Where is w=0 , where is w=0-, - PowerPoint PPT Presentation

About This Presentation
Title:

Where is w=0 , where is w=0-,

Description:

where is w=+inf, where is w=-inf, what is the system type, what is the relative order of the TF, how should you complete the nyquist plot, what are P/N/Z values as in ... – PowerPoint PPT presentation

Number of Views:20
Avg rating:3.0/5.0
Slides: 36
Provided by: Bri139
Category:
Tags: slope | stability

less

Transcript and Presenter's Notes

Title: Where is w=0 , where is w=0-,


1
  • Where is w0, where is w0-,
  • where is winf, where is w-inf,
  • what is the system type,
  • what is the relative order of the TF,
  • how should you complete the nyquist plot,
  • what are P/N/Z values as in the nyquist
    criterion,
  • is the closed-loop system stable,
  • what the is the phase margin,
  • by how much can the gain be varied without
    affecting stability?
  • how many gain cross-over points and how many
    phase cross-over points are there?

2
(No Transcript)
3
(No Transcript)
4
Open vs Closed Loop Frequency Response And
Frequency Domain Specifications
G(s)
C(s)
Goal 1) Define typical good freq resp shape
for closed-loop 2) Relate closed-loop
freq response shape to step response shape
3) Relate closed-loop freq shape to open-loop
freq resp shape 4) Design C(s) to make
C(s)G(s) into good shape.
5
(No Transcript)
6
Prototype 2nd order system closed-loop frequency
response
For small zeta, resonance freq is about wn BW
ranges from 0.5wn to 1.5 wn For good z range, BW
is 0.8 to 1.1 wn So take BW wn
z0.1
0.2
0.3
No resonance for z lt 0.7 Mr1dB for
z0.6 Mr3dB for z0.5 Mr7dB for z0.4
w/wn
7
Prototype 2nd order system closed-loop frequency
response Mr vs z
8
0.2
z0.1
0.3
0.4
wgc
In the range of good zeta, wgc is about 0.65
times to 0.8 times wn
w/wn
9
In the range of good zeta, PM is about 100z
z0.1
0.2
0.3
0.4
w/wn
10
Important relationships
  • Prototype wn, open-loop wgc, closed-loop BW are
    all very close to each other
  • When there is visible resonance peak, it is
    located near or just below wn,
  • This happens when z lt 0.6
  • When z gt 0.7, no resonance
  • z determines phase margin and Mp
  • z 0.4 0.5 0.6 0.7
  • PM 44 53 61 67 deg 100z
  • Mp 25 16 10 5

11
Important relationships
  • wgc determines wn and bandwidth
  • As wgc ?, ts, td, tr, tp, etc ?
  • Low frequency gain determines steady state
    tracking
  • L.F. magnitude plot slope/(-20dB/dec) type
  • L.F. asymptotic line evaluated at w 1 the
    value gives Kp, Kv, or Ka, depending on type
  • High frequency gain determines noise immunity

12
Desired Bode plot shape
13
Proportional controller design
  • Obtain open loop Bode plot
  • Convert design specs into Bode plot req.
  • Select KP based on requirements
  • For improving ess KP Kp,v,a,des / Kp,v,a,act
  • For fixing Mp select wgcd to be the freq at
    which PM is sufficient, and KP 1/G(jwgcd)
  • For fixing speed from td, tr, tp, or ts
    requirement, find out wn, let wgcd wn and
    choose KP as above

14
(No Transcript)
15
(No Transcript)
16
  • clear all
  • n0 0 40 d1 2 0
  • figure(1) clf margin(n,d)
  • proportional control design
  • figure(1) hold on grid Vaxis
  • Mp 10/100
  • zeta sqrt((log(Mp))2/(pi2(log(Mp))2))
  • PMd zeta 100 3
  • semilogx(V(12), PMd-180 PMd-180,'r')
  • get desired w_gc
  • xginput(1) w_gcd x(1)
  • KP 1/abs(polyval(n,jw_gcd)/polyval(d,jw_gcd))
  • figure(2) margin(KPn,d)
  • figure(3) stepchar(KPn, dKPn)

17
(No Transcript)
18
(No Transcript)
19
n1 d1/5/50 1/51/50 1 0 figure(1) clf
margin(n,d) proportional control
design figure(1) hold on grid Vaxis Mp
10/100 zeta sqrt((log(Mp))2/(pi2(log(Mp))2)
) PMd zeta 100 3 semilogx(V(12),
PMd-180 PMd-180,'r') get desired
w_gc xginput(1) w_gcd x(1) Kp
1/abs(polyval(n,jw_gcd)/polyval(d,jw_gcd)) Kv
Kpn(1)/d(3) ess0.01 Kvd1/ess z w_gcd/5
p z/(Kvd/Kv) ngc conv(n, Kp1 z) dgc
conv(d, 1 p) figure(1) hold on
margin(ngc,dgc) ncl,dclfeedback(ngc,dgc,1,1)
figure(2) step(ncl,dcl) grid figure(3)
margin(ncl1.414,dcl) grid
20
(No Transcript)
21
(No Transcript)
22
(No Transcript)
23
(No Transcript)
24
(No Transcript)
25
(No Transcript)
26
(No Transcript)
27
(No Transcript)
28
(No Transcript)
29
(No Transcript)
30
(No Transcript)
31
(No Transcript)
32
Proportional controller design
  • Obtain open loop Bode plot
  • Convert design specs into Bode plot req.
  • Select KP based on requirements
  • For improving ess KP Kp,v,a,des / Kp,v,a,act
  • For fixing Mp select wgcd to be the freq at
    which PM is sufficient, and KP 1/G(jwgcd)
  • For fixing speed from td, tr, tp, or ts
    requirement, find out wn, let wgcd wn and
    choose KP as above

33
C(s)
Gp(s)
34
(No Transcript)
35
(No Transcript)
Write a Comment
User Comments (0)
About PowerShow.com