Справочник ПользователяСодержаниеXmath Control Design Module1Important Information3Warranty3Copyright3Trademarks3Patents3WARNING REGARDING USE OF NATIONAL INSTRUMENTS PRODUCTS3Conventions4Contents5Chapter 1 Introduction9Using This Manual9Document Organization9Bibliographic References10Commonly Used Nomenclature10Related Publications11MATRIXx Help11Control Design Tutorial12Helicopter Hover Problem: An Ad Hoc Approach12Figure 1-1. Block Diagram of Helicopter System H(s) with Compensators K1(s) and K2(s) in the Feedforward Path14Figure 1-2. Locus of all Open-Loop and Closed-Loop Roots of Gs16Figure 1-3. Helicopter Velocity Response to a Step Input at the Rotor17Figure 1-4. Block Diagram of the Closed-Loop Controller18Figure 1-5. Helicopter Velocity Tracking Step Input at the Rotor20Figure 1-6. Closed-Loop System Bode Plot21Helicopter Hover Problem: State Feedback and Observer Design21Figure 1-7. Full-State Feedback Regulator22Figure 1-8. Complete Controller and Estimator22Figure 1-9. Step Response for Observer-Based Design24Figure 1-10. Multiple Plots Showing Time Needed for States to be Correctly Tracked by Estimator, Given Incorrect Initial Values26Helicopter Hover Problem: Discrete Formulation26Figure 1-11. Frequency Response of ssys and Its Discrete Equivalent ssysd27Figure 1-12. Step Response of a Discrete System Using Discretized Observer-Based Controller28Inverted Wedge-Balancing Problem: LQG Control28Figure 1-13. Response of Full-State Feedback Controller to a Unit Step Disturbance31Figure 1-14. Response of Observer-Based Controller to a Unit Step Disturbance32Chapter 2 Linear System Representation33Linear Systems Represented in Xmath33Table 2-1. Summary of Linear Systems33Transfer Function System Models34State-Space System Models37Basic System Building Functions38system( )38abcd( )40numden( )42period( )42names( )43Size and Indexing of Dynamic Systems44Using check( ) with System Objects44Discretizing a System45discretize( )45Numerical Integration Methods: forward, backward, tustins46Table 2-2. Mapping Methods for discretize( )46Pole-Zero Matching: polezero47Z-Transform: ztransform47Hold Equivalence Methods: exponential and firstorder47Figure 2-1. Comparison of Different Frequency Response Techniques49makecontinuous( )49Table 2-3. Mapping Methods for makecontinuous( )50Chapter 3 Building System Connections52Linear System Interconnection Operators52Table 3-1. Summary of Interconnection Operators52Linear System Interconnection Functions55afeedback( )55Figure 3-1. afeedback System Configuration55Algorithm56append( )57Figure 3-2. Output of a Dynamic System58connect( )59Figure 3-3. Parameters Used with the connect Command59Algorithm61feedback( )62Figure 3-4. Feedback System Configuration62Algorithm63Chapter 4 System Analysis65Time-Domain Solution of System Equations65System Stability: Poles and Zeros66poles( )67zeros( )67Algorithm69Partial Fraction Expansion69Figure 4-1. Constructing the Closed-Loop System Gcl (s) from the Open-Loop System G(s), with Input U(s) and Output Y(s)70Figure 4-2. Transient Response of the Closed-Loop System as a Function of Time72residue( )72combinepf( )73General Time-Domain Simulation74Figure 4-3. System Time Response to a Series of Step Signals76Impulse Response of a System77impulse( )77Figure 4-4. 15-Second Impulse Response79deftimerange( )79System Response to Initial Conditions80initial( )80Figure 4-5. 15-Second System Response to Unity Nonzero Conditions at Each of the States81Step Response82step( )82Figure 4-6. 15-Second Step Response, Showing Performance Measures83Chapter 5 Classical Feedback Analysis85Feedback Control of a Plant Model85Figure 5-1. Feedback Control System Block Diagram85Root Locus86rlocus( )87Figure 5-2. Root Locus of H for Gain K = 0.0788Frequency Response and Dynamic Response89freq( )89Algorithm90Figure 5-3. Representation of the Open-Loop System91Bode Frequency Analysis91bode( )94Figure 5-4. Bode Plot Showing System Gain and Phase Margins95margin( )96nichols( )98Figure 5-5. nichols( ) Gain-Phase Plot99Nyquist Stability Analysis99Figure 5-6. Closed-Loop System Containing a Variable Gain K100nyquist( )100Figure 5-7. Nyquist Plot of the Open-Loop System for Frequencies from 0.01 Hz to 10 Hz102Figure 5-8. Nyquist Plot of the Open-Loop System for Frequencies from 0.5 Hz to 5 Hz102Figure 5-9. Nyquist Contour Formed by Drawing the System’s Nyquist Plot for All Positive Frequencies103Linear Systems and Power Spectral Density104psd( )104Chapter 6 State-Space Design106Controllability106Figure 6-1. Full-State Feedback Being Used to Relocate the Eigenvalues of a Controllable System Based on the Value of the Gain K108controllable( )108Observability and Estimation109Figure 6-2. General Observer Block Diagram111observable( )111Minimal Realizations112minimal( )113stair( )114Duality and Pole Placement115poleplace( )115Linear Quadratic Regulator117Figure 6-3. Continuous-Time Regulator117regulator( )119Figure 6-4. Diagram of Plant for the Inverted Pendulum Problem120Linear Quadratic Estimator121Figure 6-5. Diagram of the Estimator Representation122estimator( )125Linear Quadratic Gaussian Compensation126Figure 6-6. Linear Quadratic Gaussian Compensator (in the Bold Rectangle)127lqgcomp( )128Figure 6-7. f and x as a Function of Time, Starting from Zero, as a Result of a Sinusoidal Force Applied to the System Input130Riccati Equation130riccati( )131Steady-State System Response Using Lyapunov Equations133lyapunov( )135Algorithm135rms( )137Balancing a Linear System138balance( )140Modal Form of a System142modal( )142mreduce( )143Figure 6-8. Modal System and Reduced Modal System147Appendix A Technical References148Appendix B Technical Support and Professional Services150Index152A-D152E-H153I-N154O-R155S156T-Z157Размер: 1,3 МБСтраницы: 157Язык: EnglishПросмотреть