Dynamic characteristics analysis and dual motor synchronous control of hydraulic lifting system for large cranes

: The hydraulic lifting system is the key part of the crane. A sliding mode control method based on the cerebella neural network is proposed to solve the problem that the robustness of the traditional control method is poor in view of the problem of the synchronous error of the double motor in the lifting process of the crane. On the basis of the master and slave control, the outlet pressure of the hydraulic pump and the angle of the hook are simulated as the control index. Finally, the experimental study is carried out on the lifting condition. The results show that, compared with the traditional method, the proposed control strategy can effectively improve the synchronisation control precision of two motors, strong anti-interference ability and good robust performance.


Introduction
Large crane usually uses two hydraulic motors to jointly raise the load. Due to the influence of load interference, the problem of synchronisation error often occurs, which affects the working performance of the crane, and even causes the safety accident [1]. Therefore, the effective control strategy should be adopted to improve the synchronous control accuracy of the two motors.
At present, the control methods used in hydraulic synchronisation mostly use the main and subordinate control mode [2], which has a good control effect. In the control strategy, the most application is the conventional proportional integral derivative (PID) control [3]. This method is simple and easy to realise, but because the parameters are fixed and cannot be adjusted on line in real time, it is very limited in application. In [4], a fuzzy PID control strategy is proposed, which has achieved good control effect. However, because the fuzzy rules often come from the expert experience, the complexity of the control is increased. Based on this, by analysing the dynamic characteristics of crane lifting system, the factors that affect the synchronisation precision are found. The cerebella neural network (CMAC) and sliding mode variable structure control (SMC) are combined with the non-linear and time-varying characteristics of the hydraulic transmission, and the master slave mode is used to synchronise the synchronous control to make the master and slave motor have more good following.

Characteristic analysis of hoisting system
The double hoist driving system of large crawler cranes is made up of two identical hoisting mechanisms to realise lifting and lowering of heavy objects, as shown in Fig. 1. Each set of hoisting mechanism uses variable pump to control the quantitative motor [5][6][7][8][9]. Its principle is that the proportional servo valve controls the displacement regulating mechanism by input control voltage, changes the tilt angle of the variable pump, realises the adjustment of the variable pump displacement, the flow of the pump exit is fixed on the motor, drives its operation, and the quantitative motor is driven. Use drum and pulley block to realise the lifting or lowering function of heavy objects. In order to find out the relative factors that affect the accuracy of synchronous control, the dynamic characteristics of hoisting system are analysed.

Displacement regulator
The displacement control mechanism of the variable displacement pump is composed of proportional valve and hydraulic cylinder, as shown in Fig. 2. i. Hydraulic cylinder flow continuity equation [10]: where C iρ -internal leakage coefficient of hydraulic cylinder; P B -pressure of oil back chamber; X -displacement of hydraulic cylinder; C eρ -leakage coefficient of hydraulic cylinder; A -the effective area of hydraulic cylinder; β evolume elastic modulus of hydraulic oil; V B -initial volume of the right chamber of a hydraulic cylinder; P A -pressure in an oil inlet; V A -The initial volume of the left cavity of a hydraulic cylinder; ii. Force balance equation of hydraulic cylinder where m -the total mass of the load and the piston; K -spring stiffness; B -viscous damping coefficient of hydraulic oil; F L -load force.

Model of pump control motor circuit
where Q 1 , Q 2 -flow of flow into a quantitative motor; P 1 , P 2outlet pressure of variable pump; V 1 , -the volume between the motor and the pipe; D m1 , D m2 -motor displacement; C im1 , C im2internal leakage coefficient of motor; θ m1 , θ m2 -motor rotation angle. [11][12][13][14] As the working pressure of the double hoist hydraulic system is closely related to the size of the lifting load, in order to analyse the dynamic characteristics of the rolling process, it is necessary to construct the load torque balance equation during the lifting process. The hoisting mechanism is shown in Fig. 3.

Model of double hoist mechanism
i. Tension equation of wire rope: where E 1 , E 2 -elastic coefficient of wire rope pulling up; n 1 , n 2 -pulley rate of the hoist mechanism; r 1 , r 2 -reel radius; L 1 , L 2 -displacement of hanging point at both ends of a hook. ii. Balance equation of the force of the hook where M -the quality of the hook and load; L -shift displacement of hook; J -the moment of inertia of the load; lhook canter distance from suspension point; φ -tilt angle of hook; φ 0 -the geometric angle of the hook.

Control mode
There are two ways to control the system. The same way is to use the same input for the two hydraulic motors to achieve the synchronous drive control. The main and subordinate mode means that the active motor uses the ideal input to input the output result as the target of the driven motor; thus maintaining the tracking control of the driven motor to the active motor so as to achieve the synchronous control [15][16][17][18][19][20] as shown in Fig. 4.

Control strategy
3.2.1 Sliding mode variable structure control: Compared with the conventional control, the SMC is discontinuous and it is a special non-linear control. The structure of the system is not fixed, according to the current state of a system with dynamic changes, forcing the system under certain conditions, a small margin along the state trajectory specified high frequency up and down movement, namely sliding mode or 'sliding mode' movement.
Since the sliding mode is independent of the object parameters and disturbances, the sliding mode control has the characteristics of fast  response, insensitivity to parameter variation and disturbance, and no online identification of the system [21][22][23]. Suppose there is a control system Define switching function: s(x), s ∈ R m , and then the control function is solved:

CMAC sliding mode control:
CMAC is the abbreviation of cerebella model articulation controller, it is modelled to establish a neural network model principle cerebella control of limb movement, is a simple and fast local approximation based on neural network, capable of learning arbitrary non-linear mapping, has fast convergence, adaptive ability, and is very suitable for realtime control [24,25]. Through the uncertainty of CMAC online learning system, the progressive tracking of expected output can be realised. The CMAC sliding mode controller consists of two parts: sliding mode control and neural network. The structure of the sliding mode controller is shown in Fig. 5.

Simulations
Based on the cross-coupling control method, the CMAC sliding mode control strategy is applied to the dual motor synchronous control system of the crane, and two hydraulic motors are, respectively, controlled, as shown in Fig. 6. The displacement pump is 0-135 mL/r, the engine speed is 1100 r/min, the motor displacement is 150 mL/r, and the sampling frequency is 50 Hz. Simulation analysis of different research objectives under different working conditions and control strategies is carried out, respectively.
i. The inclination angle of the hook is used as the simulation target [26][27][28] Assuming that the crane hook is in an inclined state at the beginning of the simulation, the inclination angle of the hook is 3°. The conventional PID control and CMAC sliding mode control are used to simulate the analysis, and the change of the hook angle during the lifting process is shown in Fig. 7.
The simulation results show that when the initial state is tilted 3° hook, hook is gradually decreased in the synchronous controller, using the conventional PID control of the hook angle overshoot of −1.15°, while the use of CMAC sliding mode control of the hook angle overshoot of −0.37°, the overshoot is reduced by 70%, which showed that the CMAC sliding mode controller small overshoot, in the process of adjustment is more stable. ii. The outlet pressure of the hydraulic pump is used as the simulation target When the two groups of systems are not synchronised, the load will be inclined, which will lead to unbalanced force on the wire rope, that is to say, the load cannot be evenly distributed to the two hydraulic system, resulting in inconsistent system pressure. Assuming that the outlet pressure difference between the two pumps is 5 MPa, take the two hydraulic pump outlet pressures as the index for simulation, the results are shown in Fig. 8.
The results show that when the two hydraulic system pressure deviates, the synchronous controller and the main and auxiliary variable pump pressure difference tends to be 0, CMAC sliding mode control effect is better than the traditional PID control, speed regulation.

Experiments
Practical analysis in order to verify the correctness of simulation and control method, a prototype of crane, crane system parameters and simulation parameters, respectively, for no-load and lifting 200 tons of the two conditions is tested under different control strategies of master-slave motor outlet pressure as shown in Figs. 9 and 10.
The experimental results show that compared with the traditional CMAC control, sliding mode control is reduced two subsystems of the pressure difference, with lifting conditions, for example, conventional PID control the average synchronisation error is 1.4 MPa, CMAC sliding mode control of the average synchronisation error is 0.28 MPa, indicating that the proposed method can effectively improve the control accuracy.

Conclusions
In order to solve the problem of synchronisation error of double hoisting system for large cranes, hydraulic lifting system as the research object, this paper puts forward a CMAC sliding mode control strategy of variable pump outlet pressure, hook angle and motor outlet pressure control parameters for simulation and test. The results show that the proposed control method can effectively overcome the disadvantages of the strategy is not online setting of traditional PID control, greatly improve the synchronisation accuracy of the two systems, and has better dynamic performance and robustness response.