Compound Control on Constant Synchronous Output of Double Pump-Double Valve-Controlled Motor System

Abstract

In this paper, a control method featuring double closed-loop compound robust is proposed to deal with the underperformances of double pump-double valve-controlled motors under external interference, such as poor stability of output speed, low controllability, and difficulties in managing synchronous output. By using this method, with the output speed of the hydraulic motor kept constant as the control objective, the sliding-mode controller of the single-channel motor is designed for the inner loop, while the double-channel cross-coupled enclosed-loop control is applied to the outer loop. Adjustments then are made to the speeds of the two motors, thus finally managing to realize the constant control on synchronous output of the two motors. Both simulation and test results indicate that this control method has produced higher control accuracy and robustness, with the system output speed difference lowered by 57.6%, the stability adjustment time shortened by 25% on average, and the synchronization error of the system output speed averaged only 1.25%, all of which have met the requirements of the stability and synchronous control on the output speed. Under the compound control method proposed in this paper, the output stability of the hydraulic servo valve-controlled motor system could be increased in complex circumstances featuring nonlinear input, and this method provides a reference for the control studies of the double-channel hydraulic servo valve-controlled motor system.

1. Introduction

The double-channel valve-controlled motor system commonly used in the biaxial synchronous mechanical devices is now widely applied in the area of engineering, for its transmission is characterized by high control precision, fast response, high-torque power output, flexible signal processing, and easily accessible parameter feedback. However, the development of the hydraulic servo system in engineering has met certain limitations for the increased difficulty in the control on constant speed output of motor systems [1,2] as a result of compressibility of oil, nonlinear friction, time variants, potential load disturbance, uncertain parameter perturbation, and so on.

The scholars at home and abroad have conducted extensive research to resolve the problem of constant speed control of motors in hydraulic servo systems and proposed the following solutions successively: Kong et al. proposed a control model with a steady-state control quantity superimposed on a small-signal linearization-based compensation control quantity in the process of studying the speed of a pump-controlled motor, and performed some statistical analysis. The results demonstrated that this control model could achieve the purpose of constant speed control under variable speed input [3]. Peng Tianhao proposed the pressure compensation control algorithm on the basis of certain optimization, and carried out certain test research, and found that it can achieve the purpose of speed compensation control under various working conditions, with obvious performance advantages [4]. In carrying out the research of constant speed control of the hydraulic motor, Ma Yu et al. established the input feedforward-feedback compound compensation model according to its control requirements and conducted a comparative study of its control performance [5]. Chai Xiaobo analyzed the control requirements for variable speed input variable pump-controlled motors and proposed a flow-based feed-forward control method, which was found to be of high application value in achieving stable speed control during the control process [6]. Long analyzed the engine output speed variation interval and proposed a control model to control the variable pump displacement with the offset of engine runout value and verified its performance. It was found that this model can achieve constant speed control purposes in the case of constant current source [7]. Li Hao developed a feedforward compensation plus closed-loop feedback control model, which can significantly reduce the interference of speed jump on speed control and help improve the stability of the system [8]. Wang Yan introduced the linear theory and established the variable-pump controlling variable-motor (VPCVM) control algorithm, which can effectively carry out the variable motor constant speed control in the application process [9]. Zheng Qi specifically analyzed the drawbacks related to the coupling interference of pump-controlled parallel motor speed output in the research process, introduced the flow adaptive distribution model method for control, and found that this method can significantly reduce the coupling effect between parallel motors in the control process, thus that the control accuracy is significantly improved [10]. Chen Lijuan et al. analyzed the hydraulic motor constant speed control problem and proposed a linear quadratic control model [11]. To solve the problem of synchronizing the dual-side track output of a tracked vehicle, Li and Yan et al. adopted a master-slave fuzzy adaptive proportional–integral–derivative (PID) synchronization control method to control the dual-side tracks. This method achieved fast synchronization to the set speed with strong anti-disturbance and fast response time [12]. Cao Fuyi specifically analyzed the problem of constant motor speed in a composite drive of hydraulic machinery under the action of pulse signals and established a double feedforward fuzzy PID control model. The disturbance is converted into the change of variable motor speed in the application process, and the disturbance is eliminated with certain flow compensation to achieve the purpose of constant speed control and regulation [13]. The above-mentioned control algorithms can reduce external interference, thus effectively improving the accuracy of the stable status and the speed of the dynamic response of the system.

In recent years, relevant experts and scholars have conducted more in-depth research on the issue of synchronous control of dual-axis hydraulic systems. Y. Koren [14] and Robert. D. Lorenz [15] et al. designed three two-axis synchronous control methods in the process of studying the control requirements of hydraulic systems, laying a good foundation for research in the field of two-axis synchronous control. K. Srini investigated the problem of variable system parameters, proposed a cross-coupled control model, and demonstrated that the control algorithm could effectively deal with time-varying problems [16]. Cao Yang discussed in detail the performance characteristics and applications of hydraulic synchronization systems, discussed the causes of their operating errors, and also gave the corresponding processing strategies [17]. Ye Haiping addressed in detail the characteristics and principles of synchronous closed-loop control algorithms for hydraulic systems and discussed the value of these algorithms in the application of synchronous output control for hydraulic systems [18]. Jinhui Xie modeled the dual hydraulic motor synchronous drive system on the basis of certain simplifying assumptions and adopted a synchronous closed-loop position feedback PID control method for the motor speed output and closed-loop feedback for the hydraulic system with the difference in angular displacement of the dual motors as the parameter. This method improved the synchronization performance of the hydraulic system [19]. Liu Chunfang et al. proposed a fuzzy adaptive controller for the characteristics and control requirements of the dual electro-hydraulic servo motor hydraulic system, and the control method can well compensate for the errors caused by time variability [20]. However, the time-varying feature of hydraulic servo systems makes it too complicated to be directly applied in most cases [21,22], which would lead to an underperformance of system transient response under actual complex working conditions, and only the general control methods are suitable for the slow time-varying system [23]. Therefore, it is especially important to study the appropriate control strategies.

This paper, with a focus on the research of the double pump-double valve-controlled motor system and by putting the constant synchronous output of the biaxial motor as the control objective, has proposed the double closed-loop compound speed control method based on the combination of sliding-mode control and cross-coupled control to solve the problem of the synchronous constant output of the double pump-double valve-controlled motor system, in a way to pave the way for the extensive application in actual engineering scenarios.

2. Modeling Analysis on Double-Channel Valve-Controlled Motor Systems

As shown in Figure 1, when it comes to the structure, the hydraulic double-pump and double-servo valve-controlled motor systems are mainly composed of two pumps, a hydraulic motor, and a relief valve. The double-channel motor, as a relatively independent servo valve-controlled motor circuit, is mainly used in mechanical transmission devices with biaxial synchronization, and the relative motion of the two motors would encounter coupling in the case of load. Therefore, it is important that the stable constant speed of the single-channel motor and the synchronous speed of the biaxial motor are guaranteed to achieve the sound operation of the hydraulic rotating system.

The modeling of double-channel valve-controlled motor system is conducted at the onset before synchronous control is delivered, and the model equations are shown below as Equations (1)–(3).

The linearized flow equations for the servo valve ports are as follows:

$$\left\{\begin{array}{l}{Q}_{L1}=K_{q1}{x}_{v1}-K_{C1}{P}_{L1}\\ Q_{L2}=K_{q2}{x}_{v2}-K_{C2}{P}_{L2}\end{array}\right.$$

(1)

The continuity equations for hydraulic motors are as follows:

$$\left\{\begin{array}{l}{Q}_{L1}=D_{m1}{\dot{\theta }}_{m1}+C_{t1}{P}_{L1}+\frac{V_{t1}}{4{\beta }_e}{\dot{P}}_{L1}\\ Q_{L2}=D_{m2}{{\theta }^{\prime }}_{m2}+C_{t2}{P}_{L2}+\frac{V_{t2}}{4{\beta }_e}{\dot{P}}_{L2}\end{array}\right.$$

(2)

The moment balance equations for hydraulic motors are as follows:

$$\left\{\begin{array}{l}{D}_{m1}{P}_{L1}=J_1{\ddot{\theta }}_{m1}+T_1\\ D_{m2}{P}_{L2}=J_2{\ddot{\theta }}_{m2}+T_2\end{array}\right.$$

(3)

where Q_L is the load flow of servo valve, x_v, the spool displacement of servo valve, K_q, the flow gain of servo valve, K_c, the flow pressure coefficient of servo valve, P_L, the load pressure drop, D_m, the hydraulic motor’s displacement, θ_m, the rotation angle of hydraulic motor, C_t, the leakage coefficient of hydraulic motor, V_t, the total volume of the two chambers of the hydraulic motor and the connected pipes, J₁ and J₂ are the inertia values of hydraulic motors, respectively, β_e, the oil volume elastic modulus, and T is the external load moment applied to the hydraulic motor shaft.

3. Controller Design for Double Pump-Double Motor Systems

To resolve the problem of the synchronous constant output of double motors as a result of the mutual coupling between the two motors in the actual working status, the control method featuring double closed-loop compound robust is adopted, where the sliding-mode control by the single-channel motor is used, the principle of which is to control and eliminate the influence of external disturbance on the constant speed output of motors; while the double-channel cross-coupled enclosed-loop control is applied to the outer loop, the real-time difference on the output speed are made to the two motor channels, meanwhile sending compensation signals to their control ends and later readjustment to their speed and eventually managing to deliver the synchronous constant control on the output speed of the two motors.

3.1. Design for Sliding-Mode Controller of Single-Channel Motor Speed

As for the design of the sliding mode controller for the single motor channel, the state variables are defined as follows:

$$x={[x_1,x_2,x_3]}^T={[{\theta }_1,{\dot{\theta }}_1,P_{L1}]}^T$$

(4)

Then the state equation is:

$$\left\{\begin{array}{l}{\dot{x}}_1=x_2\\ {\dot{x}}_2=f_{21}{x}_3-f_{21}\\ {\dot{x}}_3=f_{31}{x}_v-f_{32}{x}_3-f_{33}{x}_2\end{array}\right.$$

(5)

where

$$\left\{\begin{array}{l}{f}_{21}=D_{m1}/J,f_{22}=T_1/J\\ f_{31}=\frac{4{\beta }_e}{V_{t1}}{K}_{q1},f_{32}=\frac{4{\beta }_e}{V_{t1}}(K_{c1}+C_{t1}),f_{33}=\frac{4{\beta }_e}{V_{t1}}{D}_{m1}\end{array}\right.$$

(6)

Step 1: Define the tracking error of the system as $z_1=x_1-x_{1d}$, where $x_{1d}$ is the position command to be tracked by the system rotating angle 1, and x₂ is selected as virtual control according to the first equation in Formula (5) to stabilize the equation ${\dot{x}}_1=x_2$; let $x_{2eq}$ be the expected value of the virtual control, and the error between a₁ and real state x₂ be $z_2=x_2-x_{2eq}$, thus taking the derivative of z₁ to obtain:

$${\dot{z}}_1=x_2-{\dot{x}}_{1d}=z_2+{\alpha }_1-{\dot{x}}_{1d}$$

(7)

The virtual control law is designed as follows:

$${\alpha }_1={\dot{x}}_{1d}-k_1{z}_1$$

(8)

When the gain in Formula (8) is k₁ > 0, then

$${\dot{z}}_1=z_2-k_1{z}_1$$

(9)

The formula above is derived from the Laplace Transform and delivers the result that $G(s)=1/(s+k_1)$ is a stable transfer function. Therefore, a conclusion is arrived that when $z_2$ tends to 0, $z_1$ will inevitably level off to 0; in the following design, making $z_2$ approach 0 is regarded as the main objective; take the derivative of $z_2$ to obtain and:

$${\dot{z}}_2={\dot{x}}_2-{\dot{x}}_{2eq}=f_{21}{x}_3-f_{22}-{\dot{\alpha }}_2$$

(10)

Step 2: $x_3$ is selected as the virtual control to make Formula (10) approach the stable state, then let ${\alpha }_2$ be the expected value of the virtual control, and the error between ${\alpha }_2$ and $x_3$ under actual state be $z_3=x_3-{\alpha }_2$, then:

$${\alpha }_2=(f_{22}+{\dot{\alpha }}_2-k_2{z}_2)/f_{21}$$

(11)

When the gain in the above formula is k₂ > 0, thus obtaining:

$${\dot{z}}_2=-k_2{z}_2$$

(12)

Step 3: The sliding surface is defined, and the result is:

$$s=c_1{z}_1+c_2{z}_2+z_3$$

(13)

where, $c_1,c_2>0$

Take the derivative of s to obtain:

$$\dot{s}=c_1{\dot{z}}_1+c_1{\dot{z}}_2+f_{31}{x}_v-f_{32}{x}_3-f_{33}{x}_2-{\dot{\alpha }}_2$$

(14)

According to Formula (14), the design for the model-based controller is as follows:

$$x_v=\frac{f_{32}{x}_3+f_{33}{x}_3+{\dot{\alpha }}_2-k_{3}s-\beta sign(s)}{f_{31}}$$

(15)

Substitute Formula (15) for Formula (14) to obtain:

$$\dot{s}=-k_{3}s-\beta \mathrm{s}\mathrm{ign}\left(\mathrm{s}\right)$$

(16)

As for the verification of the stability of the single-motor channel, the Lyapunov function is defined as follows:

$$V=\frac{1}{2}{s}^2$$

(17)

Take the derivative of Formula (17) to obtain:

$$\begin{array}{l}\dot{V}=s(-k_{3}s-\beta \mathrm{s}\mathrm{ign}\left(\mathrm{s}\right))\\ \le -\beta ‖s‖\end{array}$$

(18)

As a result, the tracking error of the system tends to 0 under the condition of limited time.

3.2. Design for Cross-Coupled Controllers

Cross-coupled controllers are commonly applied in cases featuring biaxial synchronization and biaxial synergy [24,25], both of which have delivered sound control effects. With the output of the single-channel motor set at a constant speed through the sliding-mode control, the cross-coupled control method is applied to the two motor channels to ensure the accuracy of biaxial synchronous control of the double pump-double motor system. The basic scheme for relative coupling control of the double pump-double valve-controlled motor is demonstrated in Figure 2. The items inside the dashed box represent the control objects- the two motors with coupling relations.

As shown in the block diagram above, the control variables of the two channels are as follows:

$$\left\{\begin{array}{l}{U}_1=\left(R_1{F}_1-{\dot{\theta }}_1\right)G_1+\left({\dot{\theta }}_1-{\dot{\theta }}_2\right)W_1\\ U_2=\left(R_2{F}_2-{\dot{\theta }}_2\right)G_2+\left({\dot{\theta }}_1-{\dot{\theta }}_2\right)W_2\end{array}\right.$$

(19)

The outputs of the two channels include:

$$\left\{\begin{array}{l}{\dot{\theta }}_1=U_1{P}_{11}+U_2{P}_{12}\\ {\dot{\theta }}_2=U_1{P}_{21}+U_2{P}_{22}\end{array}\right.$$

(20)

Integrate the formula with the previous control-variable equation and then write in the form of the matrix:

$$\left[\begin{array}{l}{\dot{\theta }}_1\\ {\dot{\theta }}_2\end{array}\right]=\left[\begin{array}{l}{P}_{11}{P}_{12}\\ P_{21}{P}_{22}\end{array}\right]\left[\begin{array}{l}{R}_1{F}_1{G}_1\\ R_2{F}_2{G}_2\end{array}\right]+\left[\begin{array}{l}{P}_{11}{P}_{12}\\ P_{21}{P}_{22}\end{array}\right]\left[\begin{array}{l}{W}_1-G_1-W_2\\ W_2-\left(W_2+G_2\right)\end{array}\right]\left[\begin{array}{l}{\dot{\theta }}_1\\ {\dot{\theta }}_2\end{array}\right]$$

(21)

The expression of closed-loop transfer function can be reorganized into:

$$\Theta \left(s\right)={\left\{I+P\left(s\right)\left[G\left(s\right)-W\left(s\right)\right]\right\}}^{-1}P\left(s\right)G\left(s\right)F\left(s\right)$$

(22)

4. Simulation and Test

4.1. Design for Simulation and Test of Control Methods

Joint simulation is conducted with the help of software such as AMEsim and MATLAB, and the hydraulic mechanical compound transmission experiment platform is built, as shown in Figure 3 and Figure 4, where the power source of the platform serves as the driving motor with variable frequency, the Rexroth R979 series as the constant displacement pump, the SGDH-G05-TE32-L7/6/V/E-80 servo valve as the four-way valve, and the BM series cycloid motor as the motor of the experiment. Besides, the turbine flow transducer of the LWGY series, E6B2-CWZ6C1000P/R encoder of Omron, RS485 pressure sensor, and Seiko SKISIA magnetic powder brake are selected as the detecting elements of the system. The voltage signal of servo valve is supplied by the stabilized voltage module of the host computer, while the closed-loop control is completed through the feedback collection from the sensor system parameters. Simulation analysis and experimental verification are conducted on the double closed-loop speed control method, with the key parameters of simulation and experiments based on Formulas (23)–(29).

To assure the accuracy of control, the parameters of servo valve and hydraulic motor are determined according to sample comparison, and the transfer functions at all levels of the servo valve-controlled motors are obtained as follows:

(1)

Servo Amplifier

As the servo amplifier has a much higher frequency band than hydraulics, its dynamic influence on the system can be ignored and it can be simplified as a proportional component, with its transfer function as follows:

$$\frac{I\left(s\right)}{U\left(s\right)}=K_a$$

(23)

where K_a is the servo amplifier gain (A/V)

The damping ratio of electro-hydraulic servo valve is estimated as 0.6.

The control voltage of the servo valve is −10–10 v, thus the amplifier gain is $K_a=0.0016(A/V)$.

(2)

Servo Valve

When the influence of the servo valve on the hydraulic control system cannot be ignored, its dynamic can then be simplified as a second-order oscillation component.

$$G_{sv}\left(s\right)=\frac{Q_0\left(s\right)}{I\left(s\right)}=\frac{K_{sv}}{\frac{s^2}{{\omega }_{sv}^2}+\frac{2{\xi }_{sv}}{{\omega }_{sv}}s+1}$$

(24)

where

K_sv = First-order inertia constant of electro-hydraulic servo valve;

W_sv = Equivalent undamped natural frequency of electro-hydraulic servo valve;

ξ_sv = Equivalent damping ratio of electro-hydraulic servo valve;

Among them, the rated pressure of servo valve is 21 Mpa, the rated flow, 100 L/min, the phase shifted broadband of −30 dB and −90°, 620 rad/s, and the operating pressure difference is 10 Mpa. Therefore, the transfer function of electro-hydraulic servo valve is:

$$\frac{Q_{0\left(S\right)}}{I\left(s\right)}=\frac{0.0001}{\frac{s^2}{{620}^2}+\frac{1.2}{620}s+1}$$

(25)

(3)

Hydraulic Motor

The natural frequency of the hydraulic motor is

$${\omega }_h=\sqrt{\frac{4{\beta }_e{D}_m^2}{J_t{V}_t}}$$

(26)

where

$J_t$ = Total inertia of motor shaft converted from hydraulic motor and load, 1 × 10⁻³ kg·m²

${\omega }_h$ = Hydraulic natural frequency, 69.45 rad/s

$D_m$ = Output of hydraulic motor, 6.3694 × 10⁻⁵ m³/rad

${\beta }_e$ = Effective elastic modulus volume of hydraulic oil, 850 Mpa

$V_t$ = Total compressed volume, 2.355 × 10⁻⁴ m³

${\xi }_h$ = Damping ratio of hydraulic motor, 1.24

$K_{ce}$ = Pressure coefficient of flow valve, 2.06271 × 10⁻¹⁰ m³/(sPa)

The transfer function for the rotating angle of hydraulic motor shaft on external load torque is:

$$\frac{{\theta }_m}{T_L}=\frac{-\frac{K_{ce}}{D_m^2}\left(1+\frac{V_t}{4{\beta }_e{K}_{ce}}s\right)}{s\left(\frac{s^2}{{\omega }_h^2}+\frac{2{\xi }_h}{{\omega }_h}s+1\right)}$$

(27)

And then its transfer function is:

$$\frac{{\theta }_m}{T_L}=\frac{-(0.05+2\times {10}^{-5}s)}{s(\frac{s^2}{{69.45}^2}+\frac{2.48}{69.45}+1)}$$

(28)

(4)

Encoder

The mathematical model of the encoder transfer function is, and according to the selected encoder, the static gain of the speed sensor is 20 v/(rad/s).

$$\frac{U_f}{\dot{\theta }}=K_{fv}$$

(29)

where

$U_f$ = Voltage of sensor, V

$K_{fv}$ = Gain of speed sensor, 0.19 V/rad

4.2. Analysis of Simulation and Test Results

Once the system is commissioned, the hydraulic test bench is used for step test and shock test of single-channel valve-controlled motor system and cross-coupled synchronous control test of dual-channel valve-controlled motor system. The speed data and pressure data are extracted through the data transmission line. During the test, the encoder speed acquisition signal is accurate to 1 r/min, and the pressure signal is accurate to 0.1 MPa, and the sampling frequency is set to 2 Hz, and the value is taken after the speed is stabilized.

For the step test of the single-channel valve-controlled motor system, the desired speed of the hydraulic motor was set to 100 50 r/min; for the impact test, a transient resistance of 20 N-m was added to the hydraulic motor channel by the Seiko SKISIA magnetic powder brake, and then the anti-interference capability and system stability adjustment time of the single-channel hydraulic motor under the two control algorithms were compared.

Figure 5 shows the step response curves of motor speed under the two control methods. As can be seen from the figure, the corresponding simulation and test curves under the two control modes have basically the same trend, and there is no significant difference between the measured and expected values of motor speed, which are basically stable around 100 50 r/min, with stable adjustment times of 1.4 and 0.6 s, respectively, and the steady-state errors of hydraulic motor speed are ±7 and ±5 r/min. It can be seen from Figure 6 that the adjustment time of system stability is 1.6 s and 1.2 s when the single-channel valve-controlled motor system is suddenly shocked when the speed is stable, and the minimum speed of the motor is 35 r/min and 48 r/min, respectively. The comparison of the output of the hydraulic system under the test environment of the two control algorithms is shown in

Table 1. Comparison of System Output under Test Environment.

Test Content	Nin/(r·min−1)	Control Method	Adjustment Time/s	Nout/(r·min−1) Value
Impulse response	100	PID	1.6	100 ± 9
	100	Sliding mode control	1.2	100 ± 5
Step response	100→50	PID	1.4	Nin ± 7
	100→50	Sliding mode control	0.6	Nin ± 5

Note: N_in is the system input speed, r·min⁻¹; N_out is the system output speed, r·min⁻¹.

. As can be seen from Table 1, the adjustment time of the sliding mode control algorithm is shorter than that of the traditional PID control algorithm, and its anti-interference capability is better than that of the PID control algorithm.

For the cross-coupled dual closed-loop synchronous control test of the dual-channel valve-controlled motor, the desired speed of the hydraulic motor is set at 100 r/min, and at this time, a resistance of 10 N-m is added to the dual-channel hydraulic motor system by the Seiko SKISIA magnetic powder brake, and then the synchronous output of the two-channel valve-controlled motor system speed and pressure changes are compared under the three synchronous control algorithms of parallel-type PID synchronous control, cross-coupled PID control and cross-coupled sliding film synchronous control. The results are shown in Figure 7 and Figure 8.

When the two-channel hydraulic motor speed is controlled by parallel PID algorithm, the system output speed and pressure steady-state errors are ±9 r/min and ±0.68 Mpa, respectively, and the speed synchronization error reaches 6.6%; when the double closed-loop cross-coupled PID control is used, the speed synchronization error is reduced to 2.95% and the system pressure difference is unchanged; when the double closed-loop fuzzy PID control algorithm is used, the hydraulic motor speed synchronization error is only 1.25%, and the system output speed and pressure steady-state errors are ±4 r/min and ±0.40 Mpa, respectively. The synchronization test table is shown in 2.

The cross-coupled sliding film control mode improves the control stability of the system, while the output speed difference decreases significantly by 57.6%, the decrease of the stable adjustment time is 25%, and the corresponding speed error is 1.25%, as shown in

Table 2. Comparison of Synchronization Test.

Synchronization Control Method	Speed Synchronization Error/%	Nout/(r·min−1) Value	Pout/MPa
PID control	6.6	100 ± 9	4.6 ± 0.68
Cross-coupling PID control	2.95	100 ± 9	4.6 ± 0.60
Cross-coupled sliding mode control	1.25	100 ± 5	4.6 ± 0.40

Note: N_out is the system output speed, r·min⁻¹, P_out is the system output pressure.

. This test result verifies the superiority and effectiveness of the double closed-loop speed composite control method proposed in this paper.

5. Conclusions

For the problem of constant speed synchronous output of dual-channel hydraulic servo-valve motor system, a double-closed speed compound control method based on cross-coupled sliding film control is proposed. The mathematical control model of the dual-channel valve-controlled hydraulic motor is obtained by parametric modeling analysis of the hydraulic system and the slide film controller, respectively, in the paper.

In order to verify the control effect of the synchronous output of the controller, a test rig for a two-pump, two-valve-controlled motor system was built. Single-channel step and shock tests and dual-channel synchronization tests were conducted, respectively, and the length of response time, anti-interference capability, and speed synchronization error were judged as evaluation indexes. The experimental results demonstrated that the method effectively suppressed the time-varying and uncertainty of the system in external disturbances, realized the stability and synchronization control of the output speed, and effectively improved the stability and robustness of the system.

Further work will be carried out in the following areas: the cross-coupling synchronous control method will be used in practical engineering applications, and it will be optimized and improved in practical problems, thus that the control accuracy will be improved. This research can provide a reference for the research of dual-axis synchronous output control.