Electro-hydraulic proportional system real time tracking control development based on pulse width modulation method

The present work is directed to develop the dynamic performance of an electro-hydraulic proportional system (EHPS). a mathematical model of (EHPS) is presented using electrohydraulic proportional valve (EHPV) by the aim of Matlab-simulink which facilitate the simulation of the hydraulic behavior inside the main control unit. Experimental work is done and closed loop system is designed using linear variable displacement transducer sensor (LVDT). The controller of the system is an Arduino uno which is considered as the processor of the system. The model is validated by the experimental system. The study also presents a real time tracking control method based on pulse width modulation by controlling the speed of the actuator to achieve position tracking with minimum error.


INTRODUCTION
The proportional valve is a valve which produces a proportional output to an electronic control input or a valve operates by proportional solenoids instead of on-off solenoids. It can be classified to three types; pressure control valves, flow control valves and directional control valves.
The pressure control valves are designed mainly to control the pressure while the proportional flow control valves are designed mainly to control the flowrate but Proportional directional valve is used to control both the flow direction and the flow rate.
Many studies dealt with the proportional valve investigations, Vaughan-ND et al. [1] presented a nonlinear dynamic model of a high-speed direct acting solenoid valve the model accurately predicted both the dynamic and steady state response of the valve to voltage inputs. Simulated voltage, current, and displacement results were presented which agreed well with experimental results.
Lai-JiingYih et al. [2] proposed an adaptive self-tuning controller to enable a hydraulic proportional valve to achieve accurate set-point flowrate control. the performance of the closed-loop system was very robust as the system response remained the same under various operating conditions. M. F. Rahman, et al. [3] began the first step of converting a conventional on-off solenoid into a proportional solenoid. They studied the dynamic behavior of a conventional solenoid by letting the simulation depending on linear magnetic principle, by using the simulation package SIMNON. A comparison was done between the results from simulation model and experimental work.
Niksefat-Navid, et al. [4] study the development and experimental evaluation of a hydraulic force controller, using nonlinear Quantitative Feedback Theory (QFT) design method. The designed controller was implemented on an industrial hydraulic actuator equipped with a low-cost proportional valve Elmer-KF, et al. [5] presented a generic non-linear dynamic model of a directacting electro-hydraulic proportional solenoid valve. The model accurately and reliably predicted both the dynamic and steady state responses of the valve to voltage inputs.
Simulated results were presented, which agreed well with experimental results.
Dasgupta-K, et al. [6] studied the dynamics of a proportional controlled piloted relief valve through bond-graph simulation technique. The simulation results were also verified with experimental results.
Chu-MingHui, et al. [7] studied the nonlinear model of a variable displacement axial piston pump (VDAPP) with a three-way electro-hydraulic proportional valve (EHPV) which controlled the swash plate actuators. The time response for the swash plate angle was analyzed theoretically by the simulation model and experimentally, and a favorable model-following characteristic was achieved. The proposed neural controller which conducts nonlinear control in VDAPP, enhanced adaptability and robustness, and improved the performance of the control system.

MATHEMATICAL MODEL
The proposed system is mathematically done by the aim of Matlab-simulink and the system components configuration are selected as same as the experimental components.

hydraulic pump
The type of the hydraulic pump used in the electro-hydraulic system is a fixed displacement gear pump, operates with nominal speed of 600 rpm and maximum output flow rate of 6.05 liter/min. The pump is driven by an AC electric motor operates with 220 Volts, 50 Hz, and 1.5 kW.

relief valve
The relief valve is used to control the pressure in the hydraulic systems to protect its individual elements, pipes and hoses from over pressure problems, it adjusted at a pressure of 60 bar.

Proportional directional valve
The 4/3 electro-hydraulic proportional directional valve fig (2) is a Hydraulic Ring manufacture of type NG6. It has maximum operating pressure of 315 bar, its valve spool has zero overlap, and its motion is controlled by two electrical proportional solenoids.

Hydraulic actuator
The hydraulic actuator used in this study is a double acting steel with cam for operating the limit switch with diameter of 32/22 mm area ratio 1.6:1 and max pressure of 160 bar.
The flow rate equation: Continuity equations through the hydraulic actuator: These equations are modelled in Matlab-simulink to facilitate the study of fluid behavior through the hydraulic circuit and also a controller is designed by the aim of Simulink tool.  (PID) controller which is used to adjust and resolve the error of the system, it controls the system by evaluate the feedback of the system and compensate the system error, the mathematical equation of the PID controller is: Where () ut is the controller output, () et is the system error,

EXPERIMENTAL WORK
The experimental work is done by using the same components configuration as mentioned in section (3) which is the same as the mathematical model configurations.  10 Ω resistors are used in series to reduce the limitation of the signal voltage to 5V DC.
A new method of controlling the system is proposed in this study, by experimentally testing the system by means of oscilloscope connecting to the two terminals of the proportional valve, it has been found that the actuator response depending on changing the pulse width modulation (PWM).

RESULT AND DISCUTION
The mathematical model is validated by the experimental work by varying the input signal with constant input 50 mm, step input 70 mm, square signal 70 mm and sinusoidal signal with amplitude 30 mm, bias 30 mm and frequency (0.5 rad/sec) .08 HZ, these results are shown in fig (10,11,12, and 13) as it shown the model has a good agreement with the experimental result in the constant, step and square signal inputs.  The mathematical model helps in studying the fluid behavior inside the hydraulic circuit which is calculated.

CONCULUSION
The study presented a new method for controlling the electro hydraulic proportional actuator by controlling the speed of the actuator this is done by controlling the band width modulation signal that operates the two coils of the proportional valve, also this study presented a mathematical model of the system and its transfer function, also a controller of the model is done by (PID) controller.
This study also facilitates to study the pressure behavior inside the hydraulic circuit.