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)

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

_{M: sprung mass (body)}

_{c: damping coefficient of damper}

_{K: spring coefficient}

_{mw: unsprung wheel mass}

_{kt: tire stiffness (pavement)}

We have two mainly important signals:

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

(The car is split 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

_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 resonance

Wheel 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)

Indirectly 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 signals:

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

(The car is split 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 another 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