Strojniški vestnik - Journal of Mechanical Engineering 68(2022)5, 314-324 Received for review: 2021-05-29
© 2022 The Authors. CC BY-NC 4.0 Int. Licensee: SV-JME Received revised form: 2022-01-10
DOI:10.5545/sv-jme.2021.7271 Original Scientific Paper Accepted for publication: 2022-03-08
*Corr. Author’s Address: Zhejiang University of Technology, Hangzhou, China, wengzy8888@163.com 314
Switch Semi-Active Control of the Floating Raft  
Vibration Isolation System
Weng, Z.Y . – Liu, S.L. – Xu, T.Q. – Wu, X.Y . – Wang, Z. – Tang, J.
Zeyu Weng
*
 – Shengli Liu – Teqi Xu – Xiaoyu Wu – Zhe Wang – Jie Tang
Zhejiang University of Technology, College of Mechanical Engineering, China
Switch semi-active control is introduced to improve the performance of the floating raft vibration isolation system on isolating vibration in the 
vicinity of the resonance frequency. A switch-controllable linear damper based on the electromagnetic damping principle is developed, whose 
characteristic parameters are obtained by experiment. The dynamic model of a semi-active control floating raft vibration isolation system is 
established, and two switch control algorithms are proposed. Algorithm 1 aims to minimize the kinetic energy of the raft, and Algorithm 2 
balances minimizing the kinetic energy of the raft and minimizing the input energy of the system. The simulations of the original system, the 
system with the controllable damper, and the system with the damper controlled by the algorithms are carried out. The vibration acceleration 
responses of the foundation of the systems are used to evaluate the vibration isolation effect. The results show that the switching semi-active 
control using Algorithms 1 and 2 can significantly suppress the vibration of the system near the resonance frequency. Finally, the test platform 
of the switch’s semi-active controlled floating raft vibration isolation system is built, and the simulation results are verified by the experimental 
result.
Keywords: floating raft, semi-active control, vibration isolation, switch algorithm
Highlights
• 	 Two semi-active control algorithms for floating raft vibration isolation systems are proposed.
• 	 Applying these two semi-active control algorithms can improve the vibration isolation performance of the floating raft isolation 
system.
• 	 Two algorithms have different effects at different external excitation frequencies.
0  INTRODUCTION
As an extension of the double-layer vibration isolation 
system with multiple vibration sources, the floating 
raft vibration isolation system is widely used in the 
vibration isolation design of ship power units due to 
its good overall performance on vibration isolation 
[1]. However, the system has a poor isolation effect 
at low frequencies, especially near the system’s 
resonance frequency, which may even amplify the 
vibration. Increasing the damping of the system is an 
effective method of suppressing resonance, and larger 
damping leads to a better suppression effect, but it 
affects the vibration isolation effect at middle and high 
frequencies. Using a switch-controllable damper and 
applying switch semi-active control technology on a 
floating raft vibration isolation system can effectively 
solve this problem.
The basic modes of vibration control include 
passive control, active control, and semi-active 
control. Compared with passive control, active control 
generally has a better effect and better adaptability 
[2] to [5]. However, it has higher requirements on the 
controllers and a limited effective control frequency 
band. Moreover, the stability and reliability of the 
system are difficult to guarantee. Once the vibration 
isolation system fails, the active control may amplify 
the vibration and even destroy the entire system. As a 
result, the active control technology cannot be widely 
used in engineering applications. Alternatively, semi-
active control is used since it has a control effect 
close to that of active control, as well as advantages 
of lower energy consumption and better system 
stability and reliability. After failure, the system will 
degenerate into an ordinary floating raft vibration 
isolation system, which still isolates the vibration to 
some extent during the normal operation of the whole 
system.
Semi-active control on the vibration isolation 
system is essentially a kind of parameter control. 
According to the change of system input and the 
requirements of system output, the stiffness and 
damping of the system are adjusted by an appropriate 
control algorithm in real-time so that the vibration 
characteristics of the system can be improved. At 
present, semi-active control technology has been 
widely used in vehicle suspensions and seismic 
resistance of buildings [6] and [7]. For the floating 
raft vibration isolation system, Sun [8] studied the 
isolation performance of a semi-active dynamic 
vibration absorber in a floating raft system under 
multi-frequency excitation. Chen Dayue's team [9] and 
[10] studied the vibration isolation characteristics of 
the floating raft isolation system under fuzzy control 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)5, 314-324
315 Switch Semi-Active Control of the Floating Raft Vibration Isolation System 
and a synovial-film variable structure algorithm based 
on the ER damper. The results showed that different 
control algorithms could effectively improve the 
vibration isolation performance of the floating raft 
isolation system. The damper of the floating raft 
isolation system can be adjusted according to different 
requirements by using the methods of continuous 
semi-active control. This method has great potential. 
However, the adjustment range of the damper is only 
up to several times (generally no more than 10 times), 
and it is challenging to design an ideal control strategy 
due to the nonlinear damping characteristic; these 
factors limit its more comprehensive application. 
Switch semi-active control switches the state of 
a controllable damper on and off to improve the 
performance of vibration isolation. The control 
algorithm is simple and easy to operate, so the control 
system has high reliability. More importantly, the 
damping of the switch-controllable damper developed 
by our institute has strictly linear characteristics, 
the response time is down to milliseconds, and the 
damping can be adjusted up to tens of times. The 
experiments show that these characteristics and 
technical specifications are far superior to the existing 
dampers or controllable dampers that have been 
developed by some scholars, which guarantees the 
performance and reliability of semi-active control.
To summarize, it is of great significance to 
apply the switch semi-active control technology on 
the floating raft vibration isolation system with the 
self-developed switch-controllable damper. In this 
paper, we first characterize the damping properties 
of the developed controllable damper. Then, two 
switching-control algorithms are proposed to 
suppress the transmission of vibration from the unit 
to the foundation. Finally, using the acceleration 
response of the foundation as evaluation parameters, 
the effectiveness of the two algorithms is proved by 
simulation and experiment.
1 EXPERIMENTAL STUDY ON THE PERFORMANCE OF 
SWITCH-CONTROLLABLE LINEAR DAMPER
Properties characterizing the damping performance 
of the switch-controllable damper include the 
indicator, velocity, and response time, which is the 
key component to realize the semi-active control of 
the floating raft isolation system, and its performance 
determines the control effect. We independently 
developed the switch-controllable damper based on 
the electromagnetic damping principle. The control 
voltage is 24 V, direct current (DC). It has two states 
(on and off) corresponding to whether it is powered 
or not. When powered, the moving conductor and 
magnetic pole of the damper produce electromagnetic 
resistance and maintain a high damping value. 
Otherwise, it does not produce electromagnetic 
resistance, and the damper maintains a low damping 
value.
We carried out these tests on MTS849 Shock 
Absorber Test System (MTS Industrial Systems 
CO.LTD, USA) as shown in Fig. 1. 
Fig. 1.  MTS849 shock absorber performance test device used in 
the performance test
    
Fig. 2.  Indicator diagram of the switch-controllable linear damper in different state, the curves show the relationship between damping force 
and displacement, the f in the tag represents the frequency at which the damper operates; a) on state, and b) off state

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)5, 314-324
316 Weng, Z.Y. – Liu, S.L. – Xu, T.Q. – Wu, X.Y. – Wang, Z. – Tang, J.
The indicator diagrams of the on and off states 
of controllable damper are shown in Fig. 2, where 
Fig 2a is for the on state and Fig. 2b is for off state. 
The curve family in Fig. 2 shows the relationship 
between the damping force generated by the damper 
and the motion displacement under different working 
frequencies. The curves in Fig. 2a are smooth, and 
the enclosed area is full, indicating that the damper 
can effectively absorb vibration energy when it is 
powered. The area enclosed by the curves in Fig. 2b is 
close to zero, indicating that the damper absorbs little 
vibration energy when it is not powered.
Fig. 3.  Velocity characteristic curve of the switching-controllable 
linear damper in different state, the curves show the relationship 
between damping force and velocity, the f in the tag represents the 
frequency at which the damper operates;  
a) on state, and b) off state
The curves of the velocity characteristics of 
controllable damper are shown in Fig. 3; Fig. 3a is 
for the on state and Fig. 3b for off state. In Fig. 3, the 
curves show the relationship between the damping 
force generated by the damper and the motion velocity 
under different working frequency of the damper. 
The on state of the switch-controllable damper has 
great linear damping force velocity characteristics, 
meaning that the damper behaves as the pure viscous 
damper, and its damping coefficient is the slope of the 
curve. At the same time, the damping in the off state 
of the switch-controllable damper approaches a small 
constant.
It can be seen from the damper velocity 
characteristic curve that the damping characteristic of 
the controllable damper has obvious linear properties. 
We perform linear fitting on the speed characteristic 
data of the controllable damper in different states, and 
obtain that the damping coefficient of the controllable 
damper in the on state is 24050 N·m
–1
·s, and the 
damping coefficient in the off state is 1050 N·m
–1
·s.
In addition, the response time of the switch-
controllable damper can be obtained by comparing the 
electrical signals controlling the damper and damping 
force output responses.
The characterizing parameters of the controllable 
damper obtained through the tests are shown in Table 
1.
Table 1.  Performance parameters of switch damper
Parameter
Numerical value
On state Off state
Damping coefficient [N·m
–1
·s] 2.405×10
4
1050
Power consumption [W] 9.12 0
Response time [ms] 22 18
Working voltage DC [V] 24
Quality [kg] 6.3
Working distance [mm] ±32
2  DYNAMIC MODEL
According to the magnitude of the foundation 
stiffness, two kinds of dynamic models of vibration 
isolation systems are commonly used: one with rigid 
foundation and the other with flexible foundation. In 
the analysis of the vibration isolation system, some 
scholars neglected the flexibility of the foundation and 
assumed infinite stiffness, thus established the rigid 
foundation model as shown in Fig. 4.
Fig. 4.  Simplified model of rigid foundation isolation system, here 
the stiffness of the foundation is assumed to be infinite
However, from the research of Hamme [11] and 
Sykes [12], we know this simplification usually leads 
to some error. In addition, the vibration response 
on the foundation cannot be reflected in the model 
of rigid foundation, it is impossible to evaluate the 
isolation effect by foundation acceleration response. 
In conclusion, it is crucial to establish an analytical 
model of the floating raft isolation system with 
flexible foundation, as shown in Fig. 5.

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)5, 314-324
317 Switch Semi-Active Control of the Floating Raft Vibration Isolation System 
The semi-active controlled floating raft vibration 
isolation system consists of four parts: a unit, an 
elastic element, a controllable damper, a raft, and 
the foundation. As shown in Fig. 5, F represents the 
excitation force applied on the unit; m
1
, m
2
 and m
3
 are 
the equivalent mass of the unit, raft and foundation 
respectively; c
1
 and k
1
 are the equivalent damping and 
stiffness between the unit and raft; c
2
 and k
2
 are the 
equivalent damping and stiffness between the raft and 
foundation; c
3
 and k
3
 and are the equivalent damping 
and stiffness of foundation; c
4
 is the damping of the 
controllable damper, c
on
 is the high damping at on 
state while c
off
 is low damping at off state; x
1
, x
2
 and 
x
3
 are the displacement responses of the unit, raft and 
foundation respectively, ν
1
, ν
2
 and ν
3
 are the velocity 
responses, a
1
, a
2
 and a
3
 are the acceleration responses. 
Fig. 5.  Dynamic model of semi-active control floating raft  
isolation system
The dynamical equation corresponding to the 
model can be expressed as Eq. (1).
m
m
m
a
a
a
cc c
cc cc
1
2
3
1
2
3
14 1
14 2
00
00
00
0 





















 

2 2
23
1
2
3
11
1122
22
0
0
0

























cc
v
v
v
kk
kkkk
kk  






























 k
x
x
x
F
3
1
2
3
0
0
, (1)
which shows that the damping matrix of the system 
can be changed by adjusting the damping of the 
controllable damper c
4
, thus makes effect on the 
vibration response of the floating raft vibration 
isolation system.
3  ALGORITHMS
To realize switch semi-active control of the floating 
raft vibration isolation system and improve its effect, 
two switch control algorithms named Algorithms 1 
and 2 are proposed in this paper.
3.1  Algorithm 1
The goal of Algorithm 1 is to minimize the kinetic 
energy transmitted to the raft by adjusting the elastic 
energy absorbed or released by the elastic element.
The vibrational energy transited to the system by 
the excitation force transforms into the kinetic energy 
of the mass element, the potential energy of the elastic 
element, and the energy consumed by the damping 
element. The damping element consumes the energy, 
while the kinetic energy of the mass element and the 
potential energy of the elastic element are transformed 
mutually. More specifically, the vibration energy 
transmitted to the system is simultaneously converted 
into the kinetic energy of unit, the potential energy of 
the elastic element between unit and raft, the energy 
consumed by the damping element between unit and 
raft, and the kinetic energy of raft. Among them, the 
increase of kinetic energy of raft leads to the increase 
of the energy transmitted to the foundation, which 
exacerbates the vibration of the foundation. The 
kinetic energy of the raft can be reduced as much as 
possible by controlling the damping force. When 
the elastic element absorbs energy, the controllable 
damper is switched to the off state to minimize the 
damping value, which makes the elastic element 
absorb more energy and thus reduces the energy 
transited to the raft. When the elastic element releases 
energy, the controllable damper is switched to the on 
state to maximize the damping value, which makes 
the damper consume more energy and thus reduces 
the energy released from the spring to the raft.
According to the displacement and velocity 
differences between the unit and raft, the motion of the 
floating raft vibration isolation system can be divided 
into four states as shown in Fig. 6, where dotted lines 
are the equilibrium positions of the unit and raft.
In Fig. 6a, the displacement difference between 
the unit and raft is positive (x
1
 – x
2
 > 0), which means 
the spring element between unit and raft is elastically 
restored; the velocity difference is positive (ν
1
 – ν
2
 > 0), 
which means the displacement difference between the 
two will increase. In this state, the elastic element 
absorbs energy and the controllable damper should be 
in the off state.
In Fig. 6b, the displacement difference between 
the unit and the raft is positive (x
1
 – x
2
 > 0), which 
means the spring element between the unit and raft is 
elastically restored; the velocity difference is negative 
(ν
1
 – ν
2
 < 0), which means the displacement difference 
between the two will decrease. In this state, the elastic 
element releases energy and the controllable damper 
should be in the on state.

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)5, 314-324
318 Weng, Z.Y. – Liu, S.L. – Xu, T.Q. – Wu, X.Y. – Wang, Z. – Tang, J.
In Fig. 6c, the displacement difference between 
the unit and the raft is negative (x
1
 – x
2
 < 0), which 
means the spring element between unit and raft 
is compressed; the velocity difference is positive 
(ν
1
 – ν
2
 > 0), which means the displacement difference 
between the two will increase. In this state, the elastic 
element releases energy and the controllable damper 
should be in the on state.
In Fig. 6d, the displacement difference between 
the unit and the raft is negative (x
1
 – x
2
 < 0), which 
means the spring element between unit and raft 
is compressed; the velocity difference is negative 
(ν
1
 – ν
2
 < 0), which means the displacement difference 
between the two will decrease. In this state, the elastic 
element absorbs energy and the controllable damper 
should be in the off state. 
Based on the analysis of each state above, the 
control law of Algorithm 1 can be expressed as
    c
cx xv v
cx xv v
c
off
on
on
4
12 12
12 12
00
00

 
 
  
   
  
() ,( )
() ,( )
  
  
() ,( )
() ,( )
xx vv
cx xv v
PF
off
F
12 12
12 12
00
00
 
 







 v v
1
, (2)
which can be simplified as
 c
cx xv v
cx xv v
off
on
4
12 12
12 12
0
0








  
   
() ()
() ()
. (3)
3.2  Algorithm 2
Algorithm 2 aims to makes the balance on minimizing 
the input energy of the system and minimizing the 
kinetic energy of the raft.
The power of the excitation force on the unit can 
be expressed as 
 PF v
F

1
, (4)
the controllable damping force also works on the unit 
and its power can be expressed as
 Pcvvv
c14 211
  () . (5)
If both P
F
 and P
c1
 are positive, then
 PP Fc vvv
Fc
  
14 211
2
0 () , (6)
that is
 Fv v  () .
21
0 (7)
The excitation force inputs energy to the system 
and the controllable damping force will exacerbate 
this input, the controllable damper should be in the off 
state to reduce the input energy. If P
F
 is positive while   
P
c1
 is negative then
 Fc vv  
421
0 () , (8)
that is
 Fv v  () .
21
0 (9)
The excitation force inputs energy to the system 
and the controllable damping force will attenuate this 
input, so the controllable damper should be in the on 
state to reduce the input energy. If P
F
 is negative while 
P
c1
 is positive then
 Fc vv  
421
0 () , (10)
that is
 Fv v  () .
21
0 (11)
The excitation force absorbs energy from the 
system and the controllable damping force will 
enhance the absorption, so the controllable damper 
should be in the on state to increase the energy 
absorption. If both P
F
 and P
c1
 are negative then
 Fc vv  
421
0 () , (12)
that is
 Fv v  () .
21
0 (13)
The excitation force absorbs energy from the 
system and the controllable damping force will 
attenuate the absorption, so the controllable damper 
a)    b)   c)   d) 
Fig. 6.  System state decided by the displacement difference and velocity difference; a), b), c) and d) are explained in the article

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)5, 314-324
319 Switch Semi-Active Control of the Floating Raft Vibration Isolation System 
should be in the off state to increase the energy 
absorption. 
In short, when the excitation force and the 
controllable damping force are in the same direction, 
the controllable damper should be in a low damping 
state; while in the opposite direction, the controllable 
damper should be in a high damping state. The 
damping expression of the controllable damper is
 c
cF vv
cF vv
off
on
4
21
21
0
0








  
   
()
()
. (14)
Both Algorithm 1 and Eq. (14) give the 
expressions of the controllable dampers, which are 
incompatible. Algorithm 2 combines Algorithm 
1 with Eq. (14). That is: if the control results of 
Algorithm 1 and Eq. (14) are consistent, then take 
the common result as the criterion and set the state 
of the controllable damper accordingly. Otherwise, 
the controllable damper is set to the active mode to 
consume more energy. In conclusion, the control law 
of Algorithm 2 can be expressed as
c
cF vv xx vv
cF vv x
off
on
4
21 12 12
21
00
0

 

  
   
() ,( )( )
() ,(
1 12 12
21 12 12
0
00

 
xv v
cF vv xx vv
cF
on
off
)( )
() ,( )( )   
    







() ,( )( )
,
vv xx vv
21 12 12
00
 (15)
which can be simplified as
c
cF vv xx vv
cF vv x
off
on
4
21 12 12
21
00
0

 

  
   
()() ()
()(
∩
∪
1 12 12
0 





xv v )( )
. (16)
These two algorithms have different emphasis 
and both have its own advantages and disadvantages. 
Algorithm 1 only considers the energy changes of the 
elastic elements and damping elements between raft 
and unit, but doesn’t take the change of the system 
total energy into account. Algorithm 2 concerns not 
only the absorption, release, and consumption of 
local energy, but also considers the change of the total 
energy of the system.
4  SIMULATIONS AND ANALYSES
To verify the switch semi-active control algorithms, 
we simulated the floating raft vibration isolation 
system in MATLAB Simulink as shown in Fig. 7, and 
applied the control algorithms.
For comparison, the acceleration response of 
the foundation without control (including the off-
state and the on state system) is also studied both in 
time domain and frequency domain analysis. The 
simulation parameters of the model are shown in Table 
2, which is determined by the floating raft vibration 
isolation system used for tests.
Fig. 7.  Simulink model of the semi-active controlled floating raft isolation system

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)5, 314-324
320 Weng, Z.Y. – Liu, S.L. – Xu, T.Q. – Wu, X.Y. – Wang, Z. – Tang, J.
Table 2.  Model parameters for semi-active controlled floating raft 
isolation system
Parameters Value
Equivalent mass [kg]
m
1
238.8
m
2
175.1
m
3
216
Equivalent damping [N∙m
–1
∙s]
c
1
70
c
2
50
c
3
5000
Controllable damper [N∙m
–1
∙s]
c
off
2100
c
on
4.81×10
4
Equivalent stiffness [N∙m
–1
]
k
1
3.707×10
5
k
2
3.468×10
5
k
3
2.809×10
7
4.1  Time Domain Comparison of Foundation Responses
The amplitude of the excitation force acting on the 
unit in the simulation model is determined to be 500 
N referring to the magnitude of the excitation force 
in the test device used in this study, and its frequency 
range is from 0.1 Hz to 20 Hz. As shown in Fig. 8, four 
typical frequencies were selected from the simulation 
results for analysis.
The first frequency (3.9 Hz) is the first resonance 
frequency of the non-controlled system. Fig. 8a 
shows that under the harmonic excitation of 3.9 
Hz, the foundations of the systems controlled by 
Algorithms 1 and 2 both have acceleration response 
amplitudes distinctly lower than that of the off-state 
system, higher than that of the on-state system and 
that from Algorithm 2 is even lower than Algorithm 
1. These indicate that the vibration isolation effect of 
Algorithms 1 and 2 is obviously superior to that of 
the off-state system and is worse than that of the off-
state system. The effect of Algorithm 2 is better than 
Algorithm 1 at this frequency .
The second frequency (4.7 Hz) is the frequency 
near the first resonance frequency under the control 
of the algorithms. Fig. 8b shows that under the 
harmonic excitation of 4.7 Hz, the foundations of the 
systems controlled by Algorithms 1 and 2 both have 
acceleration response amplitudes distinctly higher 
than that of the off-state system. These indicate that 
the isolation effect of the off-state system is superior 
to the Algorithms 1 and 2 at this frequency.
The third frequency (6.0 Hz) is the frequency 
where the effect with and without control are close. 
Fig. 8c shows that, under the harmonic excitation of 
6 Hz, the foundations of the systems controlled by 
Algorithms 1 and 2 both have acceleration response 
amplitudes close to non-controlled system. These 
indicate that the isolation effect of non-control, 
Algorithms 1 and 2 is approximately equivalent at this 
frequency.
The last frequency (11 Hz) is the second 
resonance frequency of the non-controlled system. 
Fig. 8d shows that, under the harmonic excitation of 
a)  b) 
c)  d) 
Fig. 8.  Plot of acceleration response amplitude with respect to time; a) 3.9 Hz, b) 4.7 Hz, c) 6 Hz, and d) 11 Hz

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)5, 314-324
321 Switch Semi-Active Control of the Floating Raft Vibration Isolation System 
reduced after the installation of controllable damper. 
Comparing between systems using the controllable 
damper, the amplitudes of acceleration response on 
the foundation of the systems using two algorithms 
are significantly smaller than that of non-controlled 
system around the resonance frequency. Before 
reaching to the resonance frequency, the vibration 
isolation effect of Algorithm 1 is the worst while 
Algorithm 2 is the best; after the resonant frequency, 
the effect of these two algorithms are close to that of 
the non-controlled system. Compared with Algorithm 
2, Algorithm 1 performs better around the resonance 
frequency but is inferior to Algorithm 2 in the low 
frequency band; in the following frequency band, the 
performance of two algorithms is approximately the 
same.
From the amplitude value of the foundation’s 
acceleration response curve, the maximum values 
of the original system, the off-state system, the on-
state system and the system using Algorithms 1 and 
2 are shown in Table 3. The amplitude of the Original 
system is much larger and thus the vibration isolation 
effect is poorer; and the vibration isolation effect 
gets better when the controllable damper is used. 
Compared with non-controlled system, the amplitude 
of the system using Algorithm 1 is reduced by 60.4 
%, and using Algorithm 2 is reduced by 43.3 %; the 
amplitude using Algorithm 1 is reduced by 30.1 % 
compared with that using Algorithm 2.
Table 3.  Acceleration response maximum of five states (simulation)
State Maximum [m/s
2
]
Original system 1.012
Off-State 0.1844
On-State 0.1526
Algorithm 1 0.07296
Algorithm 2 0.1045
It can be concluded that using controllable 
damper can improve the isolation effect of the floating 
raft isolation system in the low frequency segment; 
furthermore, using the algorithms to control the 
controllable damper can further improve the vibration 
isolation effect.
5  EXPERIMENTS 
5.1  Test System and Scheme
We built the experiment setup for the semi-active 
controlled floating raft vibration isolation system, 
which consists of a floating raft vibration test bench, a 
11 Hz, the foundations of the systems controlled by 
Algorithms 1 and 2 both have acceleration response 
amplitudes distinctly lower than that of the off-state 
system. These indicate that the isolation effect of the 
off-state system is inferior to Algorithms 1 and 2; and 
there is little difference between the results of the on-
state system, Algorithms 1 and 2, which suggest that 
the Algorithm 1 is basically in line with Algorithm 2 
at this frequency.
4.2  Frequency Domain Comparison of Foundation 
Responses
For the goal of comparison with the original system 
which has no switch-controllable damper, we carried 
out the frequency domain analysis of this case in 
additional. Continuously changing the frequency of 
the excitation force on the system and recording the 
foundation’s acceleration response yields the variation 
curve of the acceleration response amplitude on the 
foundation of the system in the excitation frequency 
range from 0.1 Hz to 20 Hz, as shown in Fig. 9. There 
are two obvious resonance peaks in the response 
amplitude curve of the foundation acceleration of the 
original system.
Fig. 9.  Plot of acceleration response amplitude with respect to 
frequency obtained by simulation
According to Fig. 9, it can be seen that the 
trends of acceleration responses of the foundation 
of the four cases are basically similar, all of which 
reach the maximum at the resonance frequency. It 
is obvious that the acceleration response amplitude 
of the foundation of the original system is greatly 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)5, 314-324
322 Weng, Z.Y. – Liu, S.L. – Xu, T.Q. – Wu, X.Y. – Wang, Z. – Tang, J.
switch-controller system, and a test evaluation system. 
The block diagram is shown in Fig. 10. 
The floating raft vibration test bench is composed 
of a unit, a variable-frequency drive (VFD), upper 
isolation springs, a raft, lower isolation springs, 
foundation, and controllable dampers. The switch-
controller system is composed of acceleration 
sensors, conditioning amplifier, PCI DAQ, Industrial 
Personal Computer (IPC) and a relay. The velocities 
and displacements needed in the algorithms can be 
Fig.10.  Test block diagram of semi-active control of floating raft isolation system
obtained from integration. The test evaluation system 
has composed of 333B30 acceleration sensors (PCB 
Piezotronics, Inc., USA) and a Siglab20-42 signal 
analyser (Spectral Dynamic, Inc., USA), Siglab 
analysis software is installed on the computer.
The variable-frequency drive controls the 
excitation force on the unit to generate harmonic 
excitation at different frequencies. The switch semi-
active control algorithms are implemented by running 
the control program of LabVIEW. It switches the 
controllable damper by controlling the relay. The test 
evaluation system collects the acceleration response 
signals on the foundation for analysis. This setup of 
the experiment is shown in Fig. 11.
Fig. 11.  The experimental apparatus
5.2  Results and Analysis
We tested the original system, the non-controlled 
system (the On-State or Off-State system), and 
the semi-active switch-controlled systems using 
Algorithms 1 and 2, respectively, from which 
the variation curves of the acceleration response 
amplitudes of the foundations at the excitation 
frequency range from 1.5 Hz to 13 Hz are obtained, as 
shown in Fig. 12. 
From the amplitude value of the foundation’s 
acceleration response curve, the maximum values of 
the original system, Off-state system, On-state system, 
Algorithms 1 and 2 are obtained and shown in Table 
4. The vibration isolation effect of the original system 
is not obvious. Acceleration response amplitudes of 
the original system, the off-state system, the on-state 
system, the semi-active switch-controlled systems 
using Algorithms 1 and 2, respectively, are 0.0573, 
0.02243, 0.1826, 0.01127 and 0.01321.
Comparing Figs. 9 and 12, it can be seen that 
the simulation results are in good agreement with the 
experimental results. Around the resonance frequency, 
the vibration isolation effect of semi-active control 
using Algorithms 1 and 2 is clearly better than that of 
non-controlled system, and they are roughly the same 
at other frequencies, which shows that Algorithms 1 
and 2 can effectively improve the vibration isolation 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)5, 314-324
323 Switch Semi-Active Control of the Floating Raft Vibration Isolation System 
performance of floating raft system around the 
resonance frequency.
Fig. 12.  Plot of acceleration response amplitude with respect to 
frequency obtained by experiment test
Table 4.  Acceleration response maximum of three states (test)
State Maximum [m/s
2
]
Original system 0.0573
Off-State 0.02243
On-State 0.01826
Algorithm 1 0.01127
Algorithm 2 0.01321
It is worth mentioning that there are some 
discrepancies in the magnitude of the underlying 
acceleration between simulation and testing.
(a) Compared with the simulation results, the basic 
acceleration amplitude of the test generally 
increases gradually with the increase of the 
frequency. The reason for this is that the test 
system adopts an inertial rotation excitation 
device, and the amplitude of the excitation force 
gradually increases with the increase of the 
frequency (i.e., the rotation speed), while the 
constant amplitude excitation force is used in the 
simulation model.
(b) In the test results, the frequencies corresponding to 
the first-order peaks are basically the same except 
for the open state of the damper. In the open state 
of the damper, the frequency increases slightly. 
In the simulation results, however, the frequency 
increases in the on state and two control algorithm 
states compared to the off and original system 
states. The main reason for this discrepancy is 
that the properties and values of all damping of 
the actual floating raft vibration isolation system 
are very complex, and the damping force can 
be understood as the superposition of damping 
forces of various properties. In the simulation 
model, only the viscous damping of the system 
is considered, which makes the damping in the 
simulation model relatively small. The main 
influencing factor of the frequency corresponding 
to the first-order peak is the system damping 
(c
1
 + c
4
). When (c
1
 + c
4
) is larger, the frequency 
corresponding to the first-order peak is also 
larger. Since the parameter c
1
 in the test system is 
larger than the parameter in the simulation model, 
in the vicinity of the first-order peak frequency, 
after the algorithm is applied to the test system, 
the larger c
1
 makes c
4
 do not need to be turned on 
frequently, and the switch damper c
4
 is in the off 
state as the dominant factor. The damping (c
1
 + c
4
) 
in the test system is more in a less damped state 
and the frequency corresponding to the first-order 
peak barely increases. After the simulation model 
applies the algorithm, the smaller c
1
 makes c
4
 
need to be turned on frequently, and the switch 
damper c
4
 is in the on state as the dominant 
factor. The damping (c
1
 + c
4
) in the simulation 
model is more in the larger damping state and 
the frequency corresponding to the order peak 
increases slightly.
In addition, we only consider the viscous damping 
of the floating raft system in the simulation model and 
the amplitude of the second peak in the simulation 
results decreases as the damping increases. In the 
actual test system, when the controllable damper is in 
the off state, the characteristics of damping (c
1
 + c
4
) 
mainly depend on c
1
, and the non-viscous damping 
characteristics become obvious, which leads to 
the discrepancies between the experimental results 
(the amplitude of the second peak is small) and the 
simulation results.
6  CONCLUSIONS
To solve the problem that the vibration isolation 
effect of the floating raft vibration isolation system 
is poor near the resonance frequency and even has 
a vibration amplification effect, we developed a 
switch-controllable damper and introduced semi-
active switch control technology. Two switch control 
algorithms, Algorithms 1 and 2, are proposed. Based 
on the simulation and experiments, the following 
conclusions can be drawn:

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)5, 314-324
324 Weng, Z.Y. – Liu, S.L. – Xu, T.Q. – Wu, X.Y. – Wang, Z. – Tang, J.
(1) The controllable damper can improve the 
isolation effect of the vibration isolation system 
near the resonance frequency. Built on that, the 
vibration isolation effect of the system can be 
further greatly improved by using the proposed 
semi-control algorithms. 
(2) The two control algorithms have their own 
advantages and disadvantages. In the low 
frequency band, the overall isolation effect of 
Algorithm 2 is better than that of Algorithm 
1. However, near resonance frequency, using 
Algorithm 1 in the vibration isolation effect is 
more superior near the resonance frequency.
(3) Future work on this can be carried out in the 
direction of multi-frequency excitation, which is 
closer to the practical engineering application.
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