Transcript Slow-active suspension - University of Melbourne

Truck suspensions
Conventional passive suspension
zs
sprung mass
(body) Ms
suspension spring
unsprung mass
(wheel, axle) Mu
tyre stiffness Kt
suspension damper
zu
zr
Active suspension
Fully-active suspensions
zs
sensor
data
Ms
high bandwidth
actuator
zu
control
mC
signal
sensor
data
Mu
zr
Kt
(a)
Actuator provides total
suspension force
zs
sensor
data High BW
Ms
actuator
mC
Ks
zu
sensor
data
Mu
zr
Kt
(b)
Static load supported
by passive spring
Slow-active suspension
zs
sensor
data
Lower BW
Ms
actuator
damper
spring
zu
sensor
data
Mu
zr
Kt
mC
Slow-active suspension
Semi-active suspension
- dissipative forces only
zs  Vs
sensor
data
Ms
zu  Vu
dissipative
actuator
Fd Vs  Vu   0
sensor
data
Mu
Vs
actuator
mC
Ks
zr
Fd
Vu
Kt
Fd
Hardware-in-the-Loop simulation
E A s  K acc Zs
DAC
accelerometer
Zs
Ms
DIO
Zu
Mu
Zr
Kt
ADC
DIO
Xvc
Ks
DAC
relative
velocity
sensor
spool position
command
M68HC11
ADC
EVrel  K vel Zu  Z s 
SIMULINK model
Vs
Fd
Qv = Ap|Vrel|
V1   Ap | Vrel |
Pst
V1
Ar
P1 = Pst  DP
P1
PV
Extension: Vrel < 0
P2P
=2Pst V Ap+Ar
r
V2
V2  ( Ap  Ar ) | Vrel |
Q2
Pst
Vu
Vrel = Vu  Vs
Fd
Pst
Fd
Vs
Qv = Ar|Vrel|
V1   Ap | Vrel |
Pst
V1
Ar
P1 = Pst  DP
P1
PV
Contraction: Vrel > 0
Q1
V2  ( Ap  Ar ) | Vrel |
Vu
V2 P22=P1
Vr
Ap+Ar
Pst
Pst
P1 = P2 = Pst  DP
Vrel = Vu  Vs
Fd
Proportional control valve
orifice
flows
solenoid
LVDT
T
P
B
A
flow Qv flow Qv
pressure
pressure
P1  DP
P1
Xv
spool
displacement
Mechanical design
• Determine the leading dimensions
of the damper
–rod length, diameter and wall thickness;
–inner tube bore and wall thickness;
– outer tube bore
Remember the important specification that the
bump and rebound force-velocity characteristics
are to be symmetrical.
Damper design
• Convert the pressureflow envelope of figure 7 to
a damping forcerelative velocity envelope for
your design.
• Make plots on this chart of the damper force Fd
versus relative velocity Vrel for values of Xv = 0.1,
0.2, 0.3, 1.0.
• Make a separate plot of Fd versus Xv for different
values of Vrel.
Force controller
Vrel
MSD force
command
Fdsa 

Force
controller
Xvc
Spool
position
controller
Force
transducer
Damper
force
Xv
Damper
dynamics
Fd
Feedforward + Feedback
Vrel
Nonlinear
feedforward
controller

Fdsa

Linear
feedback
controller
Xvff
Xvfb 

Xvc
Force
transducer
Spool and
damper
dynamics
Fd
Force controller design
• Given the linearised plant model, design a
PI or PID controller for a chosen nominal
operating condition, and check its
robustness against changes in operating
point.
• A suggested nominal operating condition
is Fd0 = 2500 N, Vrel0 = 0.15 m/s.
• Recall the specification that the desired
bandwidth for the force controller is 20 Hz.
rltool
Alternative controller design
• Use the Ziegler-Nichols ‘ultimate
sensitivity’ method to design a PI or PID
controller.
• That is, initially set the integral and
derivative gains to zero, and increase the
proportional gain until the system
oscillates on the point of instability.
• Then measure the ‘ultimate gain’ Ku and
the ‘ultimate period’ Pu, and apply the
tuning rules to obtain a first-cut set of
values for the controller gains.
fctrl.mdl
MSD controller design
• Design a real-time program for the
M68HC11 microcontroller to perform the
semi-active damper control task.
– The MSD control law is defined in equations (4)
and (5). Suitable initial parameter values are
Cm = 45 kN/(m/s) and  = 0.2.
Fda  CmVrel  (1  )CmVs
(4)
Fdsa  Fda for FdaVrel  0
0
for FdaVrel  0
(5)
Implementation
• Then implement your program in a
hardware-in-the-loop simulation, using the
SIMULINK model HiL_sys provided.
– The roadway roughness input can be selected
to be deterministic (e.g., sinusoidal
corrugations) or random (corresponding to a
road profile that could be encountered on a
main road at 70 km/h).
– Time histories of simulation variables will be
written into the MATLAB workspace, so that
the performance of the controller can be
assessed.
Design tools provided
• SIMULINK model, SIM_sys
– This is identical with HiL_sys, except that a
subsystem block M68HC11 is included as a
representation of the microcontroller.
– You can modify this block to create your own
SIMULINK representation of your controller
code, to test its operation before attempting
the HiL simulation.
• Ziegler-Nichols tuning tool fctrl
– invoke with fctrl_start
SIM_sys.mdl
Schedule
Week:
4/9
11/9
18/9
25/9
2/10
9/10
16/10
Mechanical design, damper
characterisation
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PID control design
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Initial appreciation, including
mechanical design
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HC11 controller design
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System simulation
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HiL simulation in lab
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First try
Final run
Report
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PID controllers
• PID = Proportional + Integral + Derivative
• Also known as "three-term controller"
• About 90% of all control loops are closed
with some form of PID controller
• In this group of lectures we will find out:
– why PID controllers are used so often
– ways of "tuning" a PID controller
– how to deal with actuator saturation
Functions of control system
W load disturbance
Controller

R
reference
input, or
set-point
E
 sensed
Gc(s)
U 
control

Plant
Y
Gp(s)
output
error

• Track reference input, or maintain set
point,
despite:
– load disturbances (usually low frequency)
– sensor noise (usually high frequency)
• Achieve specified bandwidth, and
N
sensor
noise
Performance of control system
W load disturbance
Controller

R
reference
input, or
set-point
E
 sensed
error
Gc(s)
U 
Plant

Y
Gp(s)
control
output

Y ( s) 
GcG p ( s)
1  GcG p ( s)
R( s ) 
GcG p ( s)
1  GcG p ( s)
N ( s) 
G p ( s)
1  GcG p ( s)
W ( s)
N
sensor
noise
• Sensor noise reproduced just like reference input
– use low noise sensors!
G G ( s)
 1 at low freq.

– seek to make 1  GcG p ( s) 
0 at high freq.
c
p
1  GcG p ( s)   at disturbance freq.
• To reject disturbances, make
PID controller functions
Kp
e(t)
P
 K ()dt
I
d ()
Kd
dt
D
i
Kp
u(t) E(s)
+
• Output feedback
– from Proportional action
• Eliminate steady-state
offset
– from Integral action
• Anticipation
Ki
s
Kd s
P
I
U(s)
+
D
compare output with
set-point
apply constant control
even when error is zero
react to rapid rate of change
before error grows too big
Transfer function of PID
controller
K
U (s)
Gc ( s ) 
E (s)
 Kp 
i
s
 Kd s


1
 K p 1 
 Td s 
 Ti s

derivative time constant
Kp
Kd
where Ti 
, Td 
Ki
Kp
integral time constant,
or 'reset time'
TiTd s 2  Ti s  1
 Kp
Ti s
• If no derivative action, we have PI
K
U ( s)
controller:
Gc ( s ) 
 Kp  i
E ( s)

1 
 K p 1  
 Ti s 
T s 1
 Kp i
Ti s
s
where Ti 
Kp
proportional gain
Ki
integral gain
Effects on open-loop transfer
function
TiTd s 2  Ti s  1
Gc ( s )  K p
Ti s
• s-plane
Exampl
e: 5
Gp 
4
, Ti  0.37, Td  0.11
( s  1)( s  4)
4
pole at origin
increases Type No.
3
o
2
o
o


Imag Axis
j
1

0
Plant poles
 
-1
o
-2
-3
zeros pull root
locus branches
to left: stabilising
-4
-5
-8
-7
-6
-5
-4
-3
-2
Real Axis
Closed-loop poles for Kp = 11.5
-1
0
Effects on open-loop transfer
function
T T s  T s 1
Gc ( s )  K p
2
i d
• Frequency
response
i
Ti s
amplitude boost
at low frequencies
to reduce steady-state error
Gc   as s  0
Gc G p
1  Gc G p
Ki
s
1

2Td

4T
1  1  d
Ti




problem!
amplifies high
freq. noise
Td s
LogMag
0dB
1
Ki
+90º
1
Kd
log 
Phase
-90º
phase lead to increase
phase margin, bandwidth
Application of PID control
• PID regulators provide reasonable control
of most industrial processes, provided
performance demands not too high
• PI control generally adequate when
plant/process dynamics are essentially
1st-order
– plant operators often switch D-action off:
"dificult to tune"
• PID control generally OK if dominant plant
dynamics are 2nd-order
• More elaborate control strategies needed
if process has long time delays, or lightly-
Simulink PID models
Simulink PID models