Page 83 – 5-Second Step Response, Showing Performance Measures; Mp
  • Page 84 – Subtract domain values to get time duration:
  • Page 85 – Classical Feedback Analysis; The open-loop systems analyzed in Chapter 4,; Feedback Control of a Plant Model; Feedback Control System Block Diagram; The output of the open-loop system is; Y s
  • Page 86 – Root Locus
  • Page 87 – Graphics; pattern; RECOMPUTE; A Comparison of Several Discretization Methods
  • Page 88 – Root Locus of
  • Page 89 – Frequency Response and Dynamic Response
  • Page 90 – PHP; I A
  • Page 91 – Representation of the Open-Loop System; Frequency Response of a Simple System; track; Bode Frequency Analysis
  • Page 92 – minimum phase
  • Page 93 – KH
  • Page 94 – Analyzing a Frequency Response Using bode( )
  • Page 95 – Bode Plot Showing System Gain and Phase Margins; contributes –90
  • Page 96 – atan
  • Page 97 – Mg
  • Page 99 – Nyquist Stability Analysis
  • Page 100 – Closed-Loop System Containing a Variable Gain
  • Page 102 – Nyquist Plot of the Open-Loop System for Frequencies
  • Page 103 – Nyquist Contour Formed by Drawing the System’s Nyquist Plot; will be equal
  • Page 104 – Linear Systems and Power Spectral Density; Uspec; H q
  • Page 105 – Verifying the Response of a System to White Noise Input; j w; j w
  • Page 106 – Controllability
  • Page 107 – an
  • Page 108 – Full-State Feedback Being Used to Relocate the Eigenvalues; function returns; The system has 2 uncontrollable states
  • Page 109 – Similarly, if you form the controllability matrix for this system,; Observability and Estimation; As described in the
  • Page 110 – Du
  • Page 111 – General Observer Block Diagram; LC; A L C
  • Page 112 – Observability of a System; The system has 1 unobservable state; Similarly, if you form the observability matrix for this system,; endFor
  • Page 113 – Finding a Minimal Realization for a System
  • Page 114 – ans is null; A T
  • Page 115 – Duality and Pole Placement
  • Page 116 – Arbitrary Pole Placement for a Controllable System
  • Page 117 – Linear Quadratic Regulator; Continuous-Time Regulator
  • Page 119 – Designing a Regulator for the Inverted Pendulum
  • Page 120 – Diagram of Plant for the Inverted Pendulum Problem
  • Page 121 – Ruu; Linear Quadratic Estimator
  • Page 122 – Diagram of the Estimator Representation; A x B u G w; E G
  • Page 123 – and where the matrix
  • Page 125 – Riccati Equation
  • Page 126 – . For an example of how to design a state estimator; , which is a function of the input matrix:; Ke; Linear Quadratic Gaussian Compensation
  • Page 127 – and state estimator with gain; Linear Quadratic Gaussian Compensator (in the Bold Rectangle)
  • Page 128 – SysC; Combining the Regulator and Estimator into a Full Compensator
  • Page 129 – Set plot attributes for all three plots:; endfor
  • Page 132 – System is continuous; Discrete Riccati Equation
  • Page 133 – System is discrete, sampling at 1 seconds.; A X X B
  • Page 135 – Steady state; eye; C x
  • Page 136 – To solve the special Lyapunov equation, use the following syntax:; Discrete Lyapunov Equation; A X
  • Page 137 – Special Lyapunov Equation; Ucov; A X X A; C X C
  • Page 138 – Balancing a Linear System
  • Page 139 – T x
  • Page 140 – SysB; D u
  • Page 141 – HSV; Balancing a System
  • Page 142 – Modal Form of a System
  • Page 143 – AT; keep
  • Page 144 – Model Reduction Module
  • Page 147 – Modal System and Reduced Modal System
  • Page 152 – default frequency range
  • Page 153 – converting to continuous
  • Page 154 – linear
  • Page 155 – operators
  • Page 156 – selection matrix for adding or removing
  • Page 157 – transform
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NI MATRIXx

TM

Xmath

™

Control Design Module

Xmath Control Design Module

April 2007
370753C-01

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Summary

Page 2 - Support; Worldwide Technical Support and Product Information; Technical Support and Professional Services

Support Worldwide Technical Support and Product Information ni.com National Instruments Corporate Headquarters 11500 North Mopac Expressway Austin, Texas 78759-3504 USA Tel: 512 683 0100 Worldwide Offices Australia 1800 300 800, Austria 43 662 457990-0, Belgium 32 (0) 2 757 0020, Brazil 55 11 3262 3...

Page 3 - Important Information; Warranty; WARNING REGARDING USE OF NATIONAL INSTRUMENTS PRODUCTS

Important Information Warranty TThe media on which you receive National Instruments software are warranted not to fail to execute programming instructions, due to defects in materials and workmanship, for a period of 90 days from date of shipment, as evidenced by receipts or other documentation. Nat...

Page 4 - Conventions; response; File»Page Setup»Options; italic; monospace

Conventions The following conventions are used in this manual: < > Angle brackets that contain numbers separated by an ellipsis represent a range of values associated with a bit or signal name—for example, DIO<3..0>. [ ] Square brackets enclose optional items—for example, [ response ]. »...

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