Transcript chapter6-note

Chapter 6 Position and Speed Regulation in DC
Servomechanism
§ 6.1 DC Servo System
§ 6.2 Servo Components
§ 6.3 Component Model
§ 6.4 System Control
§ 6.1 DC Servo System (1)
• Fundamental Operations of DC Servo:
(1)Speed servo
Speed regulation, speed tracking
(2)Position servo (Servomechanism)
Position control, position tracking
§ 6.1 DC Servo System (2)
•
Control Objective:
System robustness
Command following
Disturbance rejection
Stable operation
Implies

Fast transient response
Small steady-state error
§ 6.1 DC Servo System (3)
• Generic Motor Position Control:
ysp(t)
PC
VC
CC
PC: Position controller
VC: Velocity controller
CC: Current controller
Current
Velocity
i(t)
v(t)
Amp
Motor
 ( )dt
y(t)
§ 6.1 DC Servo System (4)
• Mechatronic View Point:
Power Amp
&
DC Servo
Motor
DC Power
Supply
(External)
Servo
Controller
Motor
Gear Train
&
Load
Speed
&
Position
Sensor
§ 6.1 DC Servo System (5)
Ex: DC servo control of liquid-level process
Gc(s)
p(t)
Amplifier
ee(t)
ea(t)
Gm(s)
er(t)
eb(t)
Valve
positioner
xv(t)
Potentiometer
bridge
Kv(s)
qm(t)
x(t)
pu(t)
hc(t)
qu(t)
Pump
hv(t)
§ 6.1 DC Servo System (6)
+
1
Rf
pu(t)
-
qu(t)
qM(t)
hv(t)
eR(t) eE(t)
Kh
+
p(t)
Gc(s)
xV(t)
Gm(s)
+
Kv
-
τps+1
+
x(t)
Kh
Gm(s): Servo motor and gear train
Rf /γ
1.0
hC(t)
§ 6.2 Servo Components (1)
• Hardware Components:
Resolvers
DC motor
http://www.shangyi.com.tw/c_produact_c.htm
Rotary Encoders
http://www.encodersindia.com/products.html
http://www.encodersindia.com/products.html
§ 6.2 Servo Components (2)
Potentiometer
http://www.islproducts.com/prod/pots.htm
Optical Encoders
http://www.usdigital.com/products/hd25a/
Inductosyn Encoders
http://www.mi-technologies.com/catalog/antennas/indencdr.pdf
§ 6.2 Servo Components (3)
• Classifications of DC Motor:
DC motor
Brushless
type
Commutator type
Shunt Permanent Compound
Series wound magnet
wound
Moving coil
or ironless
armature
Field
motor
Torque Servo
Printed Shell type motor motor
circuit armature
motor (Ironless
shell or rotor) Cumulative
compound
Permanent Switched Stepper
magnet reluctance
Variable Permanent Hybrid
reluctance magnet
Differential
compound
§ 6.2 Servo Components (4)
• Feedback Devices:
Feedback Devices
Analog
Digital
Absolute
Incremental
(train of pulses) (pattern of pulses)
Position
Velocity
(output proportional
to velocity)
Rotary
Linear
Quantizer
Optical
Induction
Rotary
Optical
Tachometer
Potentiometers
Linear
Rotary Rotary
Linear
Differential
Synchro Resolver Resolver
Transformer
§ 6.2 Servo Components (5)
• Resolution of Displacement Sensors:
Optical
encoders
Inductosyn
Resolvers
Synchros
Potentiometers
Angular
resolution
§ 6.3 Component Model (1)
• DC Servomotor:
Ex: Armature Control
ia(t) Ra
if =const.
+
or Permanent magnet
va(t) eb(t) M
La
Ttd
-
(1) Static model
θ m ,Ttm , Jm , Bm, ωm
Tt
K T max
t
Tmax
(Stall)
v max
T  K T v  KB
t
max
Kb 
t
Tmax

v max
v max
max
 0

T t 0
K i  RaK T max

(Stall)
KB
KT
(No load)
max
t
Tmax

imax
§ 6.3 Component Model (2)
(2) Dynamic model
Va (s)
+
-
1
Las
Tdt (s) Load disturbance
ia
Ki
+
-
1
m (s)
Jm s
-
Ra
Bm
Kb
Electronics
Mechatronics
Mechanics
M
E
E
M
1
s
m (s)
§ 6.3 Component Model (3)
(3) Simplified Servo Motor
Td (s)
(with gear train)
Tm (s)
Va(s)
(Motor)
Tm (s)
(Motor)
+
1
Ra
K
Tmt (t) 
Ki
v a (t)
Ra
• Gear Train
m (s)
1
N
1
N
N
 (s)
(Load)
T (s)
(Load)
i
-
1
Jms+Bm
 (t) 1

m (t) N
T t (t)
N
Tmt (t)
 m(s)
1
s
 m(s)
Jmm  Bmm  Tmt (t)  Tdt (t)
§ 6.3 Component Model (4)
• Potentiometer:
Θ(s)
V(s)
Ks
v(t)
 Ks
(t)
• Tachometer:
Θ(s)
sKv
K v θ(t) = v(t)
V(s)
or
Ω(s)
Kv
V(s)
§ 6.4 System Control (1)
• Plant Dynamics:
(1) Dynamics
0
I m  C m 
Servo Motor
(2) States
m  Position
m 
Speed
 u(t)  w(t)
Command
Disturbance
§ 6.4 System Control (2)
• Closed-loop Control:
(1) Position feedback
Control law:
u(t)  uc (t)  am,a  0
By potentiometer
Closed-loop:
I m  C m  am  uc (t)  w(t)
F.B. increases stiffness
Position feedback is to increase response speed.
§ 6.4 System Control (3)
(2) Velocity feedback
Control law:
u(t)  uc (t)  b m, b  0
By tachometer
Closed-loop:
I m  (c  b) m  uc (t)  w(t)
F.B. increases damping
Velocity feedback is to decrease response overshoot.
§ 6.4 System Control (4)
(3) Position and Velocity feedback
Control law:
u(t)  uc (t)  a m  b m, a,b  0
By potentiometer By tachometer
Feedback
Closed-loop:
 m , m 
States feedback
I m  (c  b) m  a m  uc (t)  w(t)
Control overshoot Control response speed
Optimal control of fast speed and minimum overshoot by optimal
design of a and b, respectively.
Optimal control law is realized by state equations with states
feedback in modern control theory.
§ 6.4 System Control (5)
• Speed Control with Current Loop:
Td(s)
-
IR(s)
+
GCI(s)
+
-
1
L as  Ra
Ia(s)
Ki
+
-
1
Jms  Bm
Kb
For GCI (s) 
Kp
(s)
Kp (1 Ts)
i
Ts
i
1
Td(s)
IR(s)
+
-
PI
, PI control
Ki
+
1
Jms  Bm
m (s)
m (s)
§ 6.4 System Control (6)
• Digital Control Configuration:
(1) System structure
Sample & Hold
Number Seq. + Algorithm
+
ZOH
Digital
computation
A/D
Command
D/A
Hold
-
H(s)
Continuous
Sys.
G(s)
§ 6.4 System Control (7)
(2) Procedure in real-time sampling and control
sampling time, h
wait for clock
interrupt
read analog
input
compute control
singal
set analog output
update controller
variable
t
§ 6.4 System Control (8)
(3) Discrete PID
•
Continuous form
t
u(t) = KPe(t)+KI  e(τ)dτ +KD
0
•
de(t)
dt
Discretization
e(t)  e(kh), e(kh) is represented as e(k), h is sampling time
n
 e(τ)dτ  h e(i)
t
0
i=0
de(t) e(k) - e(k -1)

dt
h
•
Discrete form
n
u(k) = K Pe(k)+KIh e(i)+K D
i=0
e(k) - e(k -1)
h