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Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10389-10394 10389  
 

www.etasr.com Nguyen: Anti-Vibration Control of Turntable Ladders by a Steel Rope-Hydraulic Control System 

 

Anti-Vibration Control of Turntable Ladders by 

a Steel Rope-Hydraulic Control System 
 

Van Tinh Nguyen 

Faculty of Mechanical Engineering, Hanoi University of Civil Engineering, Vietnam 

tinhnv@huce.edu.vn  

(corresponding author) 
 

Received: 31 December 2022 | Revised: 1 February 2023 | Accepted: 9 February 2023 

 

ABSTRACT 

Anti-vibration control of turntable ladders is effective by controlling the steel ropes inserted in the hollow 

handrails. Previous studies that considered idealized conditions, such as ignoring friction, piston mass, and 

hydraulic oil compressibility, can not be strongly generalized. This study addresses these problems by 

describing in detail the equipment serving the anti-vibration solution, building a mathematical model for 

the steel rope hydraulic control system considering the above factors, and controlling the rapid 

extinguishing of vibrations on a model simulated in Matlab-Simulink. Furthermore, the simulation of the 

relationship between the control signal and oil flow through the proportional distribution valve produced a 

signal flow curve that was asymptotic to the actual. The results showed a difference compared to previous 

studies. Although the solution was only implemented on the lowest ladder section with the most 

unfavorable conditions, the time for vibration on the top ladder reached amplitudes of 3 and 5mm in 3 and 

5s for empty and full baskets, respectively. 

Keywords-aerial extension ladder; anti-vibration control; dynamic equation; steel rope hydraulic control; 

turntable ladder 

I. INTRODUCTION  

The study on vibration reduction, fast vibration quenching, 
and anti-swing for load transport equipment has high scientific 
and practical significance. Various control methods have been 
proposed to bring the load to the desired position quickly and 
accurately [1-4]. This activity makes more sense for turntable 
ladders because they transport rescued people and should help 
them feel safe in a rescue basket. Authors in [5-7] presented 
effective control methods to eliminate vibrations on turntable 
ladders. In [8-11], a new solution was presented to eliminate 
vibrations and overcome large static displacements on ladders, 
putting steel ropes inside the hollow of the handrails. These 
steel ropes were tensioned and controlled by small hydraulic 
cylinders mounted on the handrail tops, using the available 
hydraulic power of the truck. This method showed that the 
tension of the steel ropes had a positive effect on the anti-
vibration on the top ladder [8] and the control of the steel ropes 
rapidly reduced the vibrations on the ladder [9]. In [10], stress 
reduction on key ladder elements and significant reduction of 
static displacements were demonstrated by evaluating the 
ladder structure with additional steel ropes according to the 
standards [12-13]. The hydraulic circuit design and cylinder 
control according to the control principle [9] were presented in 
[11]. However, the control system model in [11] was not very 
accurate and comprehensive, as it did not consider the elasticity 
of hydraulic oil, ignored friction forces and the mass of the 
piston rod, and used approximate mathematical models for the 
flow-signal curve. This study investigated the detailed structure 

of the anti-vibration device, the dynamic model of the steel 
rope hydraulic control system, the establishment of a 
mathematical model of the system with an accurate flow-signal 
curve, and the practice of controls for rapid suppression of 
vibrations on turntable ladders. 

II. STEEL ROPE-HYDRAULIC CONTROL SYSTEM 

Figure 1 shows the structure of the devices attached to the 
hollow handrails of a ladder, omitting the ladder structure. The 
hydraulic cylinder is integrated with the position sensor 
mounted on the lower end of the handrail. 

 

 

Fig. 1.  Added components into a hollow handrail. 

A threaded joint connects the piston rod to one end of the 
steel rope. The steel rope with a high damping coefficient is 
threaded in the handrail and supported by supports. The 



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supports are lightweight plastic evenly spaced to eliminate the 
rope sag. The other end of the rope is fixed by a threaded joint 
to the other end of the ladder. Additional devices were 
implemented in the lowest ladder section for anti-vibration to 
match the size of the 30m set including the three ladder 
sections described in [14]. The control on the third ladder is the 
most effective [9]. The most effective vibration control is when 
placing the actuator closest to the fixed end of a cantilever 

beam [15]. Figure 2 shows the mechanical model of the ladder 
structure, the steel rope, and the force generated by the 
cylinder. The control system commands the actuator to 
generate a force to reduce vibration. This force moves with a 
variable velocity rule that follows or nearly follows a 
predefined rule. Based on the data in [8-11], all parameters in 
this model were entirely determined. 

 

 

Fig. 2.  Multi-body dynamics model of ladder set and steel rope in hollow handrails. 

Figure 3 shows the model of the steel rope hydraulic 
control system. During the operation of the proportional 
directional valve, when the P-A ports are connected, the high-
pressure hydraulic oil pushes the piston to the left to pull the 
steel rope. In contrast, when the A-T ports are connected, the 
oil in the cylinder chamber flows to the tank through the 
pressure sequence valve due to the tension of the rope pulling 
the piston. In this model, kc3 and cc3 are the stiffness and 
damping coefficients of the ropes in the third ladder section, Ap, 
pp are the area and the pressure of the oil chamber, and xp and xr 
are the displacements of the piston and the remaining fixed end 
of the steel rope, respectively. 

 

 

Fig. 3.  Mechanical model of steel rope-hydraulic control system. 

III. EQUATION OF MOVEMENT 

According to [9], during the vibration control performance, 
the acceleration vector of the addition motion is determined as: 

�� = −�(�)	
�(�)�� − �(�)	

(�)�  
+�(�)	
(� + ��� �contr�)   (1) 

where �� , �� , and �  are the acceleration, velocity, and 
displacement vectors of the addition motion of the rigid bodies, 
M(t), C(t), and K(t) are the mass matrix, the damping matrix, 
and the stiffness matrix, D is the load matrix including Ti 
(bending moment) and Di (damping load) caused by the steel 
rope in the i-th ladder section, F is the load matrix excluding 
the load components caused by the steel rope, and ��� =��(�)/�� with F(t) being the total generalized load matrix. 

�contr = �����1 1 1 1 �!" ��"#  (2) 
where kT3 and kT3 are the controlling factors corresponding to 
T3 and D3 in the third ladder section, respectively. The motion 
equation of the piston is given by: 

$%&% − �'"()'*" − +'"()�'*" − �, = -%.�%  (3) 
where ()'*", ()�'*"  represent the length change range and the 
length change speed of the steel rope, Ff is the friction force, mp 
is the piston mass, and .�%is the piston acceleration. The exact 
determination of the friction force is very complicated and it is 
necessary to conduct experiments on each specific object. To 
simplify the simulation, it was determined as follows [16]: 

�, =
⎩⎨
⎧ �2 + +% ⋅ 4$%&%4                      for .� % > 9:;�2 + +% ⋅ 4$%&%4< =�>=�?   for − .�: ≤ .�% ≤ 9:−�2 − +% ⋅ 4$%&%4               for .� % < −9:

     (4) 



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where v0 is the velocity whose value is a very small positive 
around zero, Fs=10

5
Ap, and cp=2%. The change range of the 

steel rope length during work is given by: 

()'*" = .% + .%: − .B     (5) 
and the length change speed of the steel rope is given by: 

()�'*" = .�% − .�B     (6) 
with xr being the longitudinal displacement of the upper end of 
the handrail. The dynamic equation for the oil compressibility 
inside the cylinder chamber can be written as [17]: 

$�% = CDEF ;G= − H�' <    (7) 
where $�% denotes the change rate of the chamber pressure, IJ 
is the oil bulk modulus, Vc denotes the oil volume, and Qx 
denotes the rate of flow entering the chamber. 

H' = HJ' + &% ;.% + .:<   (8) 
H�' = &% .�%     (9) 

where x0 is the oil length in the cylinder chamber when it is set 
to create the initial tension load, xp is the displacement of the 
piston, and VOC is the oil volume in the pipe. 

Replacing (8) and (9) in (7) gives: 

$�% = CD;EDFKL>=?<KL> => ;G= − &% .�%<  (10) 
The flow rate depends on the pressure drop which is the 

pressure difference between the inlet and outlet ports and the 
corresponding nominal flow. This is detailed in: 

G= = GMJN∗ ⋅ P Q%RQ%SDT    (11) 
where ΔpNom is the pressure drop when the flow rate is nominal, 
and the command signal is maximum, ΔpNom=5×10

5
Pa, Δpx is 

the pressure drop when working, and GMJN∗  is the flow rate 
depending on the command signal. GMJN∗  is determined as:  

GMJN∗ /GMJN = U(V)    (12) 
where u=U/Umax, U is the control voltage, Umax is the 
maximum control voltage, and QNom is the nominal flow at Umax.  

Equation (10) is rewritten in the case of the piston pulling 
the steel rope: 

$�% = CDW,(X)⋅YSDT⋅P
>DℎZ>>[>SDT 	L>=�>\;EDFKL>=?<KL>=>    (13) 

and in the case of the steel rope pulling the piston: 

$�% = CDW,(X)⋅YSDT⋅P
>>Z>D][>SDT 	L>=�>\;EDFKL> =?<KL>=>   (14) 

with poh and pou being the pressure at P and T ports, 
respectively. 

IV. ANTI-VIBRATION CONTROL 

Based on the parameters and the original characteristic 

curve of the proportional directional valve presented in [18], to 
simplify the numerical simulation process in its half 
corresponding to the positive signal, (12) can be approximated 
as:  

YSDT∗YSDT =
⎩⎪
⎨
⎪⎧    0                        for  0 ≤ V <




:"`aXb


:: − c"X
:: + "
::    for    

: ≤ V ≤ `d
::"aX
": − a":                for  `d
:: < V ≤ 1

 (15) 

Figure 4 shows the original flow curve and the approximate 
curve generated by (15). They almost coincide. 

 

 

Fig. 4.  Flow characteristic according to command signal percentage. 

The steel rope hydraulic control system model was 
established in Matlab-Simulink, as shown in Figure 5. The 
main parts of this model are: 

 Ladder structure model: a subsystem created from the 
ladder dynamic model in Matlab-Simulink, as presented in 
[9]. 

 Signal generator: The velocity sensor at the top of the third 
ladder section provides a signal to the control signal 
generator, which is the original signal that is smoothed and 
amplified before reaching the valve. As the original signal 
is taken from the ladder structure model, the phase delay of 
the control signal must be considered. Here, the tensioner 
model starts 30ms after the ladder model. A delay time of 
4ms was selected. When the amplitude of the vibration at 
the top ladder is small enough, the signal generator will 
stop working. This amplitude value can be preset. 

 Function blocks of the hydraulic devices: They determine 
the dynamic parameters of the piston and the oil pressure in 
the chamber through (3) and (13)-(15). 

 Damping load block: It receives the piston and rope end 
velocity signals and creates the damping force (+'"()�'*"). 

 Rope tension block: It has the function of generating rope 
tension (�'"()'*") based on the longitudinal deformation of 
the steel rope. 

Table I shows the modeling parameters. The largest vertical 
vibration at the top ladder may occur when the ladder is 
horizontal and fully extended. Therefore, this study implements 
anti-vibration control in this ladder state. 



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Fig. 5.  Steel rope-hydraulic control system model in Matlab-Simulink. 

TABLE I.  MODEL PARAMETERS OF CONTROL SYSTEM 

ef (Pa) gh (m) gih (m) ji (kg) ki (m2) 
1.8×10

9
 0.02 0.01 1.1 10

-3
 lfm (m3) ifn (Pa) ifo (Pa) mmp (Ns/m) qmp (N/m) 

2.1×10
-4

 21×10
6
 5×10

6
 1650 1.29×10

6
 

 

Figures 6-12 show the parameters obtained during the 
control process, including control signal, oil flow, oil pressure, 
friction force, piston speed and displacement, and damping 
force in the empty basket case. Figure 13 shows the 
displacement graphs on the top ladder for both basket cases. 
Despite the control signal's late start and phase delay, the 
vibration control through the steel rope hydraulic control 
system was highly effective. Compared to [9] and [11], these 
results overcome the expected effect after control. In the empty 
basket case, the vibration amplitude after only 3s of control 
reaches 3mm for the top ladder instead of 67mm. The control 
systems in the other studies need more than 8s to achieve this 
amplitude. In case of a full basket, the vibration amplitude of 
the top ladder after 5s of control reaches 5mm compared to the 
others that need more than 14s to achieve such amplitude. 

 

 
Fig. 6.  Control signal percentage. 

In addition to the steel rope having the effect of damping, 
the hydraulic equipment also suppresses the vibration when 
operating. The pressure and flow rate values for the cylinders 
presented in Figures 7-8 are suitable for the hydraulic system of 
a turntable ladder. The speed and displacement of the piston 
shown in Figures 10-11 are also consistent with the kinematic 
parameters of a piston used to control a precise motion system. 

 

 
Fig. 7.  Oil flow through a proportional directional valve. 

 

Fig. 8.  Oil pressure in the cylinder chamber. 



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Fig. 9.  Friction force between piston and cylinder. 

 
Fig. 10.  Piston velocity. 

 
Fig. 11.  Piston displacement. 

 
Fig. 12.  Damping force. 

V. CONCLUSION 

The paper presented a new approach to anti-vibration 
methods for turntable ladders. It also shows the feasibility of 
carrying out the novel control solution presented in [9] with 
available devices in the market. A steel rope hydraulic system 
dynamic model, including tension and damping load of steel 

the ropes, friction force between the piston and the cylinder, oil 
compressibility, piston mass, and the proportional directional 
valve characteristics, was established and simulated. This 
model was combined with the ladder set's multi-body dynamics 
model to control the vibration's rapid quenching at the top 
ladder with a unique signal generator. Friction, oil 
compressibility, and the inertia force of the piston significantly 
influence the damping of the ladder's vibrations. This model 
extinguished vibrations by controlling the steel rope hydraulic 
system more efficiently, controlling only the steel ropes. The 
vibration reduction rate was approximately three times faster 
than in other studies. 

 

 

Fig. 13.  Displacement of the top ladder. 

REFERENCES 

[1] J. Neupert, E. Arnold, K. Schneider, and O. Sawodny, "Tracking and 
anti-sway control for boom cranes," Control Engineering Practice, vol. 
18, no. 1, pp. 31–44, Jan. 2010, https://doi.org/10.1016/j.conengprac. 
2009.08.003. 

[2] B. Spruogis, A. Jakstas, V. Gican, V. Turla, and V. Moksin, "Further 
Research on an Anti-Swing Control System for Overhead Cranes," 
Engineering, Technology & Applied Science Research, vol. 8, no. 1, pp. 
2598–2603, Feb. 2018, https://doi.org/10.48084/etasr.1774. 

[3] L. A. Tuan and L. V. Duong, "Neural fractional-order control of 
telescopic truck cranes," Applied Mathematical Modelling, vol. 108, pp. 
807–824, Aug. 2022, https://doi.org/10.1016/j.apm.2022.04.006. 

[4] M. D. Duong, Q. T. Dao, and T. H. Do, "Settling Time Optimization of a 
Critically Damped System with Input Shaping for Vibration Suppression 
Control," Engineering, Technology & Applied Science Research, vol. 12, 
no. 5, pp. 9388–9394, Oct. 2022, https://doi.org/10.48084/etasr.5242. 

[5] N. Zimmert, A. Kharitonov, and O. Sawodny, "A new Control Strategy 
for Trajectory Tracking of Fire–Rescue Turntable Ladders," IFAC 
Proceedings Volumes, vol. 41, no. 2, pp. 869–874, Jan. 2008, 
https://doi.org/10.3182/20080706-5-KR-1001.00149. 

[6] N. Zimmert, A. Pertsch, and O. Sawodny, "2-DOF Control of a Fire-
Rescue Turntable Ladder," IEEE Transactions on Control Systems 
Technology, vol. 20, no. 2, pp. 438–452, Mar. 2012, https://doi.org/ 
10.1109/TCST.2011.2116021. 

[7] A. Pertsch and O. Sawodny, "Modelling and control of coupled bending 
and torsional vibrations of an articulated aerial ladder," Mechatronics, 
vol. 33, pp. 34–48, Feb. 2016, https://doi.org/10.1016/j.mechatronics. 
2015.11.009. 

[8] V. T. Nguyen, T. Schmidt, and T. Leonhardt, "Effect of pre-tensioned 
loads to vibration at the ladder tip in raising and lowering processes on a 
turntable ladder," Journal of Mechanical Science and Technology, vol. 
33, no. 5, pp. 2003–2010, May 2019, https://doi.org/10.1007/s12206-
019-0402-2. 

[9] V. T. Nguyen, T. Schmidt, and T. Leonhardt, "A new active vibration 
control method on a ladder of turntable ladders," Journal of Mechanical 
Science and Technology, vol. 35, no. 6, pp. 2337–2345, Jun. 2021, 
https://doi.org/10.1007/s12206-021-0506-3. 



Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10389-10394 10394  
 

www.etasr.com Nguyen: Anti-Vibration Control of Turntable Ladders by a Steel Rope-Hydraulic Control System 

 

[10] V. T. Nguyen, "Effect of pre-tensioned rope tensions on a ladder 
structure of turntable ladders," Journal of Science and Technology in 
Civil Engineering (STCE) - HUCE, vol. 16, no. 1, pp. 138–151, Jan. 
2022, https://doi.org/10.31814/stce.huce(nuce)2022-16(1)-12. 

[11] V. T. Nguyen, "A solution to increase the flexural stiffness and quickly 
extinguish vibrations on a ladder of turntable ladders," Tạp chí Khoa học 
Công nghệ Xây dựng (KHCNXD) - ĐHXDHN, vol. 16, no. 3V, pp. 138–
149, Jul. 2022, https://doi.org/10.31814/stce.huce(nuce)2022-16(3V)-11. 

[12] "Rules for the Design of Hoisting Appliances," Federeation Europeenne 
de la Manutention, FEM 1.001, Oct. 1998. 

[13] "High rise aerial appliances for fire and rescue service use - Turntable 
ladders with combined movements - Safety and performance 
requirements and test methods," European Committee for 
Standardization, European Standard EN 14043:2014, 2014. 

[14] M. J. Burman, S. E. Goodson, and J. D. Aiken, "Telescopic aerial 
ladders; components; and methods," US20090101436A1, Apr. 23, 2009. 

[15] K. G. Aktas and I. Esen, "State-Space Modeling and Active Vibration 
Control of Smart Flexible Cantilever Beam with the Use of Finite 
Element Method," Engineering, Technology & Applied Science 
Research, vol. 10, no. 6, pp. 6549–6556, Dec. 2020, https://doi.org/ 
10.48084/etasr.3949. 

[16] M. K. Bak and M. R. Hansen, "Analysis of Offshore Knuckle Boom 
Crane - Part One: Modeling and Parameter Identification," MIC Journal, 
vol. 34, no. 4, pp. 157–174, Jan. 2013, https://doi.org/10.4173/ 
mic.2013.4.1. 

[17] M. G. Rabie, Fluid Power Engineering, 1st ed. New York, NY, USA: 
McGraw Hill, 2009. 

[18] "Hydraulic Valves Industrial Standard," Parker Hannifin Corporation, 
2015.