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CONTROLLER DESIGN TO HYDRAULIC SYSTEM OF THE ACCELERATED PAVEMENT TESTING MACHINE IN FULL SCALE Vargas-Fonseca G. L, Reyes-Ortiz,O.J, Camacho-Tauta, J. Geotechnical Group, Civil program Nueva Granada Military University, UMNG Bogotá, Colombia E-mails:
[email protected],
[email protected],
[email protected]
Universidad Militar Nueva Granada. Estudiante EspecializaciónII. Automatización de Procesos APLLY LOAD SYSTEM
Abstract — This paper describes the development of mathematical model with a pump and a relief proportional valve used to control the pressure of a hydraulic system. This system controls an accelerated pavement testing machine designed to simulate the fatigue of a road structure. The pressure control system was composed by an Anti-Windup PID.
Fig 1 shows the apply load system of the test road to pavements, operate through of a hydraulic system which is responsable to generate a maximum load of 8 Tons, through two hydraulic cylinders, which are connected to truck wheels (295/80R22.5). These trucks wheels are in contact with the pavement and simulate the trucks real loads over the Industriales. Universidad de los Andes Key words— hydraulic actuator, PID controller with anti-wind pavement.
UP, pavement tests, proportional relief valve, dynamic loads.
I. INTRODUCTION The fatigue analysis of roads requires full scale tests, in which as pavement structure is subject to traffic loads with amplitude, frequency and number of cycles, similar in magnitude to the road operation conditions. The Geotechincal Group at the Nueva Granada Military University developed an accelerated pavement testing machine (APT) to simulate actual traffic loads and under controlled environmental conditions. Results obtained in this tests can be used to analize the design methods of pavement structures in the country. In addition, the device allows to acquire detailed results related to the damage mechanism and the influence of different factors on the mechanic behavior of the road. [1] From the mechatronic point of view, the system needs a rapid and accurate control of the hydraulic system to manage the aplied load (up to 8 Ton) and its alternating direction on a road stretch. The solution to this requeriment is PID with antiWindup that was designed and synchronized through Simulink. The control system applies the pressure by use of a proportional pressure relief valve, verifies the controller performance and a closed loop system. As a request solution of to apply load and flow direction on the pavement, the hydraulic system was mathematically modeled through which was generated the APT loads. A PID controller was,
Fig. 1. Apply load system
The hydraulic system Fig. 2, is the responsible to generate the load over the tires, this system is composed by 4 parts: the first one is the hydraulic unit, which has a Alternating current (AC) motor connect to a variable vane pump,that produce the pressure of the system with a constant flow rate of 6 gallon per minute (gpm). The second part is the proportional pressure relief valve, which depends on a voltage reference to maintain a constant system pressure, being that the main control object. The third part is the hydraulic accumulator that allow a decrease of the flow rate peaks in the pump and a solenoid directional valve of 4 ways and 3 positions that can extended and retreat the hydraulic cylinder. The fourth part is the pressure sensor and a hydraulic cylinder, the cylinder generate the force over the trucks’ tire. The force would be equal to the pressure of system by the piston area of the hydraulic system.
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adjusted to the rotor slot, because of the centrifuge force the vanes will be always in contact with stator ring’s internal wall. The spring force of control pistons must be able to overcome some friction without enough pressure to impulsive the stator to the maximum excentric position. Therefore the pump starts with the maximum flow, until the output pressure have reached to the pressure set point. During this process, the pump performance acts like a constant pressure pump [3] . According to the variable vane pump performance , it can be obtain the mathematical equation related with pump flow rate and work pressure, the Coulomb friction was ignored and the oil was assumed as a incompressible flow, because in this mathematical model those variables not affected significantly. In base with the pumps constant pressure principle, the pump output flowrate equation is defined as: ̇
Fig. 2. Hydraulic system
III. SYSTEM MODEL The closed loop control system is showed in Fig. 3 where R(t) is the pressure reference signal given by the user, B(t) is the feedback signal from pressure sensor, e(t) error signal, Vv(t) is the controller output signal and also the plant's entry , P(t) is the plant output signal in pressure units, F(t) is the load applied to the truck wheels. In addition a perturbation signal block was added to simulate the possibles variations in pressure and caused by hydraulic bomb or an small oil volume change in the chamber of the cylinder , the oil volume change could be caused if the reaction force between pavement and wheels of the apply load system is higher than the force applied by the hydraulic cylinder
Where : is the pumps flow rate constant; is the stator rings displacement; pumps leak constant; p: system work pressure ; : volume of the output pump chamber and : Oil bulk module. The sum up of forces in the pump ring stator is: ̈
Fig. 3. Closed loop system
A. Hydraulic Pump Model The stator ring of variable vane pump mantains a specific position due to two piston of control supported by springs, the pump’s slot rotor is ubicated in an excentrical way respect to impulsive axis and it spin inside of stator ring. The vanes are
̇
Where ; control pressure of the pumps chamber; : small area of the control piston cross section of the pump; : big area of the control piston cross section of the pump; M: stator ring mass; : viscose strength coefficient; : spring stator stiffness. B. Proportional Pressure Relief Valve Model The flowrate through the proportional pressure valve is proportional to the opening hole of the output and entry of the valve, the flow rate should respond to the spools displacement. The flowrate is expressed by the equations 3 and 4: √
For the realization of the pressure control system, was required a pressure pump and the proportional pressure relief valve model, it is called Plant for practical effects [2].
(
√
)
Where : output flowrate; : entry flowrate; : decrease factor coefficient defined by the fluid energy leak through the holes; : area gradient of the control valve; output holes área of the valve; : flow density. As the valve is symmetric and assumed that the hydraulic fluid is incompressible, it can be said that the flow rate that pass through the output and entry ways of the valve are the same. The equation (4) has the square root of Pc, and it was considered as a non lineal expression. The Taylor’s theorem was used to make lineal the flowrate equation , which express that if one function in an interval gived is derived infinitely, it is possible to represent this function as a potential series [4],the series was evaluated only in the fist term so that the expression converge in and .
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After the valves flow rate equation has become lineal and it was expressed in Laplace’s terms is show like this: ( ) ( ) ( ) Where , are factors that depend of the valve’s operation point. To analyze the forces acting on the valve's spool, which has: (
) ̈
̇
Where : pressure reference ; : cross section of area spool; : spool’s mass ; : spool viscose coefficient; : spring spool’s stiffness. The output pressure of the pressure valve is proportional to the entry signal in voltage.
Fig. 6. Plant open loop response.
IV. DESING AND SIMULATION CONTROLLER Where
: pressure- voltage gain; : entry voltage.
According to the transfer functions, that were obtained from hydraulic pump equations and the proportional pressure valve, the block diagram that represent the plant is:
Fig. 4. Plant block diagram.
To the pressure control, it was designed a PID control with Anti Wind-Up , with the characteristic of be a linear controller, to easy implementation and informatic low cost . In the PID, the control signal was calculated through the error, use a proportional gain type to remove directly the existing error. Although was used an integral effect, which affect the amount of time that the error continued without being correct and a derivative effect , which anticipates the future error by the change rate error in the time.[5] One of the most common phenomenons that is showed in the PID controller is the called Anti Wind-Up, which is generated when a saturation in integral term to overcome the limits of operation of the cylinder control. To apply a change in the reference point of the control loop, the control variable could be reach the operate limit of the cylinder during the transitory response, then the system was operated like open loop, because the cylinder is in the maximum and minimum operation limit, independently of output value of the process.[6]
Replacing the parameters values in the transfer functions of the Fig. 4, and making the corresponding block algebra, the transfer function of represent the fifth order plant was obtained , equation (9), where the entry is the voltage (v) apply in the proportional valve, and the output (p) is the system’s work pressure. The controller kept the constant pressure in the hydraulic ( ) cylinder, in case of possibles perturbations. Using the control ( ) ( ) architecture that is shown in Fig. 7 and MATLAB's SISOTOOL , the PID controller was sintonized. In the design’s ( ) parameters of the controller was defined that the over-shoot ( ) less than 4% and the set time less than 2 seconds. To notice the plant’s response in case of a stage entry in the Fig 6, shows that the steady-state error, despite the fact that it has oscillation and over peaks, but it can conclude that the plant has a stable performance. Fig. 7. Control architecture.
The constant values obtained through Matlab are: K_p=2.41, T_i=0.129, T_d=0.019,, the algorithm choosen to the sintonize the controller was Ziegler – Nichols. To avoid a saturation by the controller in the control cylinder (proportional valve), was making the implementation of the Anti Windup Control technique. A. Syntonize of PID wiht Anti-Windup controller The PID’s control technique with Anti-WindUp produces a feedback with the difference between output signal amd the
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effective output signal (0-10v) to the plant. This feedback permit that the respond is nule while the control cylinder is in the limit of working, and not affect the control. On the other hand when the saturation is presented add a negative value to the integral component, and eventually the integration is annulled whileas that condition is presented. AS a result the recover of the integral componete turn faster and the control become effective. The PID’s control with Anti Wind Up architecture is showed in Fig 8. Where is the follow time constant, with values that could be as a equation 11 [6]; ( 11 )
Where
, are the PID’s sontroller constants.
Fig. 10. PID wiht Anti-Windup controller response.
To implement the Anti Wind-Up control arquichecture with the plant’s model in SIMULINK, Fig 9., the controller’s manual sintonization was realized with the constant , taking as a initial point the values obtain through the sintonization doing in MATLAB’s SISOTOOLS.
Fig. 11. Output PID with Anti-Windup controller. Fig. 8. Anti-Windup architecture. Source: A. Visioli. Practical PID Control.
As a Final test the PID’s controller with Anti-WindUp, the varitation secuence was created in the reference, which simulated the pressure change between 1Mpa and 9Mpa. The Plant’s response in case of a stage entry and the controller’s output signal are showed in Fig 12 and Fig 13.[9,10]
Fig. 9. PID wiht Anti-Windup controller simulation.
The plant’s respond with PID’s controller with AntiWind UP, is shoed in Fig 10. With the new sintonization the set time was reduced to 0.8 seconds. The controller’s output signal is between control cylinder operations limits, Fig 11. [7,8] Fig. 12. Input sequence reponse of plant A.
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ACKNOWLEDGMENT The authors would like to thank Nueva Granada’s Military University, Civil Engineer faculty for the economic support with IMP-ING-1575 project. As well thanks to Eng. Mauricio Duque Escobar for his constructive comments through the project. REFERENCES O. Reyes, J. Camacho, “Influencia de la granulometria en la resistencia al ahuellamiento de mezclas asfálticas,” Colombia, Ingeniería & desarrollo ISSN: 0122-3461, Vol:23 pp 26 – 42, 2008. [2] Zou Kai-feng, Chen Yonglong, “Dynamic Trait Analysis for Variable Lamina Pump of Limit Pressure” J. Science & Technology Information, pp.116-117, 18th 2008. [3] Li Qibo, “Electro-hydraulic proportional and digital control system” China Machine Press, May 1997. [4] K. Ogata, Dinámica de Sistemas. México: Prentice-Hall.1987 [5] Faudzi A., Mustafa N., Osman K., Azman M., y Suzumori K., GPC Controller design for an intelligent pneumatic actuator. Procedia Engineering, 41, 657-663. (2012). [6] A. Visioli. Practical PID Control. Springer. 2006. [7] C. Smith & A. Corripio , Principles and practice of automatic Process Control, Wiley, New York second edition, 2005 [8] Duque, Mauricio. Gauthier, Alain. Control por computador. Control de procesos continuos utilizando un sistemadigital. Marzo 1999. Universidad de los Andes. [9] H. E. Merrit, “Hydraulic control systems”, New York, John Wiley Inc, 1967. [10] Bai Ji-zhong, Xie Ai-guo, YuXin-hua, Zhou Li-kun, “Simulation Model of Hydraulic Speed Control System and Its Parameters Identification Based on Resilient Adaptive Particle Swarm Optimization Algorithm.” Power and Energy Engineering Conference (APPEEX), Asia-Pacific, pp 1-4,March 2010. [1]
Fig. 13. Controller output.
V. CONCLUSION A hydraulic system was developed able to simulate the loads of vehicles on the pavement with a exact precision, also allows making real scale test in any type of pavement. With the PID controller with Anti Wind Up implementation, is possible make the work pressure control over the apply load system with stable and faster way. To analyze the development of closed loop control to pressure through SIMULINK, was showed a instability at the moment to choose the work operation frequency The APT's mechanical design system, permitted that the mathematical modelling only depended of hydraulic system, because of that the PID's controller with Anti Wind Up was implemented, The PID produced a economic savings because not needed a Datta Adquisicion complex system.
