Lab 2: Real-Time Automotive Suspension system Simulator TA: Aws - - PowerPoint PPT Presentation

Aws Abu-Khudhair ENGG* 4420 1

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

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Today’s Activities

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

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Lab 1 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.

Road disturbance

Step Input Harmonic Input

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Passive Suspension System

Standard vehicle suspension system Employed in the majority of commercial vehicles Advantages:

• Low cost.
• Simple implementation.

Disadvantages:

• Purely passive elements.
• On-line performance optimization

not possible

bs ks kt Tire Vehicle body zs zu zr

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Active Suspension System

Fully active system. Computer controlled active element (Fa). Advantages:

• Offers excellent performance.
• Allows for control and performance
• ptimization at any point during

lifetime.

Disadvantages:

• High cost.
• Major safety issues.
• High power demand.

Fa kt Tire Vehicle body zs zu zr

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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.

bs ks kt Tire Vehicle body bsemi zu zs zr

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Quarter-Car Suspension Model

bs ks kt mu ms zs zu zr bs ks kt mu ms bsemi zu zs zr Active element Passive Suspension System Semi-Active Suspension System

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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

,

r

z L AX X & & + = ,

r semi

z L NXb AX X & & + + =

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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

,

r semi

z L NXb AX X & & + + =

• eq. 2.11

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State Space Model

⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − − = ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = mass unsprung

• f

Velocity deflection Tire mass sprung

• f

Velocity deflection Suspension

4 3 2 1 u r u s u s

z z z z z z x x x x X & &

• Derivative of the state vector over the

sampling time.

• Derivative of the road disturbance over

the sampling time.

X &

r

Z &

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Road Disturbance

Step Input:

Isolated sudden disturbance.

• Ex. Curb with a height of 10 cm.

Time (t) Road Input Zr(t) Zr = 0.1m

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Road Disturbance cont.

Harmonic Input:

Simple road profile. Modeled as a Sine wave with:

• Freq. 1 Hz.
• Amp. 10 cm.

Phase 0°.

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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.

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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 T

x x x x x E J

2 4 4 2 3 3 2 2 2 2 1 1 2 2

lim ρ ρ ρ ρ &

• eq. 2.13

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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.

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Semi-Active Control Law (LQR) cont.

The LQR control method is summarized in table 2.2.

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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).

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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?)

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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.

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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.

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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.

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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 ‘* ’.

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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.

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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, or
• Occurrences.

synchronization SASS Plant LQR Controller Task 1 Task 2

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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, 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?