DYNAMIC ANALYSIS OF HYDRAULIC MECHANICAL SYSTEM USING PROPORTIONAL VALVE Chuyên ngành: K Mã s : 60 52 01 14... This paper presents the dynamic analysis of a mechanical - hydraulic syste
Các y u t n quá trình u khi ng
Có 3 y u t chính ng trong quá trình u khi ng c a m:
- l n ti t di n A x : H d ch chuy n x c a con t
- Nhi c t: Nhi s quy nh t c a dòng l t
Hàm Sine 0.157Hz, 0.628Hz, 3.14Hz
Xy lanh Yuken: hành trình L 0
K P =0.6256, K I =1.45, K D =-0.09447 mô hình tính vào mô hình kín Dùng K P =0.625, K I =0, K D =0, cho K I
K I =0.009, K D t là hàm Step, Pulse và Sin
Hình 5.22, 2.3mm lên 0.17 Hình 5.23, Sa 1.3mm, lên 0.44 4s
( 0.07mm ) và phi t c ào hàm Sine c
( 11.4mm) ra là xung tam giác
T LU N VÀ NG PHÁT TRI TÀI
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[3] Radu, Iulian Radoi “Theoretical And Experimental Investigations Regarding The Dynamic Performances Of The Servo-Solenoid Directional Valve”
U.P.B Sci Bull., Series D, Vol 74, Iss 2, 2012
[4] R Amirante, P.G Moscatelli, L.A Catalano “Evaluation Of The Flow Forces On A Direct (Single Stage) Proportional Valve By Means Of A Computational Fluid Dynamic Analysis” Energy Conversion and Management 48
[5] R Amirante, A Lippolis , P Tamburrano “Theoretical And Experimental Analysis Of A Coupled System Proportional Control Valve And Hydraulic Cylinder” Universal Journal of Engineering Science 1(2): 45-56 2013
[6] Tamer M Menshawy, Mohamed A Moghazy, Ahmed H Lotfy
“Investigation of Dynamic Performance of an Electro-Hydraulic Proportional System” 13th International Conference on Aerospace Sciences & Aviation Technology, ASAT- 13, May 26 – 28, 2009
[7] Adam Bure_ek1, Lumír Hružík1 and Martin Vašina “Simulation Of Dynamics Of Hydraulic System With Proportional Control Valve” EPJ Web of Conferences 114, 2016
[8] T X Bo, Indrawanto, and H Yanada “Sliding Mode Control of Single- Hydraulically Actuated Manipulator” International Journal of Mechanical &
Mechatronics Engineering IJMME-IJENS Vol: 11, No: 05 2011
74 [9] Mohga Abd Alrhman, Muawia Mohamed Ahmed “ Design of a Tuned PID Controller for a Hydraulic System” International Journal of Science and Research (IJSR) 2013
[10] Pornjit Pratumsuwan and Aphaiwong Junchangpood, “ Force And Position Control In The Electro-Hydraulic System By Using A Mimo Fuzzy Controller” IEEE 8th Conference on Industrial Electronics and Applications (ICIEA) 2013
[11] S Md Rozali, MF Rahmat, N Abdul Wahab, R Ghazali, and Zulfatman
“Pid Controller Design For An Industrial Hydraulic Actuator With Servo System”
Proceedings of 2010 IEEE Student Conference on Research and Development (SCOReD 2010)
[15] Xuan Bo Tran, War Htun Khaing, and Hideki Yanada “Effect of Friction Model on Simulation of Hydraulic Actuator” Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, Vol
[16] Xuan Bo Tran, Nur Hafizah, and Hideki Yanada “Modeling of Dynamic Friction Behaviors of Hydraulic Cylinders” Mechatronics, Vol 22, No 1, pp 65- 75, 2012, ISSN:0957-4158
[17] Xuan Bo Tran, Akinori Matsui, and Hideki Yanada, Effects of Viscosity and Type of Oil on Dynamic Behaviors of Friction of Hydraulic Cylinder, JFPS International Journal of Fluid Power System, Vol 3, No 2, pp 16-23, 2010 ISSN:1881-5286
[18] JOWN WATTON, Fundamentals Of Fluid Power Control,
[19] M GALAL RABIE, Fluid Power Engineering, USA: McGraw-Hill companies,2009
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Email: thanhluanbk@hcmut.edu.vn
THE INTERNATIONAL CONFERENCE ON ADVANCES IN COMPUTATIONAL MECHANICS ACOME 2017 August 02 - 04, Phu Quoc, Vietnam
SYSTEM USING PROPORTIONAL VALVE
INTRODUCTION
Hydraulic systems are widely in industry Providing powerfull force and having small size are the advantages of hydraulic system in comparative with electric systems
Proportional valves are significantly improved in frequency response, accuracy, feedback system and dead band Those improvement reduce the distinction between servo valves and proportional valves Proportional valves can controll actuators with more flexibility and lower cost than servo valves Therefore, proportional valves are suitable to industrial applications The only difficulty is the control of hydraulic systems with unstability
A lot of studies on proportional valves focus on the dead point of valves [1], dynamic analysis of coil of proportional valves [2], dynamic response of valve [3], dynamic analysis of fluid flow via valves [4] Those studies just concentrate on the characteristics of proportional valves without any interaction with actuators, hydraulic-mechanical systems
2 There are also some studies on hydraulic systems using proportional valves such as: the theoretical and experimental analyses of symmetric-two-cylinder systems using proportional valves [5], study on the dynamical properties of hydraulic power systems [6], [7] In these studies, the mathematical models are simplified with assumption of linearization of the hydraulic system Actually, hydraulic systems works with nonlinear characteristics, therefore the linearization is only accepted within a certain range and this assumption reduces the authenticity of systems
The control algorithms of hydraulic systems using proportional valves are recently studied Sliding mode control is applied to a lifting arm with one cylinder [8] Adaptive control is used for control fluid flow rate in a proportional valve [9] Mino fuzzy is applied to force and position control of hydraulic cylinder [10] PID control is also used to improve the control quality of hydraulic cylinder using proportional valve [11] Generally, recent studies are performed with constant loads rather than variable load as in real systems The studies also ignored the leakage, elasticity of fluid and damping of system
This paper presents a study of a hydraulics-mechanical system using a proportional valve and adhering to the real characteristics of the system in order to accurately describe the system response Firstly, the differential equations of the dynamic hydraulic system with variable load is established The equations represents the relationship between flow rate and pressure, the interaction of the valve with the hydraulic cylinder, the variable load causing system instability The mathematical model is simulated using the Matlab Simulink to compare the position response of the cylinder according to the working time and the displacement of the cylinder, with a PID controller The experiment is performed to validate the control Research has clarified the dynamics characteristics of mechanical hydraulic systems with linear change loads
This study is the first step in studies of vibrator power using proportional valve with the accuracy ± 0.2 mm to test vehicle damping systems or vibration isolation systems It is necessary to reducing cost of systems.
EXPERIMENTIAL SYSTEM
Figure 1 shows the schema of hydraulic-mechanical system using proportional valve The mechanical system includes a linear spring and a slider, which causes varied load Hydraulic system is a linear cylinder actuated by a proportional directional control valve and controlled by a displacement transducer and a PID controller The maximum flow rate of pump is set at 32 l/minute at rotating speed of 1500 rpm The pump pressure is set at 350 bar The proportional valve (PONAR - made by Netherlands) is a directional control valve with 4 ways and 3 positive overlaps Table 1 describes technical characteristics of the valve The areas of piston head and piston rod side correspondingly are 0.001963 m2 và 0.001563 m2 Maximum stroke of cylinder is 0.25m The variable resistor displacement transducer has resolution 0.01 k / mm and accuracy 0.05%
TABLE 1: SPECIFICATION OF THE PROPORTIONAL
Resistance of max hot solenoid coil 8.1
The differential equations of the dynamic hydraulic system without considering friction is :
M total mass of piston and load
Piston displacement, damping coefficient spring stiffness,
A 1 , A 2 areas of the two chamber of the cylinder, P 1 , P 2 pressures inside two chambers of the cylinder
Figure 1: Schema of the hydraulic – mechanical system
V = V + A x total volume of the first chamber,
= + total volume of the second chamber,
V 0 and L 0 dead volume and maximum stroke, effective bulk modulus,
Q 1 and Q 2 fluid flows at head - side and rod – side
Flow rate of the valve can be considered as
Width of the valve port, = , with D – diameter of the valve port spool displacement, overlapping length,
P s Supply pressure from the hydraulic pump
Assume that the displacement of spool is proportional to the controlling current i in the coil of proportional valve
When > 0, from Eq.4 and Eq 5, we have
Substitute Equations 6 and 3 into Eq 2 we have
The state-space equation of the system is
The schema of PID control system is:
Figure 2: The schema of position control system with PID controller
The mathematical model is simulated using Matlab-Simulink R2014a
The solution method is Ode45 (Dormand-Prince) The parameters used in the system are given in Table 2 The parameters Kp, Ki, Kd are chosen based on the trial and error method
In Figure 4, the system responds the displacement from 50 mm to 150 mm with settling time about 8 seconds In Figure 5, the system responds from position of 5 mm to 250 mm with a settling time more than 9 seconds and oscillation at 250 mm Input signal of Figure 4 and 5 are step signal The simulation results show that the system has a short transient response time, however with a long settling time and an error less than 0.2 mm
1 Head side area of cylinder A 1 m 2 0.0019625
2 Rod side area of cylinder A 2 m 2 0.0015826
7 Gain of proportional valve K i m/mA 0.55
11 Damping coefficient of Spring B lx N.s/m 3500
13 Diameter of the valve port D m 7.26 x 10 -3
Figure 3: System with PID controller
Figure 4: Response of the system with k p = 0.96, k i = 0.005, k d =0.01
In figure 6, pulse input has amplitude 200mm, period 8s and pulse width 50% of period
This figure shows that error of retract stroke is larger than extend stroke Figure 7 illustrates response with since signal which has frequency 0.628 rad/sec and amplitude 80 mm, it is clearly to see that simulated signal is later than designed signal
Figure 5: Response of the system with k p = 0.95, k i = 0.0009, k d =0.01
Experiments are conducted to validate the analytical results obtained in the simulation The displacement and controller parameters used in experiments are the same with the ones used in simulation The experiment uses the PCI card Ni-6221 and computer to control the proportional valve Figure 7 is the set up of the experiment Experimental results show that the settling time of 2s (Figure 8) and 4s in Figure 9 Through figure 8, 9 and 10, Transient response is faster than in simulation (settling time is shorter) In figure 11, the output signal of experimental system is the same phase with the input signal However, the system fluctuation is higher than simulation system about 0.5 mm
Figure 6: Response of the system with k p = 0.95, k i = 0.0009, k d =0.01
Figure 7: Response of the system with k p = 0.95, k i = 0.0009, k d =0.01
Figure 9 : Response of the system with k p = 0.96, k i = 0.005, k d =0.01
Figure 10: Response of the system with k p = 0.95, k i = 0.0009, k d =0.01
In this study, the mathematical model of hydraulic-mechanical systems using proportional valve with linear variable load is simulated on a Matlab - Simulink The system's displacement is controlled using a PID controller The mathematical model and its simulation are performed without considering the friction PID parameters obtained from experiments The experiment of the system shows that the established mathematical model together with its simulation can describe the dynamic characteristics and responses of the systems For further studies and for application, The speed and force controls are also need to be studied for a total research in this matter
Figure 11: Response of the system with k p = 0.95, k i = 0.0009, k d =0.01
Figure 12: Response of the system with k p = 0.95, k i = 0.0009, k d =0.01