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ENGG*4420
Real Time System Design
Lab 2: Real-Time Automotive
ENGG*4420 1
Lab 2: Real-Time Automotive Suspension system Simulator
TA: Matthew Mayhew([email protected])
Due: Fri. Oct 12th / Mon Oct 15th
Today’s Activities
� Lab 2 Introduction.
� Lab 1 Demos.
� Start work on Lab 2.
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� Note that some numbering is repeatedfor a few of the equations in the labmanual section for Lab 2. Equationsreferenced in this presentation match thenumbering currently used.
Lab 2 Development Environment
� HP PC
� LabVIEW 2009 software
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Introduction
� Types of vehicle suspension systems
� Passive Suspension System.
� Active Suspension System.
� Semi-Active Suspension System.
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� Semi-Active Suspension System.
� SASS.
� Road disturbance
� Step Input.
� Harmonic Input.
Passive Suspension System
� Standard vehicle suspensionsystem.
� Employed in the majority ofcommercial vehicles.
� Advantages:
Vehicle body
zs
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� Advantages:� Low cost.
� Simple implementation.
� Disadvantages:� Purely passive elements.
� On-line performance optimizationnot possible.
bsks
kt
Tire
zu
zr
Active Suspension System
� Fully active system.� Computer controlled active
element (Fa).� Advantages:
� Offers excellent performance.Fa
Vehicle body
zs
zu
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� Offers excellent performance.� Allows for control and performance
optimization at any point duringlifetime.
� Disadvantages:� High cost.� Major safety issues.� High power demand.
kt
Tire
zu
zr
Semi-Active Suspension System
� Hybrid system (Passive + Active elements).
� Provides excellent fail safe mechanism.
Vehicle body
zs
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mechanism.
� Relatively low cost.
� Provides a performance comparable to the active system.
� Very low power demand.
bsks
kt
Tire
bsemi
zu
zr
Quarter-Car Suspension Model
bk
ms
zs
bk
ms
b
zs
Active element
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bsks
kt
mu
zu
zr
bsks
kt
mu
bsemi
zu
zr
Passive Suspension System Semi-Active Suspension System
Quarter-Car Suspension Model cont.
� The system can be modeled usingstate space representation:
� Passive:,rzLAXX && +=
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� Semi-Active:
� The two models are equivalent when the variable damper coefficient is set to 0.
,rzLAXX &+=
,rsemizLNXbAXX && ++=
State Space Model
� In the S.S. equation:
� ‘X’ – State vector.
,rsemizLNXbAXX && ++= eq. 2.11
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� ‘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.
State Space Model
=
−
−
=
=deflection Tire
mass sprung ofVelocity
deflection Suspension
3
2
1
ru
s
us
zz
z
zz
x
x
x
X&
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−
mass unsprung ofVelocity
deflection Tire
4
3
u
ru
z
zz
x
x
&
� - Derivative of the state vector over the sampling time.
� - Derivative of the road disturbance over the sampling time.
X&
rZ&
Road Disturbance
� Step Input:
� Isolated sudden disturbance.
� Ex. Curb with a height of 10 cm.
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Time (t)0
Road Input
Zr(t)
Zr = 0.1m
Road Disturbance cont.
� Harmonic Input:
� Simple road profile.
� Modeled as a Sine wave with:
� Freq. 1 Hz.
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� Freq. 1 Hz.
� Amp. 10 cm.
� Phase 0°.
Semi-Active Suspension Control Methods
� Skyhook Control.
� Ground-hook control.
� Optimal control based on LQR.
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� Fuzzy logic control:
� GA-based fuzzy control.
� Neural-Fuzzy control.
� Adaptive Fuzzy control.
Linear Quadratic Regulator (LQR)
� The controller works towardsminimizing the performance indexgiven in equation (2.13).
T
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� The controller determines therequired “ideal” active force (Fa) tostabilize the vehicle.
++++= ∫∞→
T
T
xxxxxEJ
0
2
44
2
33
2
22
2
11
2
2lim ρρρρ& eq. 2.13
Linear Quadratic Regulator (LQR) Cont.
� The active force (Fa) can be calculated usingEquation (2.14) in the lab manual.
XGFa
×−=eq. 2.14
)( 01
SPBRGT +×= −
� The representation of ‘G’ is shown in Equation(2.15).
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eq. 2.15
Semi-Active Control Law (LQR)
� The optimal controllaw is determinedusing Fig. 2.6.
� According to the
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� According to thecalculated optimalactive force (Fa), andthe absolute velocity ofthe two masses, thedamping coefficient(bsemi) is calculated.
Fig. 2.6.
Semi-Active Control Law (LQR) cont.
� The LQR control method is summarized intable 2.2.
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Lab 2 – Implementation steps
� Step 1: Read Chapter 2 of the labmanual (further information is givenin the appendix section).
� Step 2: Implement the quarter-car
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� Step 2: Implement the quarter-carpassive and semi-active suspensionmodels in LabVIEW.
� Step 3: Implement the two roaddisturbances (step and harmonic).
Lab 2 – Implementation steps
� Step 4: Implement the LQR controller forthe semi-active suspension system.
� Step 5: Perform the following analysis:1. Compare the performance of the passive and
semi-active suspension systems.
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semi-active suspension systems.
2. Vary the weight parameters of the LQRcontroller (ρi values in Eqn. 2.15) and observethe change in performance of the SASS.
3. Provide a measure to differentiate the differencein performance of the two systems (%difference?).
Requirements
1. Fully functional passive and semi-active suspension systems, with theability to switch between the twosystems in the same project.
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systems in the same project.
2. Simulations performed using the tworoad disturbances given in section2.2.2 of the lab manual.
� Step
� Harmonic
Requirements
3. The following performance graphsmust be present on the front panel:� Vehicle ride quality ( ).
� Suspension deflection response (X1).2X&
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� Suspension deflection response (X1).
� Tire deflection response (X3).
� Input disturbance to the system.
4. LQR control must be performed usinga separate Task (loop with a timingVI) from the plant system. Real-Time LabVIEW NOT required.
Notes – Matlab Script Nodes
� The matrices can be coded using theMatLAB script node in LabVIEW.
� Matrix definitions are done in thefollowing format:
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following format:� X= [xx xx xx;
xx xx xx;
xx xx xx];
� Note that variables can be used within the matrix definition.
Notes – Matlab Script Nodes
� Matrices can be multiplied and added aslong as the dimensions are consistent.
� To transpose a matrix add a ‘’’ after the
matrix variable.
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matrix variable.
� Element wise multiplications can beperformed using a ‘.*’.
� Matrix multiplication can be performed witha ‘*’.
� Dot products can be determined with the‘dot(X,Y)’ function.
Notes – Matrix
� Another method of implementing thematrices is through using the matrixvariables in LabVIEW.
� Matrix values must be calculated by
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� Matrix values must be calculated byhand and inputted in the matricesmanually.
� Allows for the use of LabVIEW VIs toperform operations.
� Values may also be entered as an arrayand converted to Matrix form.
Notes – Plant/Controller synchronization
� A requirement of thelab is to implement thecontroller in a separatetask than the plantsystem.
SASS Plant
Task 1
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system.
� Synchronizationbetween the twosystems can beaccomplished using:� Semaphores, or
� Occurrences.
synchronization
LQR Controller
Task 2
Notes - Structures
� Queues can be used to pass valuesbetween loops. Found in the “DataCommunication” palette.
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Notes - Structures
� Flat Sequences can be used to make sureoperations occur in order.
� Timing VIs can be found in a sub-palette of“Programming”.“Programming”.
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Notes - Structures
� MatLAB nodes can be found in the“Structures” sub-palette.
� Arrays and Matrixes found in the”Programming” palette.”Programming” palette.
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Demo
� Front Panel
� Performance Metrics
� Controls
� Passive Control� Passive Control
� Semi-Active Control
� Road Profile
� Task Communication
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Report
� Can use general structure similar to first lab.
� Implementation of model and controller.
� Communication/Synchronization betweentasks.
� Implementation challenges and solutions.
� Performance Metrics.
� Semi-Active vs. Active Control.
� Effect of road profile.
� Weighting Factors.
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Deadlines and Marking
� Lab 2 is worth 8%.
� 4% for the report, and 4% for the demo.
� The Demo is due Oct 12th/Oct. 15th, 2012 in theLab.
� The Report is due Oct 12th/Oct. 15th, 2012 in the
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� The Report is due Oct 12th/Oct. 15th, 2012 in theLab.
� Physical and Electronic copy.
� A signed group evaluation sheet must be submittedwith the lab report.
� Do NOT include student numbers with the labreport.