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Real Time System Design

Lab 2: Real-Time Automotive

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Lab 2: Real-Time Automotive Suspension system Simulator

TA: Matthew Mayhew(mmayhew@uoguelph.ca)

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.