Manuel D’UtilisationTable des matièresXmath Robust Control Module1Support2Worldwide Technical Support and Product Information2National Instruments Corporate Headquarters2Worldwide Offices2Important Information3Warranty3Copyright3Trademarks3Patents3WARNING REGARDING USE OF NATIONAL INSTRUMENTS PRODUCTS3Conventions4Contents5Chapter 1 Introduction7Using This Manual7Document Organization7Bibliographic References8Commonly-Used Nomenclature8Related Publications8MATRIXx Help9Overview9Figure 1-1. RCM Function Structure10Chapter 2 Robustness Analysis11Modeling Uncertain Systems11Figure 2-1. Model of an Uncertain System11Stability Margin (smargin)13smargin( )14Figure 2-2. Nominal Closed-Loop System14Figure 2-3. SISO Tracking System with Three Uncertainties15Figure 2-4. Bound for Sensor Uncertainty16Figure 2-5. Stability Margin17Worst-Case Performance Degradation (wcbode)18wcbode( )19Figure 2-6. Performance Degradation of the SISO Tracking System20Advanced Topics20Stability Margin20Stability Margin and Structured Singular Values (μ)20Stability Margin Bounds Using Singular Values21Figure 2-7. pfscale( ) versus svd Stability Margins22Approximation with Scaled Singular Values22Figure 2-8. Results of Scaling Algorithm Options24ssv( )25osscale( )26pfscale( )26optscale( )27Reducibility27Figure 2-9. Non-Interacting Uncertain Transfer Functions27Figure 2-10. Reduction to Separate Systems28Worst-Case Performance Degradation (wcgain)28Conversion to a Stability Margin Problem28wcgain( )29Chapter 3 System Evaluation30Singular Value Bode Plots30Figure 3-1. Singular Value Plot32L Infinity Norm (linfnorm)32linfnorm( )33Figure 3-2. Singular Values of H(jw) as a Function of ω35Singular Value Bode Plots of Subsystems36perfplots( )36Figure 3-3. Typical System with Plant and Controller36Figure 3-4. Closed-Loop System37Figure 3-5. Perfplots( ) for K = 1 and K = 539clsys( )39Figure 3-6. Closed Loop System from w to z39Figure 3-7. Calculation of the Closed Loop System (SysCL)40Figure 3-8. Ill-Posed Feedback System41Chapter 4 Controller Synthesis42H-Infinity Control Synthesis42Problem Definition42Figure 4-1. Closed-Loop System with Plant P and Controller K42Extended Transfer Matrix43Building the Plant Model44Figure 4-2. Construction of Plant P44Figure 4-3. Typical Plant Configuration45Weight Selection46Restrictions on the Extended Plant48hinfcontr( )49Figure 4-4. Plant and Weights for hinfcontr( )51Figure 4-5. Perfplots for Hew53Figure 4-6. Perfplots for Hzv54singriccati( )54Linear-Quadratic-Gaussian Control Synthesis55LQG Frequency Shaping55fsregu( )55fsesti( )57fslqgcomp( )58Frequency-Shaped Control Design Commands58Figure 4-7. Frequency-Shaped Compensator61Loop Transfer Recovery (lqgltr)63Figure 4-8. LQG Feedback System for Loop Transfer Recovery64lqgltr( )64Appendix A Bibliography66Appendix B Technical Support and Professional Services69Index70A-N70O-W71Taille: 590 koPages: 71Language: EnglishOuvrir le manuel
Manuel D’UtilisationTable des matièresXmath Robust Control Module1Support2Worldwide Technical Support and Product Information2National Instruments Corporate Headquarters2Worldwide Offices2Important Information3Warranty3Copyright3Trademarks3Patents3WARNING REGARDING USE OF NATIONAL INSTRUMENTS PRODUCTS3Conventions4Contents5Chapter 1 Introduction7Using This Manual7Document Organization7Bibliographic References8Commonly-Used Nomenclature8Related Publications8MATRIXx Help9Overview9Figure 1-1. RCM Function Structure10Chapter 2 Robustness Analysis11Modeling Uncertain Systems11Figure 2-1. Model of an Uncertain System11Stability Margin (smargin)13smargin( )14Figure 2-2. Nominal Closed-Loop System14Figure 2-3. SISO Tracking System with Three Uncertainties15Figure 2-4. Bound for Sensor Uncertainty16Figure 2-5. Stability Margin17Worst-Case Performance Degradation (wcbode)18wcbode( )19Figure 2-6. Performance Degradation of the SISO Tracking System20Advanced Topics20Stability Margin20Stability Margin and Structured Singular Values (μ)20Stability Margin Bounds Using Singular Values21Figure 2-7. pfscale( ) versus svd Stability Margins22Approximation with Scaled Singular Values22Figure 2-8. Results of Scaling Algorithm Options24ssv( )25osscale( )26pfscale( )26optscale( )27Reducibility27Figure 2-9. Non-Interacting Uncertain Transfer Functions27Figure 2-10. Reduction to Separate Systems28Worst-Case Performance Degradation (wcgain)28Conversion to a Stability Margin Problem28wcgain( )29Chapter 3 System Evaluation30Singular Value Bode Plots30Figure 3-1. Singular Value Plot32L Infinity Norm (linfnorm)32linfnorm( )33Figure 3-2. Singular Values of H(jw) as a Function of ω35Singular Value Bode Plots of Subsystems36perfplots( )36Figure 3-3. Typical System with Plant and Controller36Figure 3-4. Closed-Loop System37Figure 3-5. Perfplots( ) for K = 1 and K = 539clsys( )39Figure 3-6. Closed Loop System from w to z39Figure 3-7. Calculation of the Closed Loop System (SysCL)40Figure 3-8. Ill-Posed Feedback System41Chapter 4 Controller Synthesis42H-Infinity Control Synthesis42Problem Definition42Figure 4-1. Closed-Loop System with Plant P and Controller K42Extended Transfer Matrix43Building the Plant Model44Figure 4-2. Construction of Plant P44Figure 4-3. Typical Plant Configuration45Weight Selection46Restrictions on the Extended Plant48hinfcontr( )49Figure 4-4. Plant and Weights for hinfcontr( )51Figure 4-5. Perfplots for Hew53Figure 4-6. Perfplots for Hzv54singriccati( )54Linear-Quadratic-Gaussian Control Synthesis55LQG Frequency Shaping55fsregu( )55fsesti( )57fslqgcomp( )58Frequency-Shaped Control Design Commands58Figure 4-7. Frequency-Shaped Compensator61Loop Transfer Recovery (lqgltr)63Figure 4-8. LQG Feedback System for Loop Transfer Recovery64lqgltr( )64Appendix A Bibliography66Appendix B Technical Support and Professional Services69Index70A-N70O-W71Taille: 590 koPages: 71Language: EnglishOuvrir le manuel
