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CONTROL SYSTEM TOOLBOX 9
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tfdata
11-233
tf
Specify
transfer
functions
zpkdata
Quick
access
to
zero-pole-gain
data
1
2
...
618
619
620
621
622
623
624
625
626
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...
648
649
Control System
1
How to Contact The MathWorks:
2
Control Design Tools
10
The Root Locus Design GUI
11
Design Case Studies
12
Reliable Computations
13
Reference
13
Contents
14
Preface
16
Installation
17
Typographic Conventions
19
Quick Start
21
1 Quick Start
22
LTI Models
23
Model Conversion
25
LTI Properties
27
System Interconnections
39
Other Uses of FRD Models
47
LTI Objects
47
Precedence Rules
49
Creating LTI Models
53
Pure Gains
55
MIMO Zero-Pole-Gain Models
57
Direct Property Referencing
77
Automatic Conversion
87
Time Delays
89
Distillation Column Example
91
2 LTI Models
100
References
103
Operations on LTI Models
105
3 Operations on LTI Models
106
Resizing LTI Systems
113
Arithmetic Operations
115
Multiplication
117
Concatenation of LTI Models
121
Matched Poles and Zeros
127
Arrays of LTI Models
133
4 Arrays of LTI Models
134
Introduction
135
The Concept of an LTI Array
137
Building LTI Arrays
145
Indexing Into LTI Arrays
153
Operations on LTI Arrays
157
Dimension Requirements
159
Model Analysis Tools
163
5 Model Analysis Tools
164
General Model Characteristics
165
Model Dynamics
167
State-Space Realizations
169
Time and Frequency Response
171
Frequency Response
173
Customizing the Plot Display
179
The LTI Viewer
183
6 The LTI Viewer
184
File menu has
189
Tools menu items
189
1 Click on the marker
191
Importing Models
193
The LTI Viewer Menus
197
Interactive Help
199
The Right-Click Menus
201
Characteristics or the
203
The Axes Grouping Submenu
205
Axes Grouping
205
Shift key while
209
Arrays pull-down tab
213
Index into Dimensions
217
The LTI Viewer Tools Menu
221
2 Select either:
229
Simulink LTI Viewer
231
A Sample Analysis Task
231
Model_Inputs_and_Outputs
233
Get Line arized Mod el
239
Linearized Model
239
Performing Linear Analysis
243
Saving Analysis Models
247
7 Control Design Tools
250
Root Locus Design
251
Pole Placement
253
Optimal State-Feedback Gain
257
Kalman State Estimator
257
LQG Design
259
The Root Locus Design
261
8 The Root Locus Design GUI
262
A Servomechanism Example
265
Specifying the Design Model
271
Gain text boxon the
273
As you get close to a closed
275
Zoom button to zoom in
277
Gain,andpressingthe
281
Gain box
283
Add Grid/Boundary menu
285
Tools menu
285
Edit Compensator menu item to
287
Add compensator poles here
289
Compensator
293
Marker for the
295
Then type
297
Designating the Model Source
299
Listing Poles and Zeros
301
Show Ob ject buttons in this
303
OK to close this window
303
The plant, P (Gservo)
305
The root locus
305
Sensor dynamics, H
305
Pre-filter, F
305
9 Design Case Studies
310
H = zpk(0,–0.333,1);
323
D = zpk(0.85,0,1,Ts)
333
LQG Regulation
339
Cross-Coupling Between Axes
351
MIMO LQG Design
355
Steady-State Design
359
Kalman Filtering
361
Time-Varying Kalman Filter
365
10 Reliable Computations
374
Choice of LTI Model
381
11 Reference
392
Category Tables
393
11append
402
Example The commands
403
Feedback connection
404
Parallel connection
404
Series connection
404
Syntax asys = augstate(sys)
405
Syntax sysb = balreal(sys)
406
Phase (deg); Magnitude (dB)
407
Algorithm Consider the model
408
Syntax bode(sys)
409
Syntax sysd = c2d(sys,Ts)
414
Example Consider the system
414
Modal Form
417
Companion Form
417
Examples Example 1
420
Example 2
421
Example w = logspace(1,2,2);
423
11connect
424
Center, 1976
429
Syntax [P,Q] = covar(sys,W)
430
Syntax Co = ctrb(A,B)
433
Syntax sysc = d2c(sysd)
438
Syntax sys1 = d2d(sys,Ts)
441
Syntax [Wn,Z] = damp(sys)
442
1746–1754
446
11dcgain
447
Syntax sys = delay2z(sys)
448
Syntax X = dlyap(A,Q)
451
Syntax sys = drss(n)
452
Syntax sys = dss(a,b,c,d,e)
455
Example The command
456
11dssdata
457
Syntax s = esort(p)
458
, sort Sort system poles
459
Compute system poles
459
Pole-zero map
459
Compute (transmission) zeros
459
Syntax est = estim(sys,L)
460
11evalfr
462
11feedback
463
Example 3
466
Syntax sys = filt(num,den)
467
Example Typing the commands
468
Example Type the commands
470
Create transfer functions
471
Create zero-pole-gain models
471
Set model properties
473
11freqresp
474
11gensig
477
Plot the resulting signal
478
Syntax hasdelay(sys)
483
Syntax impulse(sys)
484
Amplitude
486
Syntax initial(sys,x0)
488
Purpose Invert LTI systems
491
Syntax isys = inv(sys)
491
Example Consider
491
Syntax boo = isct(sys)
494
Syntax boo = isempty(sys)
495
Example Both commands
495
Syntax boo = isproper(sys)
496
Syntax boo = issiso(sys)
497
Continuous-Time Estimation
498
Discrete-Time Estimation
499
Syntax sys = lft(sys1,sys2)
505
Syntax rlqg = lqgreg(kest,k)
507
Syntax [K,S,e] = lqr(A,B,Q,R)
511
Form LQG regulator
512
Syntax lsim(sys,u,t)
516
Then simulate with lsim
518
Syntax ltiview
523
See Also bode Bode response
524
11margin
527
MATLAB responds with
528
Syntax sysr = minreal(sys)
530
M odel order reduction
531
Structured model reduction
531
Purpose Model order reduction
532
Syntax n = ndims(sys)
536
Example sys = rss(3,1,1,3);
536
Syntax ngrid
537
Open−Loop Gain (dB)
538
Syntax nichols(sys)
539
See Also bode Bode plot
545
Syntax nyquist(sys)
546
Syntax Ob = obsv(A,B)
549
Example Determine if the pair
549
Syntax [A,B,C,D] = ord2(wn,z)
553
Syntax [num,den] = pade(T,N)
554
N>10 should be avoided
556
11parallel
558
Purpose Pole placement design
560
Syntax K = place(A,B,p)
560
Syntax pzmap(sys)
563
Imag Axis
564
Syntax rsys = reg(sys,K,L)
566
Example sys = rss(4,1,1,2,3);
569
11rlocfind
570
Purpose Evans root locus
572
Syntax rlocus(sys)
572
Syntax rltool
575
F and H
578
Syntax sys = rss(n)
579
11series
581
Property
584
Syntax sgrid
590
Syntax sigma(sys)
592
Nichols plot
596
Nyquist plot
596
Syntax size(sys)
597
Test if LTI model is empty
598
Test if LTI model is SISO
598
Syntax msys = sminreal(sys)
599
Syntax sys = ss(a,b,c,d)
601
Conversion to State Space
602
Syntax sysT = ss2ss(sys,T)
605
Syntax [sysb,T] = ssbal(sys)
606
11ssdata
608
Syntax step(sys)
610
Syntax sys = tf(num,den)
614
Example 4
618
Discrete-Time
618
Conventions
618
11tfdata
621
Specify transfer functions
623
Syntax td = totaldelay(sys)
624
Syntax zgrid
626
Syntax sys = zpk(z,p,k)
628
Variable
630
Selection
630
Example Example 1
631
Syntax [z,p,k] = zpkdata(sys)
633
Get properties of LTI models
635
Specify zero-pole-gain models
635
See state-space models
638
See also LTI models
639
See transposition
639
See Kalman estimator
639
See time response
639
See I/O groups
640
See also InputName
640
See also Simulink LTI Viewer
641
See delays
641
See model building
641
See delay
641
See frequency response
642
See also operations
642
See LTI properties
642
See Simulink LTI Viewer
643
See LTI objects
644
See also OutputName
644
See transfer functions
647
See zeros
648
See zero
648
See also noise
648
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