Mixed Sky-Hook and ADD: Approaching the Filtering Limits of a Semi-Active Suspension

[+] Author and Article Information
Sergio M. Savaresi1

Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza L. da Vinci, 32, 20133, Milano, Italy

Cristiano Spelta

Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza L. da Vinci, 32, 20133, Milano, Italy


Corresponding author.

J. Dyn. Sys., Meas., Control 129(4), 382-392 (Nov 20, 2006) (11 pages) doi:10.1115/1.2745846 History: Received June 01, 2005; Revised November 20, 2006

The problem considered in this paper is the design and analysis of control strategies for semiactive suspensions in road vehicles. The most commonly used control algorithm is the well-known sky-hook (SH) damping. Recently, a new control approach named acceleration driven damping (ADD) has been developed, using optimal-control theory. It has been shown that SH and ADD have complementary characteristics: SH provides large benefits around the body resonance; otherwise performs similarly to a passive suspension; instead, ADD provides large benefits beyond the body resonance. The first goal of this paper is to show that—in their specific frequency domains—SH and ADD provide quasi-optimal performances, namely, that it is impossible to achieve (with the same semi-active shock-absorber) better performances. This result has been obtained using the framework of the optimal predictive control, assuming full knowledge of the disturbance. This result is very interesting since it provides a lower-bound to semi-active suspension performances. The second goal of the paper is to develop a control algorithm which is able to mix the SH and ADD performances. This algorithm is surprisingly simple and provides quasi-optimal performances.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

ADD and SH performance

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Figure 2

Response of an electrohydraulic semi-active suspension to a switching command on the damping ratio

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Figure 3

ADD and SH performance, for two different switching-times of the shock-absorber

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Figure 4

Measured acceleration and velocities (real data, taken from a motorbike negotiating a standard road surface)

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Figure 5

Comparison of the filtering performance of SH, ADD, and the numerically-computed optimal lower bound

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Figure 6

Comparison of the filtering performance of SH, ADD, and mixed SH-ADD

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Figure 7

Pictorial analysis of the inequality 8; (b) function ∣D+(ω)∣∕T (in the normalized frequency)

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Figure 8

Example of evolution of the autonomous systems z̈(t)=αż(t) and z̈(t)=−αż(t) (starting from ż(0)>0)

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Figure 9

Time responses of SH, ADD, and Mixed-SH-ADD to two pure-tone road disturbances (at 1.25Hz and at 4Hz)

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Figure 10

Acceleration responses to a step on the road profile

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Figure 11

Performance of the three control algorithms, when the road profile is a broad-band signal

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Figure 12

Estimated frequency responses from road-disturbance to contact-force variations

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Figure 13

Comparison of the filtering performance of SH, ADD, and mixed SH-ADD, for a half-car model

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Figure 14

Estimated frequency responses from road-disturbance to body acceleration, using a detailed damper model



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