Teoria - Automation and Control in Vehicles

Automation and Control in Vehicles (ACV)

28/02/2013

Chapter 1: Suspension Control

(→ three main models)

Introduction (the problem):

the chassis of the car ⇒ single RIGID BODY (3 directions)

Suspensions directly influence three main movements:

• Heave (displacement)
• Roll (rotation)
• Pitch (rotation)

undirectly sometimes influence residual movements(yaw, sway, surge)

_{M: sprungg mass (body)}

_{c: damping coefficient of damper}

_{K: spring coefficient}

_{mw: unsprung wheel mass}

_{kt: tire stiffness (pavement)}

we have two mainly important signal:

• Z_r: road profile ^INPUT
• Z: chassis height ^OUTPUT

(the car is splited in four pieces, one for each wheel.)

The suspension is a low-pass-filter:

ideal comfort ^{→ perfectly flat (Z=0)}

real comfort ^{: Low-frequency component → passHigh-frequency component → stop}

Objectives:

1. COMFORT: small body acceleration

_ẍ must be minimized

Filter → I/O transfer function (road to body)

Abs. Amplitude frequency response of transfer function _Z/Zr ^{(low-pass filter with 2 resonances)}

body resonancewheel resonance

Automation and Control in Vehicles (ACV)

28/02/2013

Chapter 1: Suspension Control (-> three main models)

Introduction (the problem):

the chassis of the car -> single RIGID BODY (3 directions)

Suspensions directly influence three main movements:

• Heave (displacement)
• Roll (rotation)
• Pitch (rotation)

undirectly sometimes influence residual movements (yaw, sway, surge)

_{M•: sprung mass (body)}

_{c: damping coefficient of damper}

_{K: spring coefficient}

_{mu: unsprung wheel mass}

_{Kt: tire stiffness}

We have two mainly important signal:

• Z_r: road profile INPUT
• Z: chassis height OUTPUT

(the car is splitted in four pieces, one for each wheel.)

The suspension is a low-pass-filter:

ideal comfort -> perfectly flat (z=0)

real comfort: Low-frequency component -> pass

High-frequency component -> stop

Objectives:

1) COMFORT: small body acceleration

Ẑ must be minimized

Filter -> I/O transfer function (road to body)

Abs. Amplitude frequency response of transfer function

magnitude (dB)

ideal

low-pass filter with 2 resonances

• Is perfect disturbance cancellation possible? Almost possible.

• Main limitations?

• We have to enlarge the bandwidth with active suspensions that allow us to deal with higher cancellation reducing the delay of control feedback.
• Actuators capability: we must have quick electric motors with large forces that bring us in a lot of power consumptions.
• Available travel of suspensions comparable to the size of the disturbances.

(Exciting one)

2) HANDLING/PERFORMANCE/SAFETY: Small road variations

The force F is split on 3 directions

• F_x = F_z . μ_x
• F_y = F_z . μ_y

μ: friction coefficient depending on road conditions

In order to increase friction, F_z must be maximized

F_z = M_g + DynamicLoad + AerodynamicLoad

Suspensions can react on this dynamical part

• Normal Load
• Weight

F_z negative part is very bad ⇒ F = ϕ means loss of contact (we don’t have F_x, F_y anymore)

I want to stay near the nominal part ⇒ SMALL ROAD VARIATION (PERFECTLY FOLLOW THE OBSTACLE)

3) STROKE LIMITATION

In order to avoid destruction of performance 1-2

Stroke limitation depends on every situation (5÷50 cm)

End-stop bushes: made of rubber to avoid contact between steel-steel

The suspension main elements:

damping regulation (compression) preload regulation damping regulation (rebound)

the spring is a dissipative element related to ΔL (stroke) and K (stiffness coefficient)

the damper is an other dissipative element related to ΔL (speed) and c (damping coefficient)

It's a very complex mechanical architecture with complex Kinematic

Our model :

Fd = - c · speed Fs = - k · stroke

Damper:

rod seal rod (shaft) special oil upper chamber piston orifices dividing piston gas-spring

Damping regulations are capable in modifying the orifices dimension.

In our case we deal with