Lab 2: Real-Time Automotive Suspension system Simulator 2 Presentation.pdf · Real Time System Design Lab 2: Real-Time Automotive Suspension system Simulator TA: ... Semi-Active Suspension

Aws Abu-Khudhair ENGG*4420 1

ENGG*4420

Real Time System Design

Lab 2: Real-Time Automotive Suspension system Simulator

TA: Aws Abu-Khudhair([email protected])

Due: Week of Oct. 12th


Today’s Activities

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


Lab 1 Development Environment

HP PCLabVIEW 2009 software


Introduction

Types of vehicle suspension systemsPassive Suspension System.Active Suspension System.Semi-Active Suspension System.

Road disturbanceStep InputHarmonic Input


Passive Suspension SystemStandard vehicle suspension systemEmployed in the majority of commercial vehiclesAdvantages:

Low cost.Simple implementation.

Disadvantages:Purely passive elements.On-line performance optimization not possible

bsks

kt

Tire

Vehicle body

zs

zu

zr


Active Suspension SystemFully active system.Computer controlled active element (Fa).Advantages:

Offers excellent performance.Allows for control and performance optimization at any point during lifetime.

Disadvantages:High cost.Major safety issues.High power demand.

Fa

kt

Tire

Vehicle body

zs

zu

zr


Semi-Active Suspension System

Hybrid system (Passive + Active)Provides excellent fail safe mechanism.Relatively low cost.Provides a performance comparable to the active system.Very low power demand.

bsks

kt

Tire

Vehicle body

bsemizu

zs

zr


Quarter-Car Suspension Model

bsks

kt

mu

ms

zs

zu

zr

bsks

kt

mu

ms

bsemizu

zs

zr

Active element

Passive Suspension System Semi-Active Suspension System


Quarter-Car Suspension Model cont.

The system can be modeled using state space representation:Passive:

Semi-Active:

The two models are equivalent when the variable damper coefficient is set to 0

,rzLAXX && +=

,rsemi zLNXbAXX && ++=


State Space Model

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

,rsemi zLNXbAXX && ++= eq. 2.11


State Space Model

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−

−

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

mass unsprung ofVelocity deflection Tire

mass sprung ofVelocity deflection Suspension

4

3

2

1

u

ru

s

us

zzz

zzz

xxxx

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.

Time (t)0

Road InputZr(t)

Zr = 0.1m


Road Disturbance cont.

Harmonic Input:Simple road profile.Modeled as a Sine wave with:

Freq. 1 Hz.Amp. 10 cm.Phase 0°.


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.


Linear Quadratic Regulator (LQR)

The controller works towards minimizing the performance index given in equation (2.13).

The controller determines the required “ideal” active force (Fa) to stabilize the vehicle.

⎥⎦

⎤⎢⎣

⎡++++= ∫∞→

T

TxxxxxEJ

0

244

233

222

211

22lim ρρρρ& eq. 2.13


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.


Semi-Active Control Law (LQR) cont.

The LQR control method is summarized in table 2.2.


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).


Lab 2 – Implementation stepsStep 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?)


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.


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.


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.


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 ‘*’.


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.


Note – Plant/Controller synchronization

A requirement of the lab is to implement the controller in a separate task than the plant system.Synchronization between the two systems can be accomplished using:

Semaphore, orOccurrences.

synchronization

SASS Plant

LQR Controller

Task 1

Task 2


Deadlines and Marking

Lab 2 is worth 8%.4% for the report, and 4% for the demoThe 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?

Documents

Lab 2: Real-Time Automotive Suspension system Simulator 2 Presentation.pdf · Real Time System Design Lab 2: Real-Time Automotive Suspension system Simulator TA: ... Semi-Active Suspension