
6 Customization
6-4
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Control System
1
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How to Contact The MathWorks:
2
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Operations on LTI Models
4
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SISO Design Tool Reference
9
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LTI Viewer Reference
10
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Function Reference
12
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Contents
14
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1 Introduction
18
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LTI Models
19
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2 LTI Models
20
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Other Uses of FRD Models
21
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LTI Properties and Methods
22
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Precedence Rules
23
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Command Summary
24
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Creating LTI Models
26
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SISO Transfer Function Models
26
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MIMO Transfer Function Models
28
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Pure Gains
29
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MIMO Zero-Pole-Gain Models
31
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Discrete-Time Models
37
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Data Retrieval
41
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LTI Properties
43
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Direct Property Referencing
49
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Sample Time
51
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Input Names and Output Names
53
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)oranoutputgroup(O)
55
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Model Conversion
58
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Automatic Conversion
59
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Time Delays
61
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Distillation Column Example
63
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Resizing LTI Systems
83
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Arithmetic Operations
85
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Multiplication
87
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Transposition
88
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Pertransposition
88
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Zero-Order Hold
94
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First-Order Hold
96
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Tustin Approximation
96
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Matched Poles and Zeros
97
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Amplitude
99
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3 Operations on LTI Models
100
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References
101
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Model Analysis Tools
103
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4 Model Analysis Tools
104
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General Model Characteristics
105
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Model Dynamics
107
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State-Space Realizations
110
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Arrays of LTI Models
113
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5 Arrays of LTI Models
114
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Introduction
114
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The Concept of an LTI Array
116
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Building LTI Arrays
124
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Indexing Into LTI Arrays
132
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Operations on LTI Arrays
136
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Customization
143
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6 Customization
144
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User Preferences
145
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SISO Design Tool
145
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LTI Viewer
145
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Setting Toolbox
147
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Preferences
147
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7 Setting Toolbox Preferences
148
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Units Page
149
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Style Page
149
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SISO Tool Page
151
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Setting Toolbox Preferences
152
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Setting Tool Preferences
153
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8 Setting Tool Preferences
154
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Parameters Page
157
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Grids Panel
160
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Fonts Panel
160
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Colors Panel
161
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Customizing Response
165
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Plot Properties
165
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Property Editor is
166
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Property Editor
167
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Labels Page
168
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Limits Page
168
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Characteristics Page
172
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Property Editing for Subplots
174
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Auto-Scale checkboxes
177
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Options Page
178
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Design Case Studies
185
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10 Design Case Studies
186
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Open-Loop Analysis
189
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Root Locus Design
193
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WOF = -K * H;
201
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(2,2) I/O pair
203
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Hard Disk Drive
204
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D = zpk(0.85,0,1,Ts)
209
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K = 4.11e+03;
211
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LQG Design for the x-Axis
218
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LQG Design for the y-Axis
225
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Cross-Coupling Between Axes
227
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Kalman Filtering
234
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Steady-State Design
235
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Now simulate with lsim
239
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Time-Varying Kalman Filter
241
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Reliable Computations
247
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11 Reliable Computations
248
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Numerical Stability
252
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Choice of LTI Model
254
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Zero-Pole-Gain Models
259
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GUI Reference
265
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12 GUI Reference
266
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Reference
267
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13 SISO Design Tool Reference
268
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Menu Bar
270
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System Name
271
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Import From
271
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System Data
271
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Exporting to the Workspace
272
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Exporting to a MAT-file
273
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Print to Figure
275
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Undo and Redo
275
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Root Locus and Bode Diagrams
275
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Customizing Loop Responses
279
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Conversion domain
281
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Draw a Simulink Diagram
283
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Compensator
283
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Changing the gain
285
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Changing the format
285
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Adding poles and zeros
286
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Deleting poles and zeros
286
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Retrieve
287
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Tool Bar
289
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Current Compensator
290
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Feedback Structure
291
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Root Locus Right-Click Menus
292
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Delete Pole/Zero
293
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Edit Compensator
293
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Settling Time
294
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Peak Overshoot
294
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Damping Ratio
294
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Natural Frequency
294
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Zoom opens this submenu
299
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Status Panel
301
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14 LTI Viewer Reference
304
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LTI Viewer Menu Bar
306
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New Viewer
307
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Import Using the LTI Browser
307
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Setting Preferences
313
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Ordering Properties
313
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Plot Type
315
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Step Response
317
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Impulse Response
318
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Bode Diagram
319
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Bode Magnitude
320
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Nyquist Diagrams
321
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Nichols Charts
322
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, which is the largest
323
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Pole/Zero
324
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Properties
325
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Axis Grouping
327
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I/O Selector
327
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Right-Click Menus for
331
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Response Plots
331
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- regroup the plots
333
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- Select subsets of I/O pairs
333
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Characteristics
334
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Properties online
337
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16 Function Reference
342
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Functions by Category
343
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Syntax S = allmargin(sys)
352
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16append
353
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Feedback connection
355
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Parallel connection
355
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Series connection
355
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Syntax asys = augstate(sys)
356
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Syntax sysb = balreal(sys)
357
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Phase (deg); Magnitude (dB)
359
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Syntax bode(sys)
361
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Syntax bodemag(sys)
366
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Syntax sysd = c2d(sys,Ts)
367
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Example Consider the system
368
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Modal Form
370
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Companion Form
370
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Examples Example 1
373
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Example 2
374
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Example w = logspace(1,2,2);
376
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16connect
377
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Syntax [P,Q] = covar(sys,W)
382
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Syntax Co = ctrb(A,B)
385
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Syntax sysc = d2c(sysd)
389
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Syntax sys1 = d2d(sys,Ts)
392
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Syntax [Wn,Z] = damp(sys)
393
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1746–1754
397
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16dcgain
398
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Syntax X = dlyap(A,Q)
402
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Syntax sys = drss(n)
403
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Syntax sys = dss(a,b,c,d,e)
406
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Example The command
406
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16dssdata
408
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Compute (transmission) zeros
410
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Syntax est = estim(sys,L)
411
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16evalfr
413
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Example 3
417
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Syntax sys = filt(num,den)
418
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Example Typing the commands
419
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Example Type the commands
421
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Create transfer functions
422
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Create zero-pole-gain models
422
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Set model properties
424
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16freqresp
425
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16gensig
428
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Syntax hasdelay(sys)
434
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16impulse
435
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Syntax impulse(sys)
435
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Syntax initial(sys,x0)
439
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Impulse response
441
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LTIsystemviewer
441
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Step response
441
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16interp
442
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Purpose Invert LTI systems
443
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Syntax isys = inv(sys)
443
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Example Consider
443
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Syntax boo = isct(sys)
445
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Syntax boo = isempty(sys)
446
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Example Both commands
446
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Syntax boo = isproper(sys)
447
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Syntax boo = issiso(sys)
448
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16kalman
449
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(Measurement noise)
450
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Syntax sys = lft(sys1,sys2)
455
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Syntax rlqg = lqgreg(kest,k)
457
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Syntax [K,S,e] = lqr(A,B,Q,R)
461
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Syntax lsim(sys,u,t)
465
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Purpose Help on LTI models
470
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Syntax ltimodels
470
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16ltiview
472
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Syntax ltiview
472
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See Also bode Bode response
473
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Nichols response
474
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Nyquist response
474
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Pole/zero map
474
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Singular value response
474
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16margin
477
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Syntax sysr = minreal(sys)
480
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Example The commands
480
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Purpose Model order reduction
482
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Syntax n = ndims(sys)
486
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Example sys = rss(3,1,1,3);
486
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Syntax ngrid
487
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Nichols plots
488
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16nichols
489
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Syntax nichols(sys)
489
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Algorithm See bode
491
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See Also bode Bode plot
491
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16nyquist
496
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Syntax nyquist(sys)
496
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Syntax Ob = obsv(A,B)
500
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Example Determine if the pair
500
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MATLAB responds with
501
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Syntax [A,B,C,D] = ord2(wn,z)
504
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Syntax [num,den] = pade(T,N)
505
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N>10 should be avoided
506
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16parallel
508
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Purpose Pole placement design
510
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Syntax K = place(A,B,p)
510
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Syntax pzmap(sys)
513
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Syntax rsys = reg(sys,K,L)
515
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Example sys = rss(4,1,1,2,3);
518
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16rlocus
519
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Purpose Evans root locus
519
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Syntax rlocus(sys)
519
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See Also pole System poles
521
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Syntax sys = rss(n)
522
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16series
524
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Property
527
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Syntax sgrid
533
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Plot pole-zero map
534
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Plot root locus
534
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Generate z-plane grid lines
534
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Syntax sigma(sys)
535
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16sisotool
539
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Syntax sisotool
539
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P to plant and the
540
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Syntax size(sys)
542
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Test if LTI model is empty
543
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Test if LTI model is SISO
543
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Syntax msys = sminreal(sys)
544
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Syntax sys = ss(a,b,c,d)
546
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Conversion to State Space
547
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Syntax sysT = ss2ss(sys,T)
550
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Syntax [sysb,T] = ssbal(sys)
551
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16ssdata
553
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Syntax step(sys)
555
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Syntax sys = tf(num,den)
558
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Example 4
561
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Discrete-Time
562
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Conventions
562
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16tfdata
565
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Specify transfer functions
567
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Syntax td = totaldelay(sys)
568
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Syntax zgrid
570
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Generate s-plane grid lines
571
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Syntax sys = zpk(z,p,k)
572
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Variable
574
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Selection
574
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Example Example 1
574
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Syntax [z,p,k] = zpkdata(sys)
577
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Specify zero-pole-gain models
579
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