A Closed-loop Control for Swing System and Energy Regeneration Analyses of the Multi-system of Grasp Steel Machine

Facing the environment problems, the improvement on the efﬁciency of the construction machinery is highly demanded, meanwhile, large energy wasted in hydraulic slewing systems, reaching the desired speed slowly and vibration in braking are widespread. In this paper, a closed-loop control swing system (CCSS) is proposed. In this system, bidirectional variable pump controls the change of oil flow by programmed software algorithm, instead of pilot actuated reversing valve, which signiﬁcant ly improves the efficiency of hydraulic circuit. Based on the model structures, we develop a hydraulic swing prototype and verify the advantages of our design means of theoretical calculation and simulation . It verifies that CCSS and based on accumulator slewing system(BASS) can respectively save 875.5 KJ and 347.2 KJ more than OCSS with operational weight of 100 tons grasp steel machine, which can support theoretical basis for energy conservation and environmental protection to study the new type of engineering machinery.


Introduction
Resource shortages and environmental pollution are the increasingly urgent global problems that have encouraged the development of energy-saving [1,2] and emission-reduction technologies [3,4]. It is meaningful to investigate the energy saving of construction machinery, especially for grasp steel machines equipped with hybrid power system due to their wide application while extremely low efficiency [5][6][7][8]. The hydraulic grasp steel machine mainly consists of chassis, upper structure and work attachment. The chassis using for a stable base includes crawler and propel drive. Upper structure that is mainly composed of swing machinery and revolving platform is responsible for rotation and transportation. Work attachment being used to perform grab operation consists of boom, arm, crab bucket and associated cylinders, etc.
Swing motion is one of fundamental motions of a hydraulic grasp steel machine, which accounts for 35% of the grasp steel machine's total operational time and is driven by hydraulic motors [9]. The characteristics of swing motion are frequent acceleration and deceleration. Sometimes, the problem of the swing motion operation is of extreme roughness and jerkiness, which is mainly related to hydraulic and mechanical properties of the actuators. Mechanical dampers, such as a viscous damper or a coulomb friction damper, are frequently used to reduce vibrations in construction machinery [10]. However, the additional mechanical dampers installed into the swing mechanism may increase cost and the weight of machinery as well as sensitivity [11].
For these reasons, only by altering the hardware mechanism may not be an adequate solution to reduce the swing motor vibration [12].
In 1996, Sepehri firstly studied the gear backlash and stick-slip friction in hydraulic swing motion [13]. In the later time, researchers pay attention to the open-loop control, which is more applicable than closed-loop control algorithm in practical application [14]. The swing inertia of the upper structure was separated into two parts: the calculation and the estimation. The function of calculation is to acquire the position of boom, arm and crab bucket, which can be measured by sensors, and another part is estimated by the payload in the crab bucket. This kind of robust control technique can realize high performance in swing velocity tracking, but it is not applicable for industry. Furthermore, it is difficult to obtain the displacement of cylinder by mounting the sensors [15]. The sliding mode observer and sliding mode control are designed to provide robust tracking performance, which reduce the serious self-exciting vibration of the electric swing motor due to the time-varying swing inertia caused by various working conditions. But the swing motion is discontinuous, it can't satisfy the practical application. Xiao et al. [16] proposed a new hydraulic system for the swing system with a hydraulic accumulator and two flow control valves. This system had some similarities with the presented system in a patent [17]. When the swing system decelerates, the flow rate from the variable displacement hydraulic motor is controlled by the flow control valve and charged to the hydraulic accumulator.
Besides, the author was also concerned about the oscillation and energy regeneration efficiency of the proposed system. They designed a control strategy based on a PID controller. Therefore, the proposed system had a much lower cost than the electric ERS system and the energy regeneration efficiency could reach up to 33.4%.
Currently, hybrid technology is regarded as one of the most effective measures to solve the energy waste problem. Heavy vehicles such as grasp steel machines with open-loop control have the characteristics of high stop-and-go duty cycles and high power flow braking energy, which need to find an efficient way to store and reuse the braking energy [18]. In many hybrid power options, lithium-ion battery and fuel cell have the characteristic of high energy density and are well suitable for light vehicles.
However, the high internal resistances and handling the wasted battery are major obstacles for commercialization [19]. Both batteries in hybrid vehicles can only marginally recycle the braking energy, and high frequency charging and discharging may lead to overheating and battery destruction [18,20]. For another energy recovery component, hydraulic accumulator that has the characteristic of high power density can provide high power for acceleration and also recycle more efficient energy during braking [20]. However, the relatively lower energy density brings the packaging limit about the increase of accumulator size [18]. Another reason for reducing fuel consumption is that the upper structure is driven by the electric swing motor, which is more efficient than the hydraulic motors used in conventional hydraulic excavators. Furthermore, the upper structure kinetic energy lost in conventional excavators can be regenerated through deceleration of swing motor [21]. If electric motor is applied to the swing system, there will be a great change in power plant, but it will increase some difficulty in design and implementation of hybrid system.
Aiming at solving the problem of OCSS, this paper presents a closed-loop control algorithmto improve the swing motion performance of grasp steel machine, which are organized as follows: the configuration and principle of all multi-system models are illustrated in section 2, the simulation and analysis is presented in Section 3, and conclusions are drawn in Section4.

The modeling of multisystem 2.1 Configuration of the original swing system
The OCSS has widespread use in slewing system of grasp steel machine because of relatively simple structure. Under the open-loop control mode ,the functions of tank include cooling system oil and precipitating impurities. However, it was the air that easily enters the system, which may lead to inaccurate action of actuator, especially the throttle valve causes great energy losses.
In addition, during braking, the mechanical vibration is of extremely sharp, which is easy to generate the hydraulic impact.  When pilot control reversing valve 2 applies to the right position, slewing platform reverse rotation. Combining the oil stored in accumulator during overflow recycling and braking with pump to drive rotary motor, which reduces the outlet power of the pump.

Modeling of closed-loop control slewing system
In short, the function of CCSS is that a hydraulic pump drives hydraulic motor. Compared with OCSS, the reversal, forward and braking can't be realized by the valve. The rotation direction of swing motors is determined by the directional function of swing pump, and the rotation speed is proportional to the amount of swing pump's volumetric displacement. When the variable displacement pump is positioned in a neutral position, there is no volumetric fluid flowing to the swing motor. Meanwhile, the turning of motor is controlled by the direction of the swash plate of variable pump, the speed of motor is controlled by the angle of swash plate of variable pump. In a word, the variable pump and variable motor are important. It is inevitable to encounter the problem of huge rotational inertia and inaccurate angle when large is turning. Therefore, applying the CCSS to slewing mechanism can realize stepless speed regulation in the braking and starting processes ,which can reduce impact and achieve energy recovery.
The model of CCSS is depicted in Fig. 4. The bidirectional variable pump 2 [22] and quantitative pump 10 are controlled by a variable motor 1. The leakage and pressure of whole system are decided by quantitative pump 10 and overflow valve 7. A quantitative pump 10 supplies oil through piloted pressure reducing valve and check valve for CCSS system to keep the pressure in each circuit, which can prevent cavitations. The pump control behavior is independent of external operating parameters due to the fact that signal symbol substitutes variable displacement control mechanism in constant power pump, which is diverged from the charging pump flow through a piloted pressure reducing valve. If there is a large load impact, the balancing valve 3 and 4 will protect pressure equilibrium. Electromagnetic directional valve 9 is free to control the motor on and off. At the end of braking, inertial kinetic energy will make hydraulic motor reversal, which causes vibration and noise. At the same time, big resilience force leads to backswing for many times, and it may cause shock. For this kind of situation, the defensive valve 9 can prevent rebounding in hydraulic rotary system and make hydraulic motor switch on or shut down. In a word, this configuration allows a highly dynamic and precise control of the pump delivery flow rate according to the input current demand. Thus, it not only reduces the system losses, but also easily and accurately regulates the flow to the swing motor as well as the rotation speed of the motor. During the braking operation, the upper structure of hydraulic shovel tends to continue to rotate until it is fully stopped due to the huge swing inertia of moving components. It is noteworthy that the setting of the time-varying swing inertia requires special processing, which can be done through analog signals and signal feedback. To sum up, compared with existing system, the proposed CCSS for swing motion of hydraulic is simpler as it is controlled by control device instead of manual adjustment system. In the next, we will demonstrate new system's advantages through simulation on a prototype swing unit of a hydraulic grasp steel machine whose operational weight is 100 tons.

3.Mathematical models
In the CCSS, the change of the variable in the variable pump depends on the swash plate swing angle of the pump which is changed by a hydraulic cylinder controlled by a proportional valve or a servo valve.
Compared with the slewing transmission mechanism of the steel grabber, the dependent variable mechanism not only has a small inertia, but also has a fast response speed. Therefore, the following derivation is a mathematical model from the swash plate swing angle of the variable pump to the motor output angle.
In order to facilitate the establishment of the modeling of closed-loop control slewing system, we make the following assumptions. The speed of the pump is constant, the leakage of the pump and the hydraulic motor is laminar flow, the oil return pressure of the casing is atmospheric pressure, and the leakage of the low pressure cavity into the casing is ignored. Because the connecting pipeline is hard and short, the pressure loss, fluid mass effect and dynamic changes in the pipeline can be ignored. The two pipes are exactly the same, the total volume of the two chambers composed of the pump, the motor and the pipe are equal, the temperature and volume elastic modulus of the oil in each chamber are constant, and the pressure is uniform and equal. There is no hysteresis in the pressure and flow of the replenishment system, ignoring the influence of instantaneous load changes. It is considered that the refueling pressure is constant, that is the low cavity pressure during work, and only the high pressure cavity pressure changes. Because the rigidity of the connection structure between the hydraulic motor and the load is very large, the influence of the structural flexibility is ignored. The input signal is small, no pressure saturation occurs. There is no pressure shock in the pipeline, and its pressure does not exceed the pressure of the safety valve The displacement equation of the variable pump is calculated as follow.
where kp is the displacement gradient of variable pump, r is the swing angle of variable pump variable mechanism.
The flow equation of the variable pump is calculated as follow.
where QP is the output flow of variable pump, ωp is the angular velocity of variable pump, Cip is the internal leakage coefficient of pump, P1 is the pressure of high pressure pipeline, Pr is the charge pressure of low pressure pipeline and assumed to be a constant. Cep is the leakage coefficient of pump.
Since Pr is a constant, by substituting Eq. (1) Where Ctm is the total leakage coefficient of hydraulic motor, which equal to Cim plus Cem.
The torque balance equation of motor and load can be described as: Where Jt is the total inertia of motor and load that is converted to the motor shaft, Bm is the total viscous damping coefficient of the motor and the load converted to the motor shaft.
The Eqs. (3), (5), and (7) are the three basic equations of the closed hydraulic system by pump-controlled motor and fully describe the dynamic characteristics of it.
The transfer function of the closed hydraulic system by pump-controlled motor can be obtained from the Eqs.
(3), (5), and (7) as follow: Where Ct is the total leakage factor and equal to Ct plus Ct. In Eq. (8), the factors such as inertial load, viscous friction load, elastic load and oil compression and motor leakage are considered. But the actual system load is often relatively simple, and some influencing factors can be ignored according to the specific usage. The load of the servo system is dominated by inertial load in many cases, and there is no elastic load or the elastic load is very small and can be ignored. In general, there is no elastic load, hydraulic motors act as actuators in Servo system. Therefore, it is assumed that there is no elastic load(G=0).
In addition, the Bm is very small, the Dm 2 /Ct is much larger than Bm. The Eq. (8) can be simplified as: Where ωh is the hydraulic natural frequency, it described as: Where ζh is the hydraulic damping ratio and described as: The transfer function of the hydraulic motor shaft angle to any external load torque, and also it's the dynamic flexibility of the system can be described as: And then, Eq. (14) can be rewritten as:

Moment of resistance in rotary (1) Wind resistance torque
Mhuifbi is the rotational resistance torque on arm and bucket caused by wind, which is defined as follows: Where Fhuifbi is wind load of arm and bucket rod, Cbi is wind power coefficient, if q1×D 2 < 3, Cbi = 1.2, D is chord diameter. The structure of the filling percentage, φ=0.3, Wind reduction factor, η= 0.575, Lbih is the height of cross section of movable arm and bucket rod, L is arm length, Xbi is the center of gravity position.
Mhuitai is the rotational resistance torque on slewing platform caused by wind, which is defined as follows: Where Fhuifai is wind load, C is wind power coefficient, C = 1.2, Stai is turntable lateral windward area, Xtai is turntable lateral centroid position.
Mhuifq is the moment of resistance caused by wind, which is defined as follows: Where Fhuifq is wind load, C is wind power coefficient, C = 1.3, Sq is load windward area, R is amplitude.
Where φ is the angle between the raceway and the level surface, , K is a factor, considering a axial clearance, the number of bearing roller will reduce, thus the maximum load on rolling element bearing will increase, K = 4, Fhui is rolling friction coefficient, fhui = 0.0025, Dhui is roller diameter.
(3) Inertia resistance moment According to formula above to process calculating and decide which version of the weight of 100 tons grasp steel machine to choose. The most unfavorable condition of rotary mechanism is that both rotating and grabbing happen simultaneously. In addition, actuator still needs to grab something in maximum weight. The related parameters can be shown in Table 1.  The requirement of choosing appropriate accumulator can be listed as follow: In a working period, the accumulator collects all the overflow and braking energy as much as possible. At the same time, releasing the absorbed energy to achieve a high energy recycling efficiency. Meanwhile, due to the limitations of the layout space of grasp steel machine, accumulator with light weight and small volume should be chosen as far as possible.
P2 is determined by the peak pressure of the whole system, and it is 26.4MPa. As auxiliary power supply, P1 is generally equal The parameters of the main hydraulic components in mode can be shown shown in Table 2. Table 2 Parameters of the proposed model The response is rapid in CCSS, the upper structure can turn to cargo location fast, then catch and unload accurately. The driver is easy to operate and improve the efficiency greatly. When grasp steel machines are used to carry and dump oil, sand and other materials in mines, quarries, and construction sites, the swing operation of upper structure is quite frequent, acceleration and deceleration time is quite short. So it is required that the speed control system should have quick speed response and avoid motor torque jerk and speed overshoot to ensure the driver's comfortability [23].

Fig. 5 Speed characteristic curve of motor
As shown in Fig. 6, the red curve is the inlet pressure of pump in OCSS. When the time from 0 to 7s, the motor is in forward condition and the inlet pressure of pump is 264 bar. When the time from 7 s to 15s, movement at a constant speed, the inlet pressure drops to 63 bar. The pressure curve in motor reversal is the same as forward. The larger changes of pump inlet pressure affect hydraulic components and cause higher calorific value, which may reduce service life of rotary system. However, the maximum differential pressure of pump in closed system is 261 bar and then it will keep at 15 bar after 2.5 s.
In general, the maximum pressure differential that is generated on both outlets of pump in CCSS is 256 bar, which is smaller than the pressure of pump in OCSS. The duration time of maximum pressure difference is 4.1s, that is much shorter than OCSS.
At the duration time, the minimum pressure value is 54 bar. Furthermore, there is an obvious jitter from 7.1 to 8.6s in the OCSS.
From the above analysis, we can conclude that small hydraulic components in CCSS withstand less impact and produce less heat, which benefit to prolong the life of the whole system, furthermore, making the rotary motion more smooth.

Fig. 6 Pressure characteristic curve of variable pump
As shown in Fig. 7, the inlet and outlet pressure curve of motor in OCSS is obvious jitter, which causes unstable movement of slewing platform in the 7.1-8.6s and 32. 2-34.3s. This kind of situation will have impact on stability of hydraulic components and system. However, in the CCSS, the duration of maximum pressure differential of the motor is 4.7 s. Comparing with the 5.3s in the OCSS, the motor has a more efficient response. In addition, as the direction of the motor in the OCSS is controlled by the reversing valve, the characteristic combination curve shows that the braking process keeps for 10s or so. In a word, the pressure curve of motor is smooth. Without an obvious dithering phenomenon, hydraulic components receive slight impact and produce less heat, which contributes to extend service life of the whole system. At the same time, the stability of turning motion is improved obviously.

Fig. 7 Pressure characteristic curve of variable motor
Putting the identified accumulator parameters into rotary energy-saving model and processing simulation, it will obtain the characteristic curve of gas volume and gas pressure of accumulator as shown in Fig. 8. During the time from 0 s to 6.28 s, slewing platform needs enough starting pressure to be driven from static to movement, but one part of oil comes from pump is used to drive rotary motor, the other changed into the form of energy will be recovered into the accumulator. Therefore, the accumulator pressure increases, the gas volume reduces accordingly. When the motor speed turns to uniform velocity during the time from 6.3 to 14.9 s, both gas pressure and volume in accumulator remain the same. As pilot control reversing valve turns to middle position during the time from 14.9 to 24.9 s, motor is characterized as a pump, and the hydraulic accumulator is full of oil by dynamic torque of rotary platform. Then the accumulator pressure increases and gas volume reduces obviously. When the slewing platform reverse rotation in no-loading condition during the time from 24.9 to 39.9 s, motor rotary is driven by accumulator and pump together. As directional control valve turns to middle position during the time from 39.9 to 49.9 s, motor is characterized as a pump again, and the hydraulic accumulator is also full of oil by dynamic torque of rotary platform.
(a) Pressure characteristic curve (b) Volume characteristic curve As the calculation above, the energy loss of OCSS is bigger in the process of excavator braking, and then the overflow energy in startup phase is also as high as 350KJ. As shown in Fig. 9, the energy curve of OCSS that whether adopt accumulator shows a trend of increasing, then the pump needs to provide more energy for the system. During the time from 0 to 15 s, the speed of rotation platform increases from 0 to the maximum speed 3934 r/m. The energy curve is rising and rising range in OCSS is more than that in BSSS. During the time from 15 to 25 s, the energy curve tends to straight line and the slewing platform in the braking stage, but the energy is wasted during the period. During the time from 25 to 45 s, the energy curve keeps rising and rising range in OCSS is also larger in comparison to BASS. When the CCSS is in full load or empty load, the energy curve is rising up and down, then rising again. At the 20th s in braking stage, there is a maximum power outlet. After that, energy curve starts to decline rapidly. Through digitization curve and MATLAB calculation, the total outlet power of CCSS is 5032.2 kJ. The total output power of OCSS and BASS is respectively 6327.7 kJ and 5638 kJ. It is verified that the energy waste more in the stage of starting and braking in OCSS under the same speed. Therefore, the CCSS is more energy efficient than OCSS and BASS.

Fig. 9
Energy curve of Hydraulic slewing system

5.Conclusion
In this paper, a set of closed-loop control swing circuit is proposed and verified in a hydraulic grasp steel machine that operational weight is 100 tons. Compared with the OCSS and BASS, the motor speed curve of CCSS is almost "double rectangle", which can achieve target speed fast and accurately whatever the loading condition is. Meanwhile, it improves the working efficiency. Moreover, there is not an obvious dithering phenomenon in motor pressure curve. Not only that, the maximum pressure differential generated by pump is smaller and shorter duration in CCSS. That is also benefit to prolong the service life of the whole system, furthermore, making the rotary motion more smooth and stability. Both operating time and energy consumption of swing motion have a great impact on working efficiency, energy conservation and environment protection. So a CCSS is proposed to reduce throttling losses and recuperating regenerative braking energy. Through modeling and simulation, it can be concluded that CCSS saves 875.5 KJ and BASS saves 347.2 KJ. So the simulation results show that the swing system with closed-loop control algorithm has better operability than OCSS and BASS and can be better adapted to the typical occasions of the Grasp Steel Machine.

Acknowledgments
The authors would like to thank the executive editor and the anonymous reviewers for their careful comments and suggestions， which improve the quality of the paper. This work is jointly supported by