ENGG*4420

Real Time System Design

Lab 2: Real-Time Automotive

Suspension system Simulator
TA: Aws Abu-Khudhair
(aabukhud@uoguelph.ca)
Due: Week of Oct. 12th
Aws Abu-Khudhair ENGG*4420 1
Today’s Activities

† Lab 2 Introduction.
† Lab 1 Demos.
† Start work on Lab 2.

Aws Abu-Khudhair ENGG*4420 2

Lab 1 Development Environment

† HP PC
† LabVIEW 2009 software

Aws Abu-Khudhair ENGG*4420 3

Introduction
† Types of vehicle suspension systems
„ Passive Suspension System.
„ Active Suspension System.
„ Semi-Active Suspension System.
† Road disturbance
„ Step Input
„ Harmonic Input

Aws Abu-Khudhair ENGG*4420 4

Passive Suspension System
† Standard vehicle suspension zs
system
Vehicle body
† Employed in the majority of
commercial vehicles
† Advantages: ks bs
zu
„ Low cost.
„ Simple implementation.
Tire
† Disadvantages:
„ Purely passive elements. zr
kt
„ On-line performance optimization
not possible
Aws Abu-Khudhair ENGG*4420 5
Active Suspension System
zs
† Fully active system.
† Computer controlled active Vehicle body
element (Fa).
† Advantages: Fa
„ Offers excellent performance. zu
„ Allows for control and performance
optimization at any point during Tire
lifetime.
† Disadvantages: kt
zr
„ High cost.
„ Major safety issues.
„ High power demand.

Aws Abu-Khudhair ENGG*4420 6

Semi-Active Suspension System
† Hybrid system (Passive + zs

Active) Vehicle body

† Provides excellent fail safe
mechanism.
k bs bsemi
† Relatively low cost. s
zu

† Provides a performance Tire

comparable to the active
system. kt
zr

† Very low power demand.

Aws Abu-Khudhair ENGG*4420 7
Quarter-Car Suspension Model
zs zs

ms ms
Active element

ks bs ks bs bsemi
zu zu

mu mu

zr zr
kt kt

Passive Suspension System Semi-Active Suspension System

Aws Abu-Khudhair ENGG*4420 8
Quarter-Car Suspension Model
cont.
† The system can be modeled using
state space representation:
† Passive:
X& = AX + Lz& r ,
† Semi-Active:
X& = AX + NXbsemi + Lz& r ,
† The two models are equivalent when
the variable damper coefficient is set
to 0
Aws Abu-Khudhair ENGG*4420 9
State Space Model
X& = AX + NXbsemi + Lz&r , eq. 2.11

† In the S.S. equation:

„ ‘X’ – State vector.
„ ‘A’ – State matrix (system description).
„ ‘N’ – Semi-active control matrix.
„ ‘L’ – Input disturbance vector.
„ ‘Zr’ – Road disturbance.
† Matrices description is provided in the lab
manual pg. 43-45
Aws Abu-Khudhair ENGG*4420 10
State Space Model

⎡ x1 ⎤ ⎡ z s − zu ⎤ ⎡ Suspension deflection ⎤
⎢ x ⎥ ⎢ z& ⎥ ⎢ Velocity of sprung mass ⎥
X = ⎢ 2⎥ = ⎢ s ⎥ = ⎢ ⎥
⎢ x3 ⎥ ⎢ zu − z r ⎥ ⎢ Tire deflection ⎥
⎢ ⎥ ⎢ ⎥ ⎢ ⎥
⎣ x4 ⎦ ⎣ z&u ⎦ ⎣Velocity of unsprung mass⎦
† X& - Derivative of the state vector over the
sampling time.
† Z& r- Derivative of the road disturbance over
the sampling time.
Aws Abu-Khudhair ENGG*4420 11
Road Disturbance
† Step Input:
„ Isolated sudden disturbance.
„ Ex. Curb with a height of 10 cm.
Zr = 0.1m

Road Input
Zr(t)

0 Time (t)
Aws Abu-Khudhair ENGG*4420 12
Road Disturbance cont.
† Harmonic Input:
„ Simple road profile.
„ Modeled as a Sine wave with:
† Freq. 1 Hz.
† Amp. 10 cm.
† Phase 0°.

Aws Abu-Khudhair ENGG*4420 13

Semi-Active Suspension Control
Methods
† Skyhook Control.
† Ground-hook control.
† Optimal control based on LQR.
† Fuzzy logic control:
„ GA-based fuzzy control.
„ Neural-Fuzzy control.
„ Adaptive Fuzzy control.

Aws Abu-Khudhair ENGG*4420 14

Linear Quadratic Regulator (LQR)
† The controller works towards
minimizing the performance index
given in equation (2.13).
⎡T 2 2⎤
J = lim E ⎢ ∫ x& 2 + ρ1 x1 + ρ 2 x 2 + ρ 3 x3 + ρ 4 x 4 ⎥
2 2 2
eq. 2.13
T →∞
⎣0 ⎦
† The controller determines the
required “ideal” active force (Fa) to
stabilize the vehicle.

Aws Abu-Khudhair ENGG*4420 15

Semi-Active Control Law (LQR)
† The optimal control
law is determined
using Fig. 2.6.
† According to the
calculated optimal
active force (Fa), and
the absolute velocity of
the two masses, the
damping coefficient
(bsemi) is calculated.
Fig. 2.6.
Aws Abu-Khudhair ENGG*4420 16
Semi-Active Control Law (LQR)
cont.
† The LQR control method is summarized in
table 2.2.

Aws Abu-Khudhair ENGG*4420 17

Lab 2 – Implementation steps
† Step 1: Read Chapter 2 of the lab
manual (further information is given
in the appendix section).
† Step 2: Implement the quarter-car
passive and semi-active suspension
models in LabVIEW.
† Step 3: Implement the two road
disturbances (step and harmonic).

Aws Abu-Khudhair ENGG*4420 18

Lab 2 – Implementation steps
† Step 4: Implement the LQR controller for
the semi-active suspension system.
† Step 5: Perform the following analysis
1. Compare the performance of the passive and
semi-active suspension systems.
2. Vary the weight parameters of the LQR
controller (P matrix in eq. 2.14) and observe
the change in performance of the SASS.
3. Provide a measure to differentiate the difference
in performance of the two systems
(% difference?)

Aws Abu-Khudhair ENGG*4420 19

Requirements
1. A fully functional passive and semi-
active suspension systems, with the
ability to switch between the two
systems in the same project.
2. Simulations performed using the two
road disturbances given in section
2.2.2 of the lab manual.

Aws Abu-Khudhair ENGG*4420 20

Requirements
3. The following performance graphs
must be present on the front panel:
† Vehicle ride quality.
† Suspension deflection response.
† Tire deflection response.
† Input disturbance to the system.
4. LQR control must be performed using
a separate Task (loop) from the plant
system.

Aws Abu-Khudhair ENGG*4420 21

Notes – Matlab Script Nodes
† The matricies can be coded using the
MatLAB script node in LabVIEW.
† Matrix definitions are done in the
following format:
„ X= [xx xx xx;
xx xx xx;
xx xx xx];
Note that variables can be used within the
matrix defintion.

Aws Abu-Khudhair ENGG*4420 22

Notes – Matlab Script Nodes
† Matricies can be multiplied and added
as long as the dimensions are
consistent.
† To transpose a matrix add a ‘’’ after
the matrix variable.
† Dot product multiplications can be
performed using a ‘*’.

Aws Abu-Khudhair ENGG*4420 23

Notes -
† Another method of implementing the
matrices is through using the matrix
variables in LabVIEW.
„ Matrix values must be calculated by
hand and inputted in the matrices
manually.

Aws Abu-Khudhair ENGG*4420 24

Note – Plant/Controller
synchronization
† A requirement of the
lab is to implement the Task 1
controller in a separate SASS Plant
task than the plant
system.
synchronization
† Synchronization
between the two Task 2
systems can be LQR Controller
accomplished using:
„ Semaphore, or
„ Occurrences.

Aws Abu-Khudhair ENGG*4420 25

Deadlines and Marking

† Lab 2 is worth 8%.

† 4% for the report, and 4% for the demo
† The Demo is due Oct. 12th, 2010 in the Lab.
† The Report is due Oct. 12th, 2010 in the
Lab.
† A signed group evaluation sheet must be
submitted with the lab report

† QUESTIONS?
Aws Abu-Khudhair ENGG*4420 26