Abstract—The problem considered in this paper is the study
and the control strategy design of semi-active suspensions
featuring the regulation of both damping and stiffness. This
work presents an evaluation of the performances and
drawbacks achieved by such suspension architecture, also in a
non-linear setting (explicitly taking into account the stroke
limits of the suspension). This paper then proposes a new
comfort-oriented variable-damping-and-stiffness control
algorithm, named Stroke-Speed-Threshold-Stiffness-Control
(SSTSC), which overcomes the critical trade-off between the
choice of the stiffness coefficient and the end-stop hitting. The
use of a variable-damping-and-stiffness suspension, together
with this algorithm, provides a significant improvement of the
comfort performances, if compared with traditional passive
suspensions and with more classical variable-damping semi-
active suspensions.
I. INTRODUCTION
HE topic of this paper is control strategy design for a
controllable suspension with variable damping and
stiffness. While the modulation of the damping coefficient is
commonly used and can be easily obtained with different
technologies (see e.g. [4], [2], [5], [9], [15], [21], [20], [18],
[17], [13], and references cited therein), the control of the
spring stiffness is a much more subtle and elusive problem.
Load-leveling or active suspensions based on hydro-
pneumatic or pneumatic technologies are subject to spring-
stiffness variations, but this is more a side-effect than a real
control variable ([3], [5], [12]).
This work contains (to the best of our knowledge) the
following innovative contribution: a detailed analysis on the
advantages and trade-offs of a variable-damping-and-
stiffness suspension systems is developed. An innovative
control strategy suited to variable-damping-and-stiffness
This work has been partially supported by MIUR project “New methods
for Identification and Adaptive Control for Industrial Systems”.
C. Spelta and F. Previdi are with the Dipartimento di Ingegneria
dell’Informazione e Metodi Matematici, Università degli Studi di
Bergamo, viale Marconi 5, 24044 Dalmine (BG) ITALY (e-mail:
cristiano.spelta@unibg.it; fabio.previdi@unibg.it).
M. Cutini and C. Bisaglia are with CRA-ING, Laboratorio di Treviglio,
via Milano 43, 24043 Treviglio (BG) ITALY (e-mail:
maurizio.cutini@entecra.it; carlo.bisaglia@entecra.it).
S. M. Savaresi and P. Bolzern are with the Dipartimento di Elettronica e
Informazione, Politecnico di Milano, P.zza L. da Vinci 32, 20133 Milano
ITALY (e-mail: savaresi@elet.polimi.it; bolzern@elet.polimi.it; del
vecchio@elet.polimi.it).
suspensions is proposed. The algorithm presented herein is
named Stroke-Speed-Threshold-Stiffness-Control (SSTSC):
it based on the recently developed Mixed SH-ADD rationale
[17].
In this work the control objective is the minimization of
the vertical acceleration of the vehicle ([9], [21], and
reference cited therein).
II. SEMI-ACTIVE SUSPENSION MODELS WITH VARIABLE
STIFFNESS AND DAMPING.
This section is devoted to the introduction and comparison
of two quarter car models as reported in Fig.1 (see for details
e.g. [9], [21]). The first (IS model) describes an ideal
suspension system with variable damping and stiffness. The
other architecture (DSS model), based on semi-active
devices, can approximate the ideal system, and can be
implemented in practice: the architecture based on passive
devices was previously introduced in [11] and was
generalized to a semi-active framework in a recent
work([19]).
Fig.1 Quarter-car suspensions systems. From left to right: ideal suspension
with variable damping and stiffness (IS); double suspension system (DSS).
Quarter-car model of an Ideal Suspension (IS) with
variable stiffness and damping:
! !
(1)
A novel Control strategy for Semi-Active suspensions with variable
damping and stiffness
Cristiano Spelta, Fabio Previdi, Sergio M. Savaresi, Paolo Bolzern,
Maurizio Cutini, Carlo Bisaglia.
T
2010 American Control Conference
Marriott Waterfront, Baltimore, MD, USA
June 30-July 02, 2010
ThC19.3
978-1-4244-7425-7/10/$26.00 ©2010 AACC 4582