Truck suspensions

Conventional passive suspension

zs

zu

zr

suspension spring suspension damper

tyre stiffness Kt

sprung mass(body) Ms

unsprung mass(wheel, axle) Mu

Active suspension

Fully-active suspensions

Ms

zs

zu

zr

C

Mu

Kt

high bandwidthactuator

controlsignal

sensordata

sensordata

(a)

Actuator provides totalsuspension force

Ms

zs

zu

zr

C

Mu

Kt

High BWactuator

sensordata

sensordata

Ks

(b)

Static load supportedby passive spring

Slow-active suspension

Ms

zs

zu

zr

C

Mu

Kt

Lower BWactuator

sensordata

sensordata

springdamper

Slow-active suspension

Semi-active suspension- dissipative forces only

Ms

C

Mu

Kt

actuator

sensordata

sensordata

Ks

ss Vz

uu Vz

zr

Fd

Fd

Vs

Vu

dissipativeactuator

0 usd VVF

ABC components

ECU

Active Body Control on Mercedes CL Coupé

Hardware-in-the-Loop simulation

Ms

Mu

zs

zu

zr Kt

Ks HC11HC11

ADC

ADC

DIO

accelerometer

relativevelocitysensor

SIMULINK model

Fdsa

PC dataacquisitioninterface

PIDPID

Fd

forcesensor

As acc sE K Z

Vrel vel u sE K Z Z

DA

CD

AC

DIO

Ms

Mu

zs

zu

zr Kt

Ks HC11HC11

ADC

ADC

DIO

accelerometer

relativevelocitysensor

SIMULINK model

Fdsa

PC dataacquisitioninterface

PIDPID

Fd

forcesensorMs

MuMu

zs

zu

zr Kt

Ks HC11HC11

ADC

ADC

DIO

accelerometer

relativevelocitysensor

SIMULINK model

Fdsa

PC dataacquisitioninterface

PIDPID

Fd

forcesensor

As acc sE K Z

Vrel vel u sE K Z Z

DA

CD

AC

DA

CD

AC

DIO

DIO

HC12

P2

Pst

V1

V2

PV

Vr

Fd

Fd

Q2

P1

P2= Pst

Vs

Extension: Vrel < 0

Qv = Ap|Vrel|

Pst

Vu

Pst

||1 relp VAV

||)(2 relrp VAAV

P1 = PstP

Vrel = Vu Vs

Ar

Ap+Ar

P2

Pst

V1

V2

PV

Vr

Fd

Fd

Q1

P1

Vs

Qv = Ar|Vrel|

Pst

Vu

Pst

||1 relp VAV

||)(2 relrp VAAV

P1 = PstP

Vrel = Vu Vs

Ar

Ap+Ar

Contraction: Vrel > 0

P1 = P2 = PstP

P2=P1

Proportional control valve

P

AB

flow Qv flow Qv

pressureP1 P

pressureP1

Xvspool

displacement

Torificeflows

solenoidLVDT

Mechanical design

• Determine the leading functional dimensions of the damper

–rod length and diameter;

–inner tube bore;

– outer tube bore

Remember the important specification that the bump and rebound force-velocity characteristics are to be symmetrical.

Damper design

• Convert the pressureflow envelope of figure 7 to a damping forcerelative 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

Forcecontroller

Forcecontroller

Spoolposition

controller

Spoolposition

controller

DamperdynamicsDamper

dynamics

Forcetransducer

Forcetransducer

Xvc Xv FdFdsa

MSD forcecommand

Damperforce

Vrel

Feedforward + Feedback

Linearfeedbackcontroller

Linearfeedbackcontroller

Spool anddamper

dynamics

Spool anddamper

dynamics

Forcetransducer

Forcetransducer

Xvfb Xvc Fd

Fdsa

Vrel

Nonlinearfeedforward

controller

Nonlinearfeedforward

controller

Xvff

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.

sisotool

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 HC12 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.

smrelmda VCVCF )1(

0for 0

0for

relda

reldadadsa

VF

VFFF(4)

(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 HC12 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

ScheduleWeek: 12/9 19/9 26/9 3/10 10/10 17/10

Mechanical design, damper characterisation

# # # # # #

PID control design # # # #

HC12 controller design # # # # # #

System simulation # # # # # #

HiL simulation in lab # # # # First try Final run

Report # # # # # #

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

• Track reference input, or maintain set point, despite:

– load disturbances (usually low frequency)

– sensor noise (usually high frequency)

• Achieve specified bandwidth, and transient response characteristics

Gc(s)Gc(s)

Controller

N

sensornoise

W load disturbance

Gp(s)Gp(s)

Plant

Ucontrol

Youtput

Rreferenceinput, orset-point

Esensed

error

Performance of control system

• Sensor noise reproduced just like reference input

– use low noise sensors!

– seek to make

Gc(s)Gc(s)

Controller

N

sensornoise

W load disturbance

Gp(s)Gp(s)

Plant

Ucontrol

Youtput

Rreferenceinput, orset-point

Esensed

error

)()(1

)()(

)(1

)()(

)(1

)()( sW

sGG

sGsN

sGG

sGGsR

sGG

sGGsY

pc

p

pc

pc

pc

pc

freq. high at

freq. low at

0

1

)(1

)(

sGG

sGG

pc

pc

• To reject disturbances, make freq. edisturbanc at )(1 sGG pc

PID controller functions

• Output feedback– from Proportional action

• Eliminate steady-state offset– from Integral action

• Anticipation– from Derivative action

Kp

+

P

I

D

e(t) u(t)

Kp

+

P

I

D

E(s) U(s)

react to rapid rate of change before error grows too big

apply constant control even when error is zero

compare output withset-point

Transfer function of PID controller

sT

sTsTTK

K

KT

K

KTsT

sTK

sKs

KK

sEsU

sG

i

idip

p

dd

i

pid

ip

di

pc

1

, where1

1

)()(

)(

2

integral time constant,or 'reset time'

derivative time constant

• If no derivative action, we have PI controller:

sT

sTK

K

KT

sTK

s

KK

sEsU

sG

i

ip

i

pi

ip

ipc

1

where1

1

)()(

)(

proportional gain

integral gain

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2-5

-4

-3

-2

-1

0

1

2

3

4

5

Real Axis

Imag

Axi

s

Effects on open-loop transfer function

• s-plane

j

oo

pole at originincreases Type No.

zeros pull root locus branchesto left: stabilising

o

o

Closed-loop poles for Kp = 11.5

Plant poles

Example: 11.0 ,37.0 ,)4)(1(

4

dip TTss

GsT

sTsTTKsG

i

idipc

1)(

2

Effects on open-loop transfer function• Frequency response

0dBiK

dK1 log

s

K i sTd

+90º

-90º

LogMag

Phase

i

d

d T

T

T

411

21

sT

sTsTTKsG

i

idipc

1)(

2

amplitude boostat low frequenciesto reduce steady-state error

phase lead to increasephase margin, bandwidth

11

0 as

pc

pc

c

GG

GG

sG

problem!amplifies highfreq. noise

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-damped vibrational modes

Simulink PID models

Simulink PID

models