National Instruments 370753C-01 manual

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Table of contents for the manual

  • Page 1

    NI MA TRIXx TM Xmath ™ Control Design Module Xmath Control Design Module April 2007 370753C-01[...]

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    Support Worldwide Technical Support and Product Info rmation ni.com National Instruments Corporate H[...]

  • Page 3

    Important Information Warranty TThe media on which you receive National In struments software are wa[...]

  • Page 4

    Conventions The follo wing con ventions are used in this manual: < > Angle brackets that cont [...]

  • Page 5

    © National Instruments Corporatio n v Xmath Control Design Module Contents Chapter 1 Introduction U[...]

  • Page 6

    Contents Xmath Control Design Module vi ni.com Chapter 3 Building System Connections Linear System I[...]

  • Page 7

    Contents © National Instruments Corporatio n vii Xmath Control Design Module Bode Frequency Analysi[...]

  • Page 8

    Contents Xmath Control Design Module viii ni.com Appendix A Technical References Appendix B Technica[...]

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    © National Instruments Corporatio n 1-1 Xmath Control Design Module 1 Introduction The Control Desi[...]

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    Chapter 1 Introduction Xmath Control Design Modul e 1-2 ni.com particular system properti es or to c[...]

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    Chapter 1 Introduction © National Instruments Corporatio n 1-3 Xmath Control Design Module • H ( [...]

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    Chapter 1 Introduction Xmath Control Design Modul e 1-4 ni.com Control Design T utorial This tutoria[...]

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    Chapter 1 Introduction © National Instruments Corporatio n 1-5 Xmath Control Design Module ssys (a [...]

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    Chapter 1 Introduction Xmath Control Design Modul e 1-6 ni.com Input Names ----------- Rotor Angle O[...]

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    Chapter 1 Introduction © National Instruments Corporatio n 1-7 Xmath Control Design Module One appr[...]

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    Chapter 1 Introduction Xmath Control Design Modul e 1-8 ni.com Figure 1-2. Locus of all Open-Loop an[...]

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    Chapter 1 Introduction © National Instruments Corporatio n 1-9 Xmath Control Design Module Close th[...]

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    Chapter 1 Introduction Xmath Control Design Module 1-10 ni.com Figure 1-4. Block Diagram of the Clos[...]

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    Chapter 1 Introduction © National Instruments Corporatio n 1-11 Xmath Contr ol Design Module Becaus[...]

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    Chapter 1 Introduction Xmath Control Design Module 1-12 ni.com Figure 1-5. Helicopter Velocity T rac[...]

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    Chapter 1 Introduction © National Instruments Corporatio n 1-13 Xmath Contr ol Design Module Figure[...]

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    Chapter 1 Introduction Xmath Control Design Module 1-14 ni.com Y ou can verify that your system is c[...]

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    Chapter 1 Introduction © National Instruments Corporatio n 1-15 Xmath Contr ol Design Module Specif[...]

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    Chapter 1 Introduction Xmath Control Design Module 1-16 ni.com Y ou can choose to scale the system o[...]

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    Chapter 1 Introduction © National Instruments Corporatio n 1-17 Xmath Contr ol Design Module When y[...]

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    Chapter 1 Introduction Xmath Control Design Module 1-18 ni.com Figure 1-10. Multiple Plots Showing T[...]

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    Chapter 1 Introduction © National Instruments Corporatio n 1-19 Xmath Contr ol Design Module Y ou c[...]

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    Chapter 1 Introduction Xmath Control Design Module 1-20 ni.com Figure 1-12. Step Respon se of a Disc[...]

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    Chapter 1 Introduction © National Instruments Corporatio n 1-21 Xmath Contr ol Design Module The li[...]

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    Chapter 1 Introduction Xmath Control Design Module 1-22 ni.com Because this system is open-loop unst[...]

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    Chapter 1 Introduction © National Instruments Corporatio n 1-23 Xmath Contr ol Design Module Figure[...]

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    Chapter 1 Introduction Xmath Control Design Module 1-24 ni.com Figure 1-14. Respo nse of Observer -B[...]

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    © National Instruments Corporatio n 2-1 Xmath Control Design Module 2 Linear System Representation [...]

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    Chapter 2 Linea r System Representation Xmath Control Design Modul e 2-2 ni.com T ransfer Function S[...]

  • Page 35

    Chapter 2 Linear S ystem R epresentation © National Instruments Corporatio n 2-3 Xmath Control Desi[...]

  • Page 36

    Chapter 2 Linea r System Representation Xmath Control Design Modul e 2-4 ni.com be used so long as a[...]

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    Chapter 2 Linear S ystem R epresentation © National Instruments Corporatio n 2-5 Xmath Control Desi[...]

  • Page 38

    Chapter 2 Linea r System Representation Xmath Control Design Modul e 2-6 ni.com Again, you create th[...]

  • Page 39

    Chapter 2 Linear S ystem R epresentation © National Instruments Corporatio n 2-7 Xmath Control Desi[...]

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    Chapter 2 Linea r System Representation Xmath Control Design Modul e 2-8 ni.com Example 2-3 Using sy[...]

  • Page 41

    Chapter 2 Linear S ystem R epresentation © National Instruments Corporatio n 2-9 Xmath Control Desi[...]

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    Chapter 2 Linea r System Representation Xmath Control Design Module 2-10 ni.com numden( ) [num,den] [...]

  • Page 43

    Chapter 2 Linear S ystem R epresentation © National Instruments Corporatio n 2-11 Xmath Contr ol De[...]

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    Chapter 2 Linea r System Representation Xmath Control Design Module 2-12 ni.com outputNames = "[...]

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    Chapter 2 Linear S ystem R epresentation © National Instruments Corporatio n 2-13 Xmath Contr ol De[...]

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    Chapter 2 Linea r System Representation Xmath Control Design Module 2-14 ni.com discretization metho[...]

  • Page 47

    Chapter 2 Linear S ystem R epresentation © National Instruments Corporatio n 2-15 Xmath Contr ol De[...]

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    Chapter 2 Linea r System Representation Xmath Control Design Module 2-16 ni.com The exponential ke y[...]

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    Chapter 2 Linear S ystem R epresentation © National Instruments Corporatio n 2-17 Xmath Contr ol De[...]

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    Chapter 2 Linea r System Representation Xmath Control Design Module 2-18 ni.com Many of the discreti[...]

  • Page 51

    Chapter 2 Linear S ystem R epresentation © National Instruments Corporatio n 2-19 Xmath Contr ol De[...]

  • Page 52

    © National Instruments Corporatio n 3-1 Xmath Control Design Module 3 Building System Connections L[...]

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    Chapter 3 Building System Connections Xmath Control Design Modul e 3-2 ni.com Sys = Sys2 * Sys1 Casc[...]

  • Page 54

    Chapter 3 Building System Connections © National Instruments Corporatio n 3-3 Xmath Control Design [...]

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    Chapter 3 Building System Connections Xmath Control Design Modul e 3-4 ni.com Linear System Intercon[...]

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    Chapter 3 Building System Connections © National Instruments Corporatio n 3-5 Xmath Control Design [...]

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    Chapter 3 Building System Connections Xmath Control Design Modul e 3-6 ni.com if the conditio n esti[...]

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    Chapter 3 Building System Connections © National Instruments Corporatio n 3-7 Xmath Control Design [...]

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    Chapter 3 Building System Connections Xmath Control Design Modul e 3-8 ni.com append( ) performs a c[...]

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    Chapter 3 Building System Connections © National Instruments Corporatio n 3-9 Xmath Control Design [...]

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    Chapter 3 Building System Connections Xmath Control Design Module 3-10 ni.com 2 C -1.5 1.5 D 0 X0 0 [...]

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    Chapter 3 Building System Connections © National Instruments Corporatio n 3-11 Xmath Contr ol Desig[...]

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    Chapter 3 Building System Connections Xmath Control Design Module 3-12 ni.com -1 1 D 0 X0 0 0 State [...]

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    Chapter 3 Building System Connections © National Instruments Corporatio n 3-13 Xmath Contr ol Desig[...]

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    © National Instruments Corporatio n 4-1 Xmath Control Design Module 4 System Analysis This chapter [...]

  • Page 66

    Chapter 4 System Analysis Xmath Control Design Modul e 4-2 ni.com The time-response of discrete syst[...]

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    Chapter 4 System Analysis © National Instruments Corporatio n 4-3 Xmath Control Design Module and d[...]

  • Page 68

    Chapter 4 System Analysis Xmath Control Design Modul e 4-4 ni.com directly from the roots of the tra[...]

  • Page 69

    Chapter 4 System Analysis © National Instruments Corporatio n 4-5 Xmath Control Design Module ans ([...]

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    Chapter 4 System Analysis Xmath Control Design Modul e 4-6 ni.com Example 4-3 Dynamic Response th ro[...]

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    Chapter 4 System Analysis © National Instruments Corporatio n 4-7 Xmath Control Design Module 0 0 I[...]

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    Chapter 4 System Analysis Xmath Control Design Modul e 4-8 ni.com Figure 4-2. T ransient Response of[...]

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    Chapter 4 System Analysis © National Instruments Corporatio n 4-9 Xmath Control Design Module and o[...]

  • Page 74

    Chapter 4 System Analysis Xmath Control Design Module 4-10 ni.com (s + 1) (s + 0.79s + 0.16) initial[...]

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    Chapter 4 System Analysis © National Instruments Corporatio n 4-11 Xmath Contr ol Design Module Oft[...]

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    Chapter 4 System Analysis Xmath Control Design Module 4-12 ni.com Figure 4-3. System Time Response t[...]

  • Page 77

    Chapter 4 System Analysis © National Instruments Corporatio n 4-13 Xmath Contr ol Design Module Imp[...]

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    Chapter 4 System Analysis Xmath Control Design Module 4-14 ni.com Note A continuous system and its d[...]

  • Page 79

    Chapter 4 System Analysis © National Instruments Corporatio n 4-15 Xmath Contr ol Design Module Fig[...]

  • Page 80

    Chapter 4 System Analysis Xmath Control Design Module 4-16 ni.com The maximum time, Tmax , is comput[...]

  • Page 81

    Chapter 4 System Analysis © National Instruments Corporatio n 4-17 Xmath Contr ol Design Module The[...]

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    Chapter 4 System Analysis Xmath Control Design Module 4-18 ni.com Step Response The response of a sy[...]

  • Page 83

    Chapter 4 System Analysis © National Instruments Corporatio n 4-19 Xmath Contr ol Design Module Fro[...]

  • Page 84

    Chapter 4 System Analysis Xmath Control Design Module 4-20 ni.com Get indices of all v alues > 0.[...]

  • Page 85

    © National Instruments Corporatio n 5-1 Xmath Control Design Module 5 Classical Feedback Analysis T[...]

  • Page 86

    Chapter 5 Classica l Feedback Analysis Xmath Control Design Modul e 5-2 ni.com Because open-loop sys[...]

  • Page 87

    Chapter 5 Classical Feedback Analysis © National Instruments Corporatio n 5-3 Xmath Control Design [...]

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    Chapter 5 Classica l Feedback Analysis Xmath Control Design Modul e 5-4 ni.com Figure 5-2. Root Locu[...]

  • Page 89

    Chapter 5 Classical Feedback Analysis © National Instruments Corporatio n 5-5 Xmath Control Design [...]

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    Chapter 5 Classica l Feedback Analysis Xmath Control Design Modul e 5-6 ni.com For discrete-time sta[...]

  • Page 91

    Chapter 5 Classical Feedback Analysis © National Instruments Corporatio n 5-7 Xmath Control Design [...]

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    Chapter 5 Classica l Feedback Analysis Xmath Control Design Modul e 5-8 ni.com because they can be u[...]

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    Chapter 5 Classical Feedback Analysis © National Instruments Corporatio n 5-9 Xmath Control Design [...]

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    Chapter 5 Classica l Feedback Analysis Xmath Control Design Module 5-10 ni.com Referring to Figure 5[...]

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    Chapter 5 Classical Feedback Analysis © National Instruments Corporatio n 5-11 Xmath Contr ol Desig[...]

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    Chapter 5 Classica l Feedback Analysis Xmath Control Design Module 5-12 ni.com Each of these contrib[...]

  • Page 97

    Chapter 5 Classical Feedback Analysis © National Instruments Corporatio n 5-13 Xmath Contr ol Desig[...]

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    Chapter 5 Classica l Feedback Analysis Xmath Control Design Module 5-14 ni.com Note margin( ) also r[...]

  • Page 99

    Chapter 5 Classical Feedback Analysis © National Instruments Corporatio n 5-15 Xmath Contr ol Desig[...]

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    Chapter 5 Classica l Feedback Analysis Xmath Control Design Module 5-16 ni.com plant is open-loop st[...]

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    Chapter 5 Classical Feedback Analysis © National Instruments Corporatio n 5-17 Xmath Contr ol Desig[...]

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    Chapter 5 Classica l Feedback Analysis Xmath Control Design Module 5-18 ni.com Figure 5-7. Nyquist P[...]

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    Chapter 5 Classical Feedback Analysis © National Instruments Corporatio n 5-19 Xmath Contr ol Desig[...]

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    Chapter 5 Classica l Feedback Analysis Xmath Control Design Module 5-20 ni.com -0.52263 0.00336213 +[...]

  • Page 105

    Chapter 5 Classical Feedback Analysis © National Instruments Corporatio n 5-21 Xmath Contr ol Desig[...]

  • Page 106

    © National Instruments Corporatio n 6-1 Xmath Control Design Module 6 State-Space Design The functi[...]

  • Page 107

    Chapter 6 State-Space Design Xmath Control Design Modul e 6-2 ni.com matrix B, then the mode of the [...]

  • Page 108

    Chapter 6 State-Space D esign © National Instruments Corporatio n 6-3 Xmath Control Design Module F[...]

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    Chapter 6 State-Space Design Xmath Control Design Modul e 6-4 ni.com X0 0 Input Names ----------- In[...]

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    Chapter 6 State-Space D esign © National Instruments Corporatio n 6-5 Xmath Control Design Module B[...]

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    Chapter 6 State-Space Design Xmath Control Design Modul e 6-6 ni.com Figure 6-2. General Observer Bl[...]

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    Chapter 6 State-Space D esign © National Instruments Corporatio n 6-7 Xmath Control Design Module E[...]

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    Chapter 6 State-Space Design Xmath Control Design Modul e 6-8 ni.com minimal( ) [SysM,T,nuco] = mini[...]

  • Page 114

    Chapter 6 State-Space D esign © National Instruments Corporatio n 6-9 Xmath Control Design Module a[...]

  • Page 115

    Chapter 6 State-Space Design Xmath Control Design Module 6-10 ni.com Duality and Pole Placement The [...]

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    Chapter 6 State-Space D esign © National Instruments Corporatio n 6-11 Xmath Contr ol Design Module[...]

  • Page 117

    Chapter 6 State-Space Design Xmath Control Design Module 6-12 ni.com pairs as poles( ) . For eac h p[...]

  • Page 118

    Chapter 6 State-Space D esign © National Instruments Corporatio n 6-13 Xmath Contr ol Design Module[...]

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    Chapter 6 State-Space Design Xmath Control Design Module 6-14 ni.com The optimal estimator and regul[...]

  • Page 120

    Chapter 6 State-Space D esign © National Instruments Corporatio n 6-15 Xmath Contr ol Design Module[...]

  • Page 121

    Chapter 6 State-Space Design Xmath Control Design Module 6-16 ni.com Ruu is a scalar because you ha [...]

  • Page 122

    Chapter 6 State-Space D esign © National Instruments Corporatio n 6-17 Xmath Contr ol Design Module[...]

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    Chapter 6 State-Space Design Xmath Control Design Module 6-18 ni.com numerical diff iculties are enc[...]

  • Page 124

    Chapter 6 State-Space D esign © National Instruments Corporatio n 6-19 Xmath Contr ol Design Module[...]

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    Chapter 6 State-Space Design Xmath Control Design Module 6-20 ni.com this measurement up date, deriv[...]

  • Page 126

    Chapter 6 State-Space D esign © National Instruments Corporatio n 6-21 Xmath Contr ol Design Module[...]

  • Page 127

    Chapter 6 State-Space Design Xmath Control Design Module 6-22 ni.com a compensator is shown in Figur[...]

  • Page 128

    Chapter 6 State-Space D esign © National Instruments Corporatio n 6-23 Xmath Contr ol Design Module[...]

  • Page 129

    Chapter 6 State-Space Design Xmath Control Design Module 6-24 ni.com simulate the system’ s respon[...]

  • Page 130

    Chapter 6 State-Space D esign © National Instruments Corporatio n 6-25 Xmath Contr ol Design Module[...]

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    Chapter 6 State-Space Design Xmath Control Design Module 6-26 ni.com continuous-time Riccati equatio[...]

  • Page 132

    Chapter 6 State-Space D esign © National Instruments Corporatio n 6-27 Xmath Contr ol Design Module[...]

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    Chapter 6 State-Space Design Xmath Control Design Module 6-28 ni.com 0 1 0 B 1 0 0 C 1 0 0 D 0 X0 0 [...]

  • Page 134

    Chapter 6 State-Space D esign © National Instruments Corporatio n 6-29 Xmath Contr ol Design Module[...]

  • Page 135

    Chapter 6 State-Space Design Xmath Control Design Module 6-30 ni.com or the follo wing for the discr[...]

  • Page 136

    Chapter 6 State-Space D esign © National Instruments Corporatio n 6-31 Xmath Contr ol Design Module[...]

  • Page 137

    Chapter 6 State-Space Design Xmath Control Design Module 6-32 ni.com Special L yapunov Equation A = [...]

  • Page 138

    Chapter 6 State-Space D esign © National Instruments Corporatio n 6-33 Xmath Contr ol Design Module[...]

  • Page 139

    Chapter 6 State-Space Design Xmath Control Design Module 6-34 ni.com For discrete-time systems, the [...]

  • Page 140

    Chapter 6 State-Space D esign © National Instruments Corporatio n 6-35 Xmath Contr ol Design Module[...]

  • Page 141

    Chapter 6 State-Space Design Xmath Control Design Module 6-36 ni.com T is the transforma tion relati[...]

  • Page 142

    Chapter 6 State-Space D esign © National Instruments Corporatio n 6-37 Xmath Contr ol Design Module[...]

  • Page 143

    Chapter 6 State-Space Design Xmath Control Design Module 6-38 ni.com accurate. Gi ven a v ariable Sy[...]

  • Page 144

    Chapter 6 State-Space D esign © National Instruments Corporatio n 6-39 Xmath Contr ol Design Module[...]

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    Chapter 6 State-Space Design Xmath Control Design Module 6-40 ni.com 0 0 0 0.924711 B -0.00116788 0.[...]

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    Chapter 6 State-Space D esign © National Instruments Corporatio n 6-41 Xmath Contr ol Design Module[...]

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    Chapter 6 State-Space Design Xmath Control Design Module 6-42 ni.com Figure 6-8. Modal System and Re[...]

  • Page 148

    © National Instruments Corporatio n A -1 Xmath Co ntrol Design Modu le A T echnical References [BeV[...]

  • Page 149

    Appendix A T echnical References Xmath Control Design Modul e A-2 ni.com [Kai80] T . Kailath, Linear[...]

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    © National Instruments Corporatio n B -1 Xmath Co ntrol Design Modu le B T echnical Support and Pro[...]

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    of fice W eb sites, which provide up-to-date contact informati on, support phone numbers, email addr[...]

  • Page 152

    © National Instruments Corporatio n I-1 Xmath Control Design Module Index A abcd, 1-16, 2-8 adjoint[...]

  • Page 153

    Index Xmath Control Design Modul e I-2 ni.com converting to continuous equivalent, 2-19 from a conti[...]

  • Page 154

    Index © National Instruments Corporatio n I-3 Xmath Control Design Module I impulse, 4-13 input, 4-[...]

  • Page 155

    Index Xmath Control Design Modul e I-4 ni.com steady-state response to white noise, 6-29 white proce[...]

  • Page 156

    Index © National Instruments Corporatio n I-5 Xmath Control Design Module rms, 6-32 root locus, plo[...]

  • Page 157

    Index Xmath Control Design Modul e I-6 ni.com T technical support, B-1 time domain simulation, gener[...]