28-11-2012, 03:10 PM
Semi-Active Suspension System Simulation Using SIMULINK
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Abstract
This paper describes a simulation design procedure aimed to achieve improved performance
of the vehicle semi-active suspension. The issues related to the design of vehicle models with
skyhook control are discussed. Three basic models with linear parameters are explained: quarter-,
half- and full-car. The road profile is generated from a spatial power spectral density (PSD) to
represent a typical road (based on ISO 8608 classification). The normalized root-mean-square
values of sprung mass acceleration and tyre load forces are used to assess the vehicle ride comfort
and handling performance based on five benchmark road profiles employed in industrial tests.
Introduction
Demands for better ride comfort, road handling and controllability of passenger cars have
motivated automotive industries to use active and semi-active suspensions in middle-top range
vehicles due to their effectiveness in order to increase the car comfort and stability.
Suppression of vibration in passive suspensions depends on the spring stiffness, damping
coefficient, and car mass. Due to the fact that they cannot satisfy the comfort requirement under
different road conditions, significant interest is being devoted to the control of active and semiactive
suspension in both academia and industry.
Many analytical and experimental studies on active and semi-active suspensions have been
performed to improve ride quality and handling performance. The results of studies show that active
and semi-active suspensions can provide substantial performance improvements over passive
suspensions in general (Williams, 1997).
The design of controlled suspension systems for road vehicles aims to optimize the
performance of the vehicle with regard to comfort and road handling. Vehicle suspensions should
serve several conflicting purposes. In addition to counteracting the body forces resulting from
cornering, acceleration or braking and changes in payload, suspensions must isolate the passenger
compartment from road irregularities. For driving safety, a permanent contact between the tyres and
the road should be assured. Passive suspension systems built of springs and dampers have serious
limitations. Their parameters have to be chosen to achieve a certain level of compromise between
road holding, load carrying and comfort, under wide variety of road conditions.
Vehicle models
There exist many possibilities arraying for describing the car suspension behaviour (quartercar
model, half-car model and full-car model). There is an extensive amount of literature relating to
these models (Croizet and Gatignol, 2002). The full-car model is presented in the following section.
The full-vehicle suspension system is represented as a linear seven degree-of-freedom
(DOF) system. It consists of a single sprung mass (car body) connected to four unsprung masses
(front-left, front-right, rear-left and rear-right wheels) at each corner. The sprung mass is free to
bounce, pitch and roll while the unsprung masses are free only to bounce vertically with respect to
the sprung mass. All other motions are neglected for this model. Hence this system has seven
degrees of freedom and allows simulation of tyre load forces in all four tyres, body acceleration and
vertical body displacement as well as roll and pitch motion of the car body. The suspensions
between the sprung mass and unsprung masses are modelled as linear viscous dampers and linear
spring elements, while the tyres are modelled as simple linear springs without damping. For
simplicity, all pitch and roll angles are assumed to be small.
Road profiles
As with any random signal, the elevation profile measured over a length of road can be
decomposed by a Fourier transformation into a series of sine waves varying in their amplitudes and
phase relationships. A plot of the amplitudes against spatial frequency can be represented as PSD.
Spatial frequency is expressed as the wave-number with units of cycles/meter and is the inverse of
the wavelength of the sine wave on which it is based. From experimental measurements of the road
profile a law h(x) can be defined and its power spectral density can be obtained through harmonic
analysis. Note that the profile is a function of space and not of time and the frequency referred to
space λ is expressed in rad/m or cycles/m and not in rad/s or Hz. The power spectral density S of
law h(x) is thus expressed in m2/(rad/m) or in m2/(cycles/m).
A real road surface is taken as a random exciting function, which is used as input to the
vehicle road model. It is noted that the main characteristic of a random function is uncertainty. That
is, there is no method to predict an exact value at a future time. The function should be described in
terms of probability statements as statistical averages, rather than explicit equations. In road models,
power spectral density has been used to describe the basic properties of random data.
Skyhook control
One of the most popular and implemented controllers for the semi-active suspensions in
commercial applications is the skyhook damping concept. In the skyhook damping process a
damper is placed between the sprung mass and an imaginary point in the sky. This is equivalent to
the negative feedback of the sprung mass velocity with appropriate amplification such that there is
no force applied to the unsprung mass (the wheel and tyre assembly). Such a scheme is shown to be
very effective in controlling the sprung mass acceleration and is attractive because of its inherent
simplicity from a practical point of view.
The key issue with the skyhook approach is that it is not practically implementable, because
finding an imaginary point in the sky for fixing the damper is not possible. The practical
implementation calls for the use of an actuator between the sprung and the unsprung masses, see
Figure 2. However, this leads to deterioration of the unsprung mass dynamic performance as the
controller force input has to be applied on both the sprung as well as the unsprung masses. Thus the
dynamic response of the practical skyhook damping system is considerably worse than that of the
ideal skyhook-based suspension system.
On-off skyhook control
The philosophy of the on-off skyhook control method is to emulate the effect of a passive
damper “hooked” between the body mass and the “sky”, as shown in Figure 3. In this two-state
skyhook control, the damper is adjusted to a maximum or minimum damping. These are referred to
as high-state and low state damping, respectively. The determination of whether the damper is to be
adjusted to either its high state or its low state depends on the product of the relative speed of the
suspension damper and the absolute speed of the sprung mass attached to that damper.
Handling performance evaluation
The handling characteristics of an automobile are concentrated on the characteristics of the
tyres. Tyres are the vehicle's reaction point with the roadway. They manage the input of forces and
disturbances from the road, and they are the final link in the driver's chain of output commands.
Tyre characteristics are therefore a key factor in the effect the road has on the vehicle, and in the
effectiveness of the output forces that control vehicle stability and cornering characteristics. The
tyre's basic characteristics are managed by the system of springs, dampers, and linkages that control
the way in which tyres move and react to disturbances and control inputs.
Tyres play a significant part in vehicle handling characteristics. Low profile sidewalls
improve steering response but also stiffen the ride, so for optimum handling, the tyres, springs and
shock absorbers must all work together as a package.
Conclusion
The research presented in this paper is directed to the simulation and design of a semi-active
suspension. Although based on the well-known physical models for investigating the vertical
dynamics of suspension systems (Hrovat, 1997; Kruczek and Stribrsky, 2004), it is expanded with
an extensive set of simulations based on SIMULINK modelling and benchmark road profiles
employed in real industrial tests (such as sine wave hole test, short back, drain well, etc.). More
accurate analysis is achieved by extension to a full-car model, which is subjected to the benchmark
tests. The skyhook control strategy is evaluated by means of multiple criteria, i.e., the comfort and
handling are defined by equations (9) and (10), respectively, for all the classes of road profiles.
Moreover, additional comfort criteria are evaluated for some of the profiles.
For example, in regards to the bounce results obtained in the simulations, skyhook control
shows good improvements over passive system performance for the random profile and sine wave
hole test. The use of this kind of road profile allows a deeper analysis on how the skyhook
controller works in order to achieve such performance enhancements.