2020 European Control Conference (ECC)

May 12-15, 2020. Saint Petersburg, Russia

Optimization Based Sliding Mode Control in Active Suspensions:

Design and Hardware-in-the-Loop Assessment
Debora Quaini1 , Kamil Sazgetdinov2 , Valentin Ivanov2 , Antonella Ferrara1

Abstract— The paper presents an optimization based slid- actuator, the force needed to improve the suspension work.
ing mode controller designed to provide the correct amount Clearly the construction cost of the suspension is higher,
of force to the actuator of an active suspension system in but this is amply repaid by the benefit of providing better
order to guarantee ride comfort. First, the description of
the mechanics of the active suspension system is provided. vehicle comfort in a wider range of road conditions and
Then, the mathematical state space form of the quarter-car driving scenarios.
active suspension model is introduced. A Sliding Mode Control
controller is designed to properly manage the active force pro- The suspension performance is assessed in simulation
duction. The parameters of the proposed controller are tuned, and experimentally considering indexes which take into
relying on an optimization procedure, so as to improve the account many factors such as ride comfort, suspension de-
quality of the ride, in particular in terms of ride comfort, road
flection and road holding. The control strategy has to provide
holding and suspension deflection. First, the performance of
the controlled active suspension are assessed in simulation using balanced results with respect to each indicator. The conven-
the formulated quarter-car mode. Then, the proposed optimized tional solution, as for other automotive control subsystems,
sliding mode controller is tested on an experimentally validated is the PID controller which has been implemented by many
full-car model of a Range Rover Evoque in a Hardware-in-the- researchers to control suspension systems both of semi-active
Loop (HiL) test rig available at the Automotive Engineering
[4] and active type [5]. The PID controller offers a simple and
Department of TU Ilmenau, also comparing its performance
with those obtained by using a standard PID controller. The efficient way to control the displacement of the suspension,
HiL test rig is equipped with an active electromechanical but does not provide any guarantee in terms of robustness
suspension system. Simulation and HiL test results confirm that versus uncertainty terms and disturbances.
the proposed SMC controller provides better ride quality than
the standard PID controller, which corroborates its suitableness In the present paper, a sliding mode control (SMC)
for practical implementation. based strategy is proposed for active suspensions which
aims to improve the ride comfort during the vehicle motion,
I. INTRODUCTION achieving a smooth displacement dynamics of the suspen-
sion. A SMC can be designed even if a perfect knowledge
Active suspension systems are increasingly widespread of the system model is not available by virtue of its invari-
in modern cars, also in view of the present tendency to make ance property versus matched uncertainty. This makes the
vehicles increasingly automated and autonomous. In a not methodology particularly suitable to deal with applications,
too futuristic perspective of vast penetration of autonomous like the automotive ones, in which the availability of accurate
vehicles [1], safety will in fact be the first requisite, but models rarely occurs [6]. The SMC requires the design of
comfort and the quality of the travel experience will follow the so-called sliding surface to which the controlled system
immediately after. Comfort and handling are also fundamen- state has to be steered and confined in a finite time. The
tal aspects at the basis of agile and sporty driving [2], which sliding surface choice significantly influences the controlled
is increasingly in demand in mid-high range cars. system performance, thus being one of the key aspect of the
design phase. SMC has been intensively used in automotive
By efficiently controlling the active suspension systems systems control for more than two decades (see, for instance,
in a car, it is possible to reduce the impact of the road on the [7], [8], [9], [10] and the references therein cited).
vehicle and its passengers, improving driving safety and ride
comfort in any terrain conditions [3]. This clearly requires to In the context of suspensions control, SMC has been
adopt robust control solutions, so as to be able to guarantee implemented in different settings, including the High Order
suspension performance which are invariant with respect to SMC [11], the Fuzzy SMC [12] and other design variants
the several sources of uncertainty that affect the modelling [13], on various kind of suspensions. Yet, the solution
phase. presented in this paper differs from the previously available
solutions. It concerns the design and implementation of an
An active suspension system is characterized by the Optimal Sliding Mode Control (OSMC) in which, relying
supply of energy in order to generate, via a dedicated on a quarter-car electromechanical active suspension model,
1 Dip. di Ing. Industriale e dell’Informazione, University of Pavia, via
the more efficient tuning of the parameters involved in the
Ferrata 5, 27100 Pavia, Italy design of the SMC strategy is achieved, further enhancing
2 Automotive Engineering Group, Technische Universität Ilmenau, Ehren- the robustness features naturally provided by SMC. The
bergstr. 15, 98693 Ilmenau, Germany

978-3-907144-02-2©2020 EUCA 1607

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 Fig. 2. Active suspension model in MATLAB Simulink environment

itself, modelled as a spring; bs represents the damper; Kt is

the vertical stiffness of the tyre; Fa is the active force from
Fig. 1. Active suspension system in quarter-car model the actuator; Zs , Zu and Zr are the vertical displacements
from static equilibrium of the sprung mass, unsprung mass
and the road respectively. The output depends on Zs , Zu ,
performances of the proposed optimized sliding mode con- which can be measured by sensors placed inside the quarter-
troller, as well as of the PID one, are assessed first in high car suspension system, and on their derivatives. From the
fidelity simulations based on the joint use of Simulink and differential equations, the state space model can be derived.
IPG CarMaker. Then, they are assessed experimentally by (
using a Hardware-in-the-Loop (HiL) test rig available at Ẋ = AX + BU + KW
(3)
the Automotive Engineering Department of TU Ilmenau. Y = CX + DU
Simulation and HiL test results confirm that the proposed
where the vector X is
SMC controller provides better ride quality than the standard  
 
PID controller, thus opening the door to further experimental x1 zu
verification activity on real vehicles in proving grounds.  x2   zs 
 x3  =  z˙u
X=   
 (4)
The present paper is organized as follows. In Section II, x4 z˙s
the adopted mathematical model and the formulation of the
control problem are introduced. In Section III, the proposed and the matrices A, B, C, D, K, W and U are
solution is described with some details. In Section IV the 0 0 1 0
 
case study is presented, together with simulation and HiL  0 0 0 1 
test results. Some conclusions are finally reported in Section A=  −(Kt +Ks ) Ks −bs bs 

Mu Mu Mu Mu
V. Ks −Ks bs −bs
Ms Ms Ms Ms
  
II. PROBLEM FORMULATION 0 1 0 0 0
 0   0 1 0 0 
B= −1  , C = 
   (5)
A. Description of the adopted mathematical model
 M
u
0 0 1 0 
1 Ks −Ks bs −bs
Ms Ms Ms Ms Ms
The suspension is a vibration control system that con- 0

 
0

trols the vertical movement of the wheels respect to the  0   0 
chassis of the vehicle. Different kinds of suspensions can  0  , K =  Ku 
D=   
Mu
be chosen, but in this study the electromechanical active 1
Ms 0
suspension is considered. The external actuator of the active
suspension acts to maintain the sprung mass stable while the W = [ Zr ] , U = [ F a ]
tyre follows the behaviour of the road.

From the scheme, two differential equations that de- B. Problem statement
scribe the system are formulated:
  The quarter-car model is chosen to represent the active
Mu Z̈ u + bs Ż u − Ż s + Kt (Zu − Zr ) + suspension, because it can capture the important charac-
(1)
+Ks (Zu − Zs ) + Fa = 0, teristics of the system. From the quarter-car model, the
  differential equations are derived.
Ms Z̈ s + bs Ż s − Ż u + Ks (Zs − Zu ) − Fa = 0, (2)
In the active suspension model, Fa 6= 0 and its value has
where Ms and Mu are the sprung and the unsprung mass to be correctly calculated and balanced in order to emulate
of the quarter-car respectively; Ks represents the suspension the dynamics of the suspension system, modelled as a spring.

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The model of the road behaviour is discussed in section on the control input. The presence of an exponential term in
IV. To properly establish the necessary value of Fa , two εe allows to reduce the chattering phenomenon of a certain
types of controllers have been implemented: PID and SMC level, while mantaining high speed of the reaching phase.
controllers. According to Eq. (6), a new equation (9) can be found:

III. T HE PROPOSED SOLUTION ˙ = CT Ẋ = CT (AX + BU + KW )

S (X) (9)

Sliding mode control is a well-established method for ˙ (Eq.

By unifying the two equations that define S(X)
designing control laws for systems with disturbances and un- (8) and (9)) the control law U is formulated and shown in
certainties [14]. In conventional SMC the controller synthesis Eq. (10):
is based on the choice of a suitable sliding manifold, i.e. a U = (−CT B)
−1
[CT AX + CT KW +
subspace of the system state space where the controlled sys- (10)
+εe sgn (S (X)) + ke S (X)]
tem state is forced to slide, after a transient called “reaching
phase”, and where the controlled system exhibits the desired In the following subsection, in order to improve the
dynamic properties, the latter depending on the choice made quality of the ride, a procedure to optimize parameters (c1 ,
of the sliding manifold. In this paper, the proposed SMC c2 , c3 , c4 , εe and ke ) of the SMC controller will be described.
controller design differs from the standard one. It is divided
in three steps: the design of the sliding surface to which
the control needs to lead, the formulation of the control law 3) Optimization of the SMC controller parameters:
and the final optimization of the switching function through Considering the indexes to be analysed to improve the
Genetic Algorithm. quality of the ride (ride comfort, road holding and suspension
deflection), it is possible to build a cost function which
1) Design of the sliding surface: Considering the enables, in principle, to find the optimal parameters of the
continuous-time system in regular form given by (3), a SMC controller. Usually, the evaluation of the suspension
switching function S (X) is defined. performance is subject to the evaluation of the passengers’
maximum absolute vertical acceleration Z̈ s (it relates to the
S (X) = CT X = c1 x1 + c2 x2 + c3 x3 + c4 x4 , (6) comfort of the drive), of the wheel hop Zu − Zr (it relates
to the vehicle stability on the road and displacement), and of
Zs − Zu (it relates to the suspension rattle space). In order
where X is the state vector of Eq. (4) and CT =
to balance these three performance indicators, a quadratic
[c1 c2 c3 c4 ] is the switching matrix. As stated by
objective function expression is taken in the following form
the design criteria of the sliding surface, the polynomial
c4 p3 + c3 p2 + c2 p1 + c1 is supposed to satisfy the Routh-
Hurwitz stability criterion. The conditions that must be Z T
satisfied for the stability of the given system are shown in 1 2 2 2
J= [Z̈ s + δ1 (Zu − Zr ) + δ2 (Zs − Zu ) ]dt,
Eq. (7). T 0

c1 > 0 (11)
c4 c1
c2 >
c3 (7) where T represents the total travel time of the ride
c3 > 0 and δ1 , δ2 denote the weight coefficients of the wheel hop
c4 > 0 and the displacement in the suspension system, respectively.
A penalty function method will be used to transform the
constrained optimization problem into an unconstrained one
2) Formulation of the control law: In order to improve
by penalizing the objective function corresponding to the
the dynamic quality and alleviate the chattering phenomenon
infeasible solution. The penalty function is the inverse of
of the SMC caused by its switching behaviour, the exponen-
the fitness function, i.e.
tial reaching law is applied, which is shown in Eq. (8):
˙ = −εe sgn (S (X)) − ke S (X) F (x) = min J + M min g 2 (x) , 0
   
S(X) (8) , M = 10000
(12)
The coefficient εe determines the speed of reaching
the switching surfase, εe > 0, while ke is the coefficient where g (x) = c3 c2 − c4 c1 . Eq. (12) is built according
that determines the speed before reaching the switching to what previously established about the cost function and
surface, ke > 0. Eq. (8) contains the discontinuous term considering the constraints of the system indicated in (7).
−sgn (S (X)) which may lead to the phenomenon of chat- Among different techniques, one of the most efficient meth-
tering: by increasing εe , the reaching time will be faster and ods was optimization based on the Genetic Algorithm (GA),
robustness is provided as well as higher levels of chattering successfully implemented in the overall control systems by

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several researchers [15], [16]. Smaller values of the objective
function (11) will approve the better performance of the
optimization algorithm. To access the performance according
to the classical genetic algorithm approach, however we
−1
will use fitness function F (x) , with the bigger values
denoting the enhanced controller results. We perform genetic
optimization algorithm with MATLAB Optimization Toolbox
to obtain the optimal parameters for our sliding surface of
OSMC.
IV. T HE CASE STUDY

A. Simulation tests with the quarter-car model and the Fig. 3. Road roughness input signal graph (C-class road, ISO 8608)
experimentally validated full-car model

To test the designed controllers and check the be- processing line analysing Car.tz, Car.Roll and Car.Pitch from
haviour of the active suspension system under the applied the CarMaker, which are the position of the CoG of the
force Fa , the quarter-car model was implemented in MAT- vehicle (in the vehicle’s Z-axle direction), the roll angle of
LAB/Simulink. In order to assess the performance of the de- the vehicle and the pitch angle of the vehicle, respectively.
veloped controllers for the individual chassis corner control The designed controllers are implemented in the full-car
of the active suspension system, the experimentally validated model provided by IPG CarMaker and the results are shown
full-car model of the Range Rover Evoque (Fig. 7) from the in Section IV-B.
Automotive Engineering Department of TU Ilmenau is used.
The standard co-simulation interface of the IPG CarMaker 2) Road roughness signal model: The final Simulink
and Matlab is used during the controllers tests. scheme is shown in Fig. 2, where the Road Excitation (Zr )
is modelled with a white noise input signal. The road signal
1) Parameters of the car models: The quarter-car model is created according to the ISO standard 8608 (1995),
model is implemented in Simulink using the the experimen- with which it is possible to choose a certain degree of
tally validated parameters shown in Table I. road roughness considering the vehicle velocity. The model
presented in this study uses the ISO 8608 average degree of
TABLE I roughness and the vehicle velocity equal to 20 m/s. In Fig.
PARAMETERS FOR THE SUSPENSION MODEL 3, the graphical behaviour of the road input is presented.

PARAMETER VALUE DIMENSION 3) SMC tuning parameters: The tuning process of the
Sprung mass (Ms ) 450 Kg SMC controller allows to find the optimal values of c1 , c2 ,
Unsprung mass (Mu ) 30 Kg c3 , c4 , εe and ke , respecting the constraints indicated in (7).
Ks 20000 N/m
Kt 225400 N/m The obtained values are
bs 1000 N.s/m
bt 50 N.s/m
Maximum Fa 3700 N c1 = 1 · 10−4 , c2 = 45,
Bump height (Zr ) 40 mm
c3 = 1 · 10−3 , c4 = 450, (13)
−2
εe = 35, ke = 1 · 10 .
Note that the full-car model of the Range Rover Evoque
is built using the MSC Adams software [17]. To compare 4) Comparison with a standard PID controller: To
the controllers’ performances, the default chassis parameters assess the performance of the proposed SMC solution a
were properly modified as shown in Table II. comparison was made with a standard PID controller, tuned
taking into account the full-car model of the Range Rover
TABLE II Evoque. In particular, once established the parameters of
PARAMETERS ( ON FRONT AND REAR AXLES ) FOR THE FULL - CAR MODEL the car model with consideration of the upper saturation
limits (3700 N for the front axle), the following three gain
PARAMETER VALUE DIMENSION parameters were obtained for the PID controller
Suspension stiffness 2000 N/m
Damping coefficient 1000 Ns/m
Amplification ratios for the stabilizer 0 KP = 40859, KI = 5771, KD = 39838. (14)

The controllers read the signals coming from the IPG The tuning process of the developed PID controller was
CarMaker during the testing simulation using the Read completed through the application of the Ziegler-Nichols
CarMaker Dictionary Variable block in Simulink. The main tuning method and the final Trial and Error method to refine
signals used by controllers go through the acquisition and the gain values.

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 The value N is the number of samples of asi . The stan-
dard ISO 2631 shows that if the vibration level RMS (m/s2 )
is lower then 0.315, the road comfort can be defined as not
uncomfortable. For the road comfort criteria assessment, an
embedded code was written in MATLAB using a number of
blocks in Simulink to get the data from the simulation model
and calculate our evaluation parameter J. The values of ride
comfort criteria based on RMS values of vehicle sprung mass
acceleration are presented in the Table III.

TABLE III
Fig. 4. Controllers benchmarking on displacement (Zs ) (Passive, PID,
OSMC) RMS VALUES IN m/s2 OF THE VERTICAL ACCELERATION OF THE VEHICLE ’ S
SPRUNG MASS AND IMPROVEMENTS IN % FROM PASSIVE SUSPENSION

Type of road Type of suspension system

input Passive PID control OSMC control
Road input
(ISO 8608
0.297 0.170 42.76% 0.084 71.8%
C-Class
Road)

The RMS values and the relative percentages show us

the presence of major improvements from passive suspension
Fig. 5. Controllers benchmarking on active force (Fa ) produced by the
results in the road driving comfort level.
actuator (Passive, PID, OSMC)
2) HiL test results on the full-car model: The tests on
the controlled full-car model were done within the Hardware-
B. Simulations and HiL test results in-the-Loop testing procedures of TU Ilmenau, using the
dSpace Control desk facilities and TU Ilmenau test rig
One of the main criteria for the comfort evaluation of for the systems HiL testing. According to the International
the designed controller structure is to perform the so-called Standard for the vehicle handling dynamics testing procedure
real road-testing simulation. The controller response to the (ISO 3888-2:1998), the Double-Lane Change test is designed
step and sine input are less important in terms of the real- and used for the developed controllers. They are integrated
driving scenarios. Therefore, to evaluate the designed PID through the co-simulation procedure into the 15 DoF full-
and SMC controllers effectiveness, the MATLAB/Simulink sport utility vehicle model with the experimentally identified
simulation results obtained with the road input signal spec- Range Rover Evoque chassis parameters. The designed con-
ified by the International standard, ISO 8608 C-Class road trollers (PID and OSMC) are implemented with the same
are hereafter reported. control parameters for both quarter-car and full-car models.
The Hil test rig is equipped with an active electromechanical
1) Simulation result on the quarter-car model: Fig. 4 suspension system.
shows the behaviour of the displacement Zs of the sus-
pension when no control, PID and SMC are applied. The TABLE IV
comparison includes the Skyhook algorithm performance, RMS VALUES OF THE OF THE VEHICLE ’ S BODY ROLL ANGLE AND ROLL VELOCITY
which is not explained in this study. References to the DURING THE D OUBLE - LANE - CHANGE TEST WITH ADAPTED R ANGE ROVER
implementation of the Skyhook controller can be found in E VOQUE MODEL AND IMPROVEMENTS IN % FROM PASSIVE SUSPENSION
Ref. [18]. In order to estimate the comfort, according to
the ISO 2631-1 the vertical motion (Zs ) and acceleration Double-lane Type of suspension system
test Passive PID control OSMC control
(Z̈ s ) of the chassis have to be studied. The vertical motion Roll angle
0.0228 0.0069 69.7% 0.0045 80.3%
(Zu ) and the deflection (Zdef ) of the axle give information (rad)
about the road holding. The control goal in this work was to Roll velocity
0.0738 0.0166 77.5% 0.0136 81.6%
(rad/s)
improve ride comfort of the vehicle. According to the ISO Lateral
2631 standard, the parameter J (Eq. (15)) can be found, acceleration 0.2531 0.0358 85.9% 0.0342 86.5%
which has to be minimized to increase the drive comfort: (m/s2 )

v
u
u 1 X N
! Table IV, Table V as well as Fig. 6, show the improve-
2
J= t (Z̈ s )si [k] (15) ments of PID control with respect of passive suspension and
N even greater ones of OSMC.
k=1

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 results reported in the paper, several simulation and HiL
tests results were collected in the development process. All
of them showed the consistent improvement in ride comfort
provided by the proposed controller over the results of PID
controller and passive suspensions. Future work will be
devoted to understand more deeply the attitude of the active
suspension controlled by the proposed SMC in different
scenarios and road conditions, so as to further improve its
performance.
Fig. 6. Spider diagram of the vehicle’s roll angle (rad) on the left and pitch
acceleration (m/s2 ) on the right. The four controllers (Passive, Skyhook, R EFERENCES
PID, OSMC) are compared during Double-lane-change test

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