CN116551695A - A hydraulic swing joint position servo system and its NDOB-SMC control method - Google Patents

Abstract

The invention relates to a hydraulic swing joint position servo system and its NDOB-SMC control method. Firstly, the hydraulic swing joint position servo system is designed. In the system, the servo valve and the cylinder body of the hydraulic cylinder are integrated and directly connected, and the oil pipe connection is abandoned. The structure is more compact, and some interference factors are reduced; secondly, a sliding mode control strategy based on a nonlinear disturbance observer is designed, which combines the nonlinear disturbance observer and sliding mode control to give full play to their respective advantages and improve the tracking of hydraulic swing joints Accuracy and response speed; Finally, combined with the rich component model library of the AMEsim platform and the powerful numerical computing capabilities of the Matlab platform, the joint simulation of the two platforms is realized by creating the S-Function interface, and the effectiveness and superiority of the proposed control method are verified.

Description

A hydraulic swing joint position servo system and its NDOB-SMC control method

Technical field:

The invention relates to the technical field of hydraulic swing joint control, and in particular to a hydraulic swing joint position servo system and an NDOB-SMC control method thereof.

Background technology:

At present, most robot joints are driven by motors, but their output power is low, especially in special tasks such as rescue, exploration and military, their load capacity is difficult to meet the needs. After research and discovery by scholars, hydraulic robots driven by electro-hydraulic servo systems have the advantages of high power-to-volume ratio, stable operation and fast response speed. They have been gradually used in modern industry, military and other fields, and their control issues have gradually become the focus of people's attention.

The electro-hydraulic servo system is affected by the nonlinearity of the servo valve flow, the uncertainty of system parameters and models, and other interference factors, which increases the difficulty of developing high-performance controllers for electro-hydraulic servo systems. Conventional PID control is widely used because of its simple algorithm and relatively independent control parameters. However, in nonlinear fields such as electro-hydraulic servo systems, the positioning control ability is poor. Therefore, many scholars have proposed many control strategies to address the problems of system nonlinearity, parameter uncertainty, and the influence of external interference on system tracking accuracy. For example, adaptive control, robust control, fuzzy control, active anti-interference control, observer-based control and sliding mode control. Among them, sliding mode control is insensitive to system parameter changes and disturbances compared to its control, and has good adaptability and robustness, making it widely used in military, aviation, transportation and other nonlinear control fields. However, due to the existence of sliding mode, sliding mode control will cause "chattering" phenomenon when controlling input. Therefore, how to reduce chattering without affecting the performance of sliding mode controller is a topic studied by many scholars today. For example, Rubagotti et al. designed an integral sliding mode surface, which enhances the robustness of the system. The sliding mode controller designed by Xue et al. can make the position error converge to zero within a certain period of time, but it requires no external interference, and the output parameters of the controller still have jitter. Gao et al. proposed a terminal sliding mode control that can converge faster, and studied the adaptive sliding mode control law. Yang et al. proposed a sliding mode controller based on an adaptive high-order neural network, which effectively reduced the jitter of the sliding mode controller and achieved better control accuracy by combining multiple control strategies. Therefore, with the increase in system complexity and control requirements, many scholars have tried to combine multiple control methods to achieve the optimal performance of the entire control system. Some of these scholars introduced the disturbance observer method to compensate for the controller input. Nonlinear disturbance observers are more accurate than linear ones.

The design of disturbance observer is more difficult, while nonlinear disturbance observer can better eliminate the uncertainty and unknown disturbance in nonlinear system and estimate the disturbance in real time. For example, the disturbance observer used by Zhu et al. successfully suppressed the external disturbance and improved the accuracy of the system. Bu et al. designed a new type of nonlinear disturbance observer based on improved sliding mode differentiator, which can effectively suppress nonlinear disturbance and improve the robustness of the system. The effectiveness of the observer was verified by simulation. The designed observer was also simulated in this paper. After the problem of elastic state cannot be measured was solved, the accuracy was also improved.

In the simulation experiment process, most scholars first conducted simulation experiments based on a single software platform. This method can effectively shorten the development cycle, cost and risk, and ensure good reliability. However, due to the increasing complexity of the system and the continuous improvement of requirements, the electro-hydraulic servo system has inherent nonlinear behavior and modeling uncertainty, which makes it very difficult to establish an accurate mathematical model. The use of a single software platform for simulation experiments is far from meeting the needs of simulation at this stage. Therefore, in recent years, some scholars have adopted the method of joint simulation to conduct research and experiments on electro-hydraulic servo systems and other related aspects. Its application areas mainly involve automobile suspension, machine tools and lifting actuators. For the study of joint simulation, Liu et al. studied the modeling method of virtual prototypes and simplified the dynamic system that replaced them, but the model was not established accurately. Zhang et al. used the S-function interface to call the AMEsim platform and conducted a joint simulation of the AMEsim and Matlab platforms, which enhanced the control strategy development capabilities of the electro-hydraulic lifting system and well verified the control accuracy of the proposed observer-sliding mode control strategy. In order to solve the problem of valve core sticking, Chen et al. used Matlab, AMEsim and Fluent platforms for joint simulation, and obtained the key flow data of each oil port in the sliding valve through experiments.

Through the analysis and research of existing literature, it can be seen that existing scholars have made a lot of research contributions in sliding mode control, nonlinear disturbance observer and joint simulation. However, when it comes to the hydraulic swing joint position servo system, especially the nonlinearity of the electro-hydraulic position servo system and the uncertainty of its model, how to achieve high-performance control and how to conduct joint simulation verification of the control strategy have become new technical challenges.

It should be noted that the above contents belong to the technical knowledge of the inventor and do not necessarily constitute prior art.

Summary of the invention:

The purpose of the present invention is to solve the problems existing in the prior art and provide a hydraulic swing joint position servo system and its NDOB-SMC control method. Firstly, a hydraulic swing joint position servo system is designed. In the system, the servo valve and the cylinder body of the hydraulic cylinder are directly connected in an integrated manner, and the oil pipe connection is abandoned, which not only makes the structure more compact, but also reduces some interference factors; secondly, a sliding mode control strategy based on a nonlinear disturbance observer is designed, which combines the nonlinear disturbance observer and the sliding mode control to give full play to their respective advantages and improve the tracking accuracy and response speed of the hydraulic swing joint; finally, combining the rich component model library of the AMEsim platform and the powerful numerical computing ability of the Matlab platform, by creating an S-Funcution interface, the joint simulation of the two platforms is realized, and the effectiveness and superiority of the proposed control method are verified.

The present invention achieves the above-mentioned purpose by adopting the following technical solutions:

A hydraulic swing joint position servo system comprises a hydraulic swing joint, wherein the hydraulic swing joint comprises an upper connecting plate, a swing hydraulic cylinder is arranged on the upper connecting plate, a piston rod of the swing hydraulic cylinder is designed to be in an arc shape, a lower connecting plate is arranged on the piston rod, the lower connecting plate rotates and swings following the piston rod, an angle sensor is arranged at the rotation and swinging center of the lower connecting plate, a servo valve is arranged on the cylinder body of the swing hydraulic cylinder, the servo valve is connected to a hydraulic station, the angle sensor is connected to a computer, and the computer is connected to the servo valve.

A hollow shaft is provided at the rotation and swing center of the cylinder body corresponding to the lower connecting plate, and bearings are provided at both ends of the hollow shaft. Each bearing is provided with a lower connecting plate, and a bearing stopper is provided on the outer side wall of the lower connecting plate. The two lower connecting plates are symmetrically installed on the piston rod.

The cylinder body adopts a split design, including an inner cylinder and an outer cylinder of symmetrical design, the inner cylinder and the outer cylinder are connected by threads, a servo valve is provided on the side wall of the outer cylinder, the angle sensor is arranged in a hollow shaft, the rotating shaft of the angle sensor is installed on one of the lower connecting plates, and the rotating shaft is collinear with the rotation and swing center of the lower connecting plate.

An NDOB-SMC control method for a hydraulic swing joint position servo system includes the hydraulic swing joint position servo system as described above, and the specific steps are as follows:

S1. Establish a mathematical model of the hydraulic swing joint position servo system, specifically including:

The load torque balance equation of the hydraulic swing joint position servo system is established, and its expression is:

_PL = _p1 - _p2 ;

k _q =C _d w(1/ρ) ^1/2

Where A is the effective area of the piston, _PL is the flow gain, _p1 is the upper chamber pressure, _p2 is the lower chamber pressure, _Cd is the flow coefficient, w is the area gradient of the servo valve, ρ is the hydraulic oil density, R is the piston rod rotation radius, _TL is the external load torque, _BP is the equivalent viscous damping coefficient, _JL is the moment of inertia, are all unmodeled disturbances in the system;

Define the state variables:

Then the state equation of the hydraulic swing joint position servo system is expressed as:

In the formula, α＝[ _α1 ， _α2 ， _α3 ， _α4 ] ^{T , α1＝BpR2} _{/ JL , d1} (t)＝[f(t， _x1 ， _x2 )+ _TL ]/ _JL , _d1 (t)＝( _4ARβe / _VtJL )Q(t), _d2 ( _t ) is the composite interference of the uncertain factors of the system mismatching model, _α2 ＝ _{4ARβekt / VtJL} , α3＝ ^4A2R2βe / _{VtJL ,} ^α4 ＝ _4βeCi / _Vt , _{λ1 ＝} [ _{ps - x3sign} (u _{) JL} / ^AR ] _1/2 , _βe is the _elastic modulus of the oil, _{V t} is the total volume of the two chambers, Q(t) is the time-varying modeling error, u is the total control law of the system, _kt is the total flow gain, _Ci is the internal leakage flow coefficient, _Ce is the external leakage flow coefficient, and _ps is the supply pressure;

S2. Design a super spiral interference observer, specifically including:

The superhelical interference observer of the mismatched model is constructed, and its expression is as follows:

In the formula

Where, parameters a ₁ and a ₂ are both positive numbers, and the interference estimate of d ₁ (t) is:

The superhelical interference observer of the matching model is constructed, and its expression is as follows:

In the formula,

Wherein, the parameters a ₃ and a ₄ are both positive numbers, and the interference estimate of d ₂ (t) is:

S3. Design a sliding mode controller to obtain the overall control law of the system, which includes:

Assuming the angle expected signal of the hydraulic swing joint position servo system is x _d , and the actual angular displacement output signal of the hydraulic swing joint position servo system is x ₁ , the error vector of the hydraulic swing joint position servo system is as follows:

make Then the control object can be rewritten as:

Combining this formula with the state equation of the hydraulic swing joint position servo system, we get:

From this conversion formula we can get:

If [c ₁ ,c ₂ ,1] ^T are all greater than zero, the switching function of the sliding surface is:

s(x)＝c ₁ e ₁ +c ₂ e ₂ +e ₃

Derivative both sides of the above equation and Substituting the equation into the equation, we get:

in:

By Japanese style The compensation control law can be obtained for:

The design method of sliding mode controller with exponential reaching law is:

The overall control law u of the system is obtained as:

Where, k ₁ and k ₂ are discontinuous gains of the sliding mode controller, and both are greater than zero;

The hydraulic swing joint is precisely controlled according to the system's overall control law u;

S4. Conduct joint simulation experiments, including:

Firstly, the construction and parameter setting of the hydraulic swing joint position servo system model are completed on the AMEsim platform, and the SimuCosim interface is established. The hydraulic swing joint position servo system model is operated to generate the S function and output information including angle, angular velocity, and pressure to connect with Matlab/Simulink; secondly, the sliding mode control model is established and run on the Matlab/Simulink platform to generate an output control signal u to the AMEsim platform to realize real-time control of the AMEsim platform; finally, the AMEsim platform feeds back the information to the Matlab platform to realize joint simulation.

In the step S1, setting 1: the angle expected signal of the hydraulic swing joint position servo system is x _d , x _d ∈ C ³ , and when the hydraulic swing joint position servo system works normally, the swing hydraulic cylinder satisfies: 0＜ _pr ＜p ₁ ＜ _ps , 0＜ _pr ＜p ₂ ＜ _ps , p ₁ is the upper chamber pressure, p ₂ is the lower chamber pressure, p _s is the supply pressure, p _r is the return oil pressure; and | _PL | is smaller than p _s to ensure that α ₂ λ ₁ ≠0;

Setting 2: The composite disturbance d _i (t) is bounded and d _i (t) is differentiable.

In step S1, Lemma 1 is: Assume 1≤i≤n, and consider the controlled system:

Among them, x~ _i is the state variable, d _i (t) is the composite disturbance, and the first-order derivative of d _i (t) is exist;

Using super-helical control law:

u _si (t)=u _1i (t)+u _2i (t);

Assume that a _i and a _i+1 are positive numbers and satisfy:

From this we can get:

Therefore, the hydraulic swing joint position servo system is stable and converges to zero in finite time.

In step S2, the estimated error between the super-helical disturbance observer and the hydraulic swing joint position servo system is set to:

Will and

Subtracting:

Combine the above formula with Combined to get:

According to Lemma 1, and will converge to zero in a finite time, so the interference estimate of d ₁ (t) is:

Similarly, and

Subtracting them gives:

According to Lemma 1, and will converge to zero in a finite time, so the interference estimate of d ₂ (t) is:

In step S3, the Lyapunov function of the hydraulic swing joint position servo system is taken as:

Take the derivative of both sides of the equation and as well as

Substituting in, we get:

By It can be seen that when (γ-k ₂ )＜0 and k ₁ ＞0, then Always holds, and only when s＝0, Therefore, the closed-loop system is stable.

The present invention adopts the above structure, which can bring the following beneficial effects:

Based on the research of other scholars, this paper first innovatively designs a hydraulic swing joint position servo system. The biggest improvement of this system is that the servo valve is directly connected to the cylinder body, and the use of the oil delivery pipeline between the servo valve and the traditional hydraulic cylinder is abandoned, which greatly improves the space utilization, weakens the nonlinear problem of the volume change of the delivery pipeline caused by oil pressure and oil temperature, and reduces some interference factors. On the above basis, a sliding mode control strategy based on nonlinear disturbance observer is designed, and the mathematical model of the hydraulic swing joint position servo system is established. On this basis, the method of disturbance observer is used to compensate for the uncertain factors and interference of the system to reduce their influence on the hydraulic swing joint position servo system. The overall controller adopts sliding mode control to improve the tracking accuracy and response speed of the hydraulic swing joint. Finally, the model of the hydraulic swing joint position servo system is constructed using the AMEsim platform, and the sliding mode controller based on the nonlinear disturbance observer is set up on the Matlab/Simulink platform. Finally, the AMEsim platform is called through the S-function interface to carry out joint simulation, and the effectiveness and superiority of the proposed control method are verified.

Description of the drawings:

FIG1 is a schematic structural diagram of a hydraulic swing joint according to the present invention;

FIG2 is a schematic structural diagram of the hydraulic swing joint of the present invention from another perspective;

FIG3 is an exploded view of the hydraulic swing joint of the present invention;

FIG4 is an exploded view of the hydraulic swing joint of the present invention from another perspective;

FIG5 is a schematic diagram of the structure of the hydraulic swing joint of the present invention installed on a wearable device;

FIG6 is a working principle diagram of the hydraulic swing joint position servo system of the present invention;

FIG7 is a schematic diagram of collaborative simulation between AMEsim16 and Matlab 2016a of the present invention;

FIG8 is a schematic diagram of a hydraulic system model in AMEsim of the present invention;

FIG9 is a schematic diagram of the NDOB-SMC controller in Matlab of the present invention;

FIG10 is a simulation result diagram of the effectiveness verification of the NDOB-SMC constant load of the present invention;

FIG11 is a graph showing a variable load sub-model and its mass variation curve of the present invention;

FIG12 is a diagram showing the combined simulation results of the present invention using variable load;

FIG13 is a comparison diagram of angle errors under variable amplitude sinusoidal signals of the present invention;

FIG14 is a comparison diagram of angle tracking curves under variable amplitude sinusoidal signals of the present invention;

FIG15 is a comparison diagram of angle tracking curves under a triangular wave signal of the present invention;

FIG16 is a comparison diagram of angle tracking curves under variable amplitude signals of the present invention;

FIG17 is a comparison diagram of angle errors under a triangular wave input signal of the present invention;

FIG18 is a comparison diagram of angle errors under variable amplitude input signals of the present invention;

In the figure, 1. upper connecting plate, 2. swing hydraulic cylinder, 201. cylinder body, 202. piston rod, 203. inner cylinder, 204. outer cylinder, 3. lower connecting plate, 4. angle sensor, 401. rotating shaft, 5. servo valve, 6. hydraulic station, 601. oil tank, 602. hydraulic pump, 603. motor, 604. safety valve, 605. oil suction filter, 7. computer, 8. hollow shaft, 9. bearing, 10. bearing stop plate, 11. wearable device.

Specific implementation method:

In order to more clearly illustrate the overall concept of the present invention, a detailed description is given below in an exemplary manner in conjunction with the accompanying drawings.

In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the protection scope of the present invention is not limited to the specific embodiments disclosed below.

The various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referenced to each other, and each embodiment focuses on the differences from other embodiments.

Furthermore, the terms "upper", "lower", "rotational swing", "inner", "outer", etc. are used for descriptive purposes only and are not to be understood as indicating or implying relative importance or implicitly indicating the position of the indicated technical features.

In the present invention, it should be noted that in order to facilitate description and better understand the present application scheme, the present application sets (n) after the formula, n is a positive integer, and (n) only represents the sequence number of the formula.

In the present invention, unless otherwise clearly specified and limited, the terms "provided with", "set", "connected" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection; it can be directly connected or indirectly connected through an intermediate medium. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

As shown in Fig. 1-6, a hydraulic swing joint position servo system includes a hydraulic swing joint, the hydraulic swing joint includes an upper connecting plate 1, a swing hydraulic cylinder 2 is provided on the upper connecting plate 1, the piston rod 202 of the swing hydraulic cylinder 2 is designed to be arc-shaped, a lower connecting plate 3 is provided on the piston rod 202, the lower connecting plate 3 rotates and swings following the piston rod 202, an angle sensor 4 is provided at the rotation and swing center of the lower connecting plate 3, a servo valve 5 is provided on the cylinder body 201 of the swing hydraulic cylinder 2, the servo valve 5 is connected to the hydraulic station 6 through an oil circuit, the angle sensor 4 is connected to the computer 7 for communication, and the computer 7 is connected to the servo valve 5 for communication. In hydraulically driven robots, the linear telescopic piston cylinder type and the swing cylinder type are the most common driving modes. Robots using linear telescopic piston cylinder type hydraulic drive indirectly realize the movement of robot joints, but the excessive size and additional nonlinear problems caused by the structure restrict the performance of the robot. In view of the above problems, this paper designs a compact hydraulic swing joint with integrated cylinder servo valve. The servo valve 5 is installed on the swing hydraulic cylinder 2, and the use of the oil delivery pipeline between the servo valve 5 and the traditional hydraulic cylinder is abandoned, which greatly improves the space utilization, weakens the nonlinear problem of the volume change of the delivery pipeline caused by oil pressure and oil temperature, and reduces some interference factors. The working process of the hydraulic swing joint position servo system, first, the oil in the system flows under the action of the hydraulic pump 602 (a component of the hydraulic station 6, the hydraulic pump 602 is driven by the motor 603, and the entire oil circuit is also equipped with an oil tank 601, a safety valve 604, an oil suction filter 605, etc.), and the flow and direction of the oil are controlled by the servo valve 5, and then supplied to the swing hydraulic cylinder 2, so that the piston rod 202 in the swing hydraulic cylinder 2 starts to operate and drives the rotation and swing of the joint. When the joint is swinging, the angle sensor 4 observes the rotation angle of the swing joint and outputs an angle signal to the computer 7. After calculation by the computer 7, a control signal is output to adjust the opening direction and opening degree of the servo valve 5, thereby realizing the angle position control of the hydraulic swing joint. In actual application, the hydraulic swing joint position servo system of the present application needs to be installed on a wearable device 11 to realize interaction with the human body through the wearable device.

The cylinder body 201 is provided with a hollow shaft 8 at the rotation and swing center of the lower connecting plate 3, and bearings 9 are respectively provided at both ends of the hollow shaft 8, and a lower connecting plate 3 is provided on each bearing 9, and a bearing stopper 10 is provided on the outer wall of the lower connecting plate 3, and the two lower connecting plates 3 are symmetrically mounted on the piston rod 202. By designing the hollow shaft 8 and the bearing 9, the rotation of the lower connecting plate 3 can be supported, and the structural strength and rotation and swing stability of the lower connecting plate 3 are better.

The cylinder body 201 adopts a split design, including a symmetrically designed inner cylinder 203 and an outer cylinder 204, the inner cylinder 203 and the outer cylinder 204 are connected by threads (connected by bolts, nuts and other threaded structures, the installation holes are schematically shown in the figure), a coil spring 11 is provided between the outer cylinder 204 and the lower connecting plate 3 located on the outside, a coil spring 11 is provided between the inner cylinder 203 and the lower connecting plate 3 located on the inside, a servo valve 5 is provided on the side wall of the outer cylinder 204, the angle sensor 4 is arranged in the hollow shaft 8, the rotating shaft 401 of the angle sensor 4 is installed on one of the lower connecting plates 3, and the rotating shaft 401 is collinear with the rotation and swing center of the lower connecting plate 3. The cylinder body 201 adopts a split design, which is not only convenient for the installation and disassembly of the piston rod 202, but also convenient for directly processing the required oil circuit on the outer cylinder 204 to achieve direct connection with the servo valve 5 (without oil pipe connection).

As shown in FIGS. 7-9 , a NDOB-SMC control method for a hydraulic swing joint position servo system includes the hydraulic swing joint position servo system as described above, and the specific steps are as follows:

S1. Establish a mathematical model of the hydraulic swing joint position servo system, specifically including:

First, the flow equation of the servo valve 5 can be expressed as:

Q _L =(Q ₁ +Q ₂ )/2 (2)

P _L = p ₁ - p ₂ (3)

k _q ＝C _d w(1/ρ) ^1/2 (4)

Where, Q _L is the load flow, Q ₁ is the flow of the high liquid level cavity, Q ₂ is the flow of the low liquid level cavity, X _v is the valve core displacement of the slide valve, P _s is the supply pressure, _PL is the flow gain, C _d is the flow coefficient, w is the area gradient of the servo valve, and ρ is the hydraulic oil density;

Among them, sign(X _v ) can be described as:

The present application uses a high-response servo valve, so the control of the servo valve 5 is proportional to the displacement of the slide valve, that is, X _v = k _v u, where k _v is the amplification gain of the servo amplifier and u is the overall control law of the system, so formula (1) can be converted to:

k _t = k _v k _q (7)

Where _kt is the total flow gain relative to u.

The flow continuity equation of the swing hydraulic cylinder is:

The above equations (8) and (9) can be transformed into the pressure dynamics equations of the two chambers of the swing hydraulic cylinder:

Where Q(t) is the time-varying modeling error (caused by internal leakage, parameter deviation, unmodeled pressure dynamics, etc.), _Ci is the internal leakage flow coefficient, _Ce is the external leakage flow coefficient, _V1 is the effective volume of the upper chamber, _V2 is the effective volume of the lower chamber, _Vt is the total volume of the two chambers, _{and βe} is the elastic modulus of the oil.

The hydraulic swing joint proposed in this paper is built and controlled based on the mathematical model of the arc hydraulic cylinder. Compared with the load force balance equation of the traditional straight rod piston hydraulic cylinder, the arc swing hydraulic cylinder adopts the load moment balance equation. Because the motion characteristics of the hydraulic cylinder power element are affected by the load, including viscous damping force, inertia force, elastic force, cylinder wall friction force and random load force, the load moment balance equation of the hydraulic swing joint position servo system can be expressed as:

P _L = p ₁ - p ₂ (12)

k _q ＝C _d w(1/ρ) ^1/2 (13)

Where A is the effective area of the piston, _p1 is the upper chamber pressure, _p2 is the lower chamber pressure, R is the piston rod rotation radius, _TL is the external load torque, _BP is the equivalent viscous damping coefficient, _JL is the moment of inertia, are all unmodeled disturbances in the system;

Define the state variables:

Then the state equation of the hydraulic swing joint position servo system is expressed as:

In ^{the formula, α＝[α1，α2，α3，α4]T, α1＝BpR2} _{/ JL , d1} ⁽ _{t ) ＝ [} f(t， _x1 ， _x2 )+ _TL ]/ _JL , _d1 (t) is the composite interference of the uncertain factors of the system mismatching model, _d2 (t)＝( _4ARβe / _VtJL )Q(t), _d2 ( _t ⁾ is the composite interference of the uncertain factors of the system _matching model, _α2 ＝ _4ARβekt / _VtJL , _α3 ＝ _4A2R2βe ^/ _VtJL , _α4 ＝ _{4βeCi / Vt} , _λ1 ＝[ _ps - _x3sign (u _{) JL} / ^AR ] ₁₂ .

Assumption 1: The angle expected signal of the hydraulic swing joint position servo system is x _d , x _d ∈ C ³ . When the hydraulic swing joint position servo system works normally, the swing hydraulic cylinder satisfies: 0＜ _pr ＜p ₁ ＜ _ps , 0＜ _pr ＜p ₂ ＜ _ps , where p _r is the return oil pressure; and | _PL | is smaller than p _s to ensure that α ₂ λ ₁ ≠0;

Assumption 2: The composite disturbance d _i (t) is bounded, that is, there exists an unknown positive real number ψ _i ＞0 such that |d _i (t)|≤ψ _i , and at the same time d _i (t) is differentiable, that is, there exists

Lemma 1: Let 1≤i≤n and consider the controlled system:

in, is the state variable, d _i (t) is the composite disturbance, and the first-order derivative of d _i (t) is exist;

Using super-helical control law:

u _si (t)＝u _1i (t)+u _2i (t) (17)

Assume that a _i and a _i+1 are positive numbers and satisfy:

From this we can get:

Therefore, the hydraulic swing joint position servo system is stable and converges to zero in finite time.

S2. Design a super spiral interference observer, specifically including:

According to formula (15) and under the premise of assumptions 1 and 2, the superhelical interference observer of the mismatch model is constructed, and its expression is as follows:

In the formula

Where, parameters a ₁ and a ₂ are both positive numbers, and the interference estimate of d ₁ (t) is:

According to formula (15) and under the premise of assumptions 1 and 2, the superhelical interference observer of the matching model is constructed, and its expression is as follows:

In the formula,

Wherein, the parameters a ₃ and a ₄ are both positive numbers, and the interference estimate of d ₂ (t) is:

Verify the above calculations:

The estimated error between the super-helical disturbance observer and the system is assumed to be:

In formula (15), Subtracting from formula (22) we get:

Combining equation (23) with equation (29), we can obtain:

According to Lemma 1, and will converge to zero in a finite time, so the interference estimate of d ₁ (t) is obtained as equation (24).

Similarly, we can transform Subtracting from formula (25) we get:

According to Lemma 1, and will converge to zero in a finite time, so the interference estimate of d ₂ (t) is obtained as equation (27).

S3. Design a sliding mode controller to obtain the overall control law of the system, which includes:

Assuming the angle expected signal of the hydraulic swing joint position servo system is x _d , and the actual angular displacement output signal of the hydraulic swing joint position servo system is x ₁ , the error vector of the hydraulic swing joint position servo system is as follows:

make Then the control object can be rewritten as:

Combining this formula with the state equation of the hydraulic swing joint position servo system, we get:

From this conversion formula we can get:

If [c ₁ ,c ₂ ,1] ^T are all greater than zero, the switching function of the sliding surface is:

s(x)＝c ₁ e ₁ +c ₂ e ₂ +e ₃ (36)

Derivative both sides of the above equation and Substituting the equation into the equation, we get:

in:

By Japanese style The compensation control law can be obtained for:

The design method of sliding mode controller with exponential reaching law is:

The overall control law u of the system is obtained as:

In formula (41), k ₁ and k ₂ are discontinuous gains of the sliding mode controller, and both are greater than zero;

The hydraulic swing joint is precisely controlled according to the system's overall control law u.

Stability analysis:

Take the Lyapunov function of the system as:

Deriving both sides of equation (42) at the same time, and substituting equation (37) and equation (40) into equation (43) we can get:

By It can be seen that when (γ-k ₂ )＜0 and k ₁ ＞0, then Always holds, and only when s＝0, Therefore, the closed-loop system is stable.

S4. Conduct joint simulation experiments, including:

The nonlinearity and modeling uncertainty of the electro-hydraulic servo control system make it difficult to directly establish an accurate mathematical model. However, the AMEsim and Matlab joint simulation platform not only integrates the fluid simulation capabilities of AMEsim for mechanical and hydraulic systems, but also makes full use of the powerful numerical calculation capabilities of Matlab. For this reason, the S-function interface is used to call the two platforms, drawing on the advantages of both, which can achieve perfect complementarity. A joint simulation model is built in Matlab 2016a and AMEsim 16 to verify the effectiveness of the proposed controller.

Firstly, the construction and parameter setting of the hydraulic swing joint position servo system model are completed on the AMEsim platform, and the SimuCosim interface is established. The hydraulic swing joint position servo system model is operated to generate the S function and output information including angle, angular velocity, pressure, etc. to connect with Matlab/Simulink; secondly, the sliding mode control model is established and run on the Matlab/Simulink platform to generate an output control signal u to the AMEsim platform to realize real-time control of the AMEsim platform; finally, the AMEsim platform feeds back the information to the Matlab platform to realize joint simulation.

The main parameters of AMEsim hydraulic system are as follows:

In order to verify the effectiveness and superiority of the sliding mode control method based on nonlinear disturbance observer proposed in this paper in the hydraulic swing joint position servo system. Simulation comparison experiments were carried out on three control schemes: NDOB-SMC, traditional PID and traditional SMC. This section mainly designs the following two simulation scenarios: (1) When the input signal is a sinusoidal signal, the effectiveness analysis of NDOB-SMC control under two working conditions of constant load and variable load is considered. (2) Under the premise of variable load, the three control methods are input with sinusoidal signals, triangular wave signals and variable amplitude signals, and the superiority is analyzed.

(1) Effectiveness analysis

When the load force is constant, the swing time of the hydraulic swing joint is t = 24s, and the sinusoidal motion is -20° to 20°. The given amplitude is 20, the frequency is π/4, and the phase is -π/2. The sinusoidal signal, and the constant load is 15kg. The NDOB-SMC control parameters are k ₁ = 3.9e3, k ₂ = 5, c ₁ = 4e4, c ₂ = 400. The disturbance observer parameters are as follows: a ₁ = 5, a ₂ = 3, a ₃ = 5, a ₄ = 3, and the gains of the disturbance observer are 0.8e-5 and 0.6e-6 respectively. The simulation results are shown in Figure 10.

At the same time, in order to better verify the effectiveness of the proposed control, variable load is used instead of constant load, but there is no sub-model that meets the requirements in AMEsim. Therefore, the AMEsim set function in the AMEsim platform is used to design a sub-model with variable load, so that it changes sinusoidally in the range of 5kg to 25kg. Its sub-model design diagram and load change curve are shown in Figure 11. As shown in Figure 12, it is the joint simulation result using variable load.

Through the above joint simulation experiments, NDOB-SMC can stabilize the tracking accuracy within a fixed range regardless of constant load or variable load operation, and its effectiveness has been confirmed.

(2) Superiority Analysis

In order to verify the superiority of the proposed control algorithm, this experiment compares the traditional PID control and the traditional SMC control. PID is widely used in the control field due to its structural advantages. Its parameters are as follows: P = 0.04, I = 0.1, D = 0. The SMC controller parameters are as follows: k ₃ = 3.9e3, k ₄ = 5, c ₃ = 4e4, c ₄ = 400. Similarly, a sinusoidal signal is given with an amplitude of 20, a frequency of π/4, and a phase of -π/2. The load is still a variable load, and its curve is shown in Figure 10. The error curve results of the simulation experiment are shown in Figure 13, and the angle tracking curve is shown in Figure 14.

It can be clearly observed from Figures 13 and 14 that, under the same sinusoidal desired signal input, the angle error of SMC control is within the range of ±0.15°, while the angle error of traditional PID control reaches ±0.2°. From the data in Figure 11, it can be seen that the sliding mode control with the addition of a nonlinear disturbance observer can stably control the angle error to around ±0.1°, which has better tracking accuracy than traditional SMC and traditional PID control.

At the same time, in order to fully verify the superiority and adaptability of the NDOB-SMC control proposed in this paper in the practical application of the hydraulic swing joint position servo system. The experiment uses the expected signal as a triangle wave signal of ±20° and a variable amplitude sine signal ranging from -20° to 90° to investigate the performance of the three controllers. The angle tracking results of the triangle wave signal of the simulation experiment are shown in Figure 15, and the angle tracking results of the variable amplitude sine signal are shown in Figure 16. The angle errors under the two signals are shown in Figures 17 and 18 respectively.

As shown in Figures 15 and 17, when the expected signal is a triangular wave, compared with the traditional PID control (error ±0.1°) and the traditional SMC control (error ±0.15°), although there is a large fluctuation near the turning point of the triangular wave, the NDOB-SMC control can still stabilize the angle error within ±0.05°, make the tracking angle converge quickly, and obtain better tracking accuracy.

As shown in Figures 16 and 18, when the variable amplitude is used as the expected signal, the overall angle error of NDOB-SMC can be stably controlled within ±0.5°, with better tracking accuracy, while the angle error of traditional PID control fluctuates within the range of ±1°, and the angle error of traditional SMC control fluctuates within the range of ±0.75°, which is worse than the tracking effect of NDOB-SMC control. While accepting the input of multiple signals, NDOB-SMC control can adapt well to various changes in load quality. The above experimental results show that the control strategy proposed in this paper has higher control accuracy, and can also enable the system to obtain better dynamic performance and stable state, which can meet the needs of actual working conditions.

The above specific implementation manner cannot be used as a limitation on the protection scope of the present invention. For those skilled in the art, any substitution, improvement or change made to the implementation manner of the present invention falls within the protection scope of the present invention.

The matters not described in detail in the present invention are all known technologies to those skilled in the art.

Claims (8)

1. A hydraulic swing joint position servo system, characterized in that it includes a hydraulic swing joint, the hydraulic swing joint includes an upper connecting plate, a swing hydraulic cylinder is arranged on the upper connecting plate, the piston rod of the swing hydraulic cylinder is designed to be in an arc shape, a lower connecting plate is arranged on the piston rod, the lower connecting plate rotates and swings following the piston rod, an angle sensor is arranged at the rotation and swinging center of the lower connecting plate, a servo valve is arranged on the cylinder body of the swing hydraulic cylinder, the servo valve is connected to the hydraulic station, the angle sensor is connected to a computer, and the computer is connected to the servo valve. 2. A hydraulic swing joint position servo system according to claim 1, characterized in that a hollow shaft is provided at the rotation and swing center of the cylinder body corresponding to the lower connecting plate, bearings are provided at both ends of the hollow shaft, each bearing is provided with a lower connecting plate, a bearing stop plate is provided on the outer side wall of the lower connecting plate, and the two lower connecting plates are symmetrically installed on the piston rod. 3. A hydraulic swing joint position servo system according to claim 2, characterized in that the cylinder body adopts a split design, including a symmetrically designed inner cylinder and outer cylinder, the inner cylinder and the outer cylinder are connected by threads, a servo valve is provided on the side wall of the outer cylinder, the angle sensor is arranged in a hollow shaft, the rotating shaft of the angle sensor is installed on one of the lower connecting plates, and the rotating shaft is collinear with the rotation and swing center of the lower connecting plate. 4. A NDOB-SMC control method for a hydraulic swing joint position servo system, characterized in that it comprises a hydraulic swing joint position servo system according to any one of claims 1 to 3, and the specific steps are as follows: S1. Establish a mathematical model of the hydraulic swing joint position servo system, specifically including: The load torque balance equation of the hydraulic swing joint position servo system is established, and its expression is: _PL = _p1 - _p2 ; k _q =C _d w (1/ρ ^{) 1/2} ; Where A is the effective area of the piston, _PL is the flow gain, _p1 is the upper chamber pressure, _p2 is the lower chamber pressure, _Cd is the flow coefficient, w is the area gradient of the servo valve, ρ is the hydraulic oil density, R is the piston rod rotation radius, _TL is the external load torque, _BP is the equivalent viscous damping coefficient, _JL is the moment of inertia, are all unmodeled disturbances in the system; Define the state variables: Then the state equation of the hydraulic swing joint position servo system is expressed as: In ^{the formula, α＝[α1，α2，α3，α4]T, α1＝BpR2} _{/ JL , d1} ⁽ _{t ) ＝ [} f(t， _x1 ， _x2 )+ _TL ]/ _JL , _d1 (t) is the composite disturbance of the uncertain factors of the system mismatching model, _d2 (t)＝( _4ARβe / _VtJL )Q(t), _d2 ( _t ⁾ is the composite disturbance of the uncertain factors of the system matching model, _α2 ＝ _4ARβekt / _VtJL , _α3 ＝ _4A2R2βe / _VtJL , _α4 ＝4βeCi _{/ Vt} ^{, λ1＝[ps-x3sign(u)JL/AR]1/2} _{, βe is the elastic modulus of} ^the _{oil ,} V _t is the total volume of the two chambers, Q(t) is the time-varying modeling error, u is the total control law of the system, _kt is the total flow gain, _Ci is the internal leakage flow coefficient, _Ce is the external leakage flow coefficient, and _ps is the supply pressure; S2. Design a super spiral interference observer, specifically including: The superhelical interference observer of the mismatched model is constructed, and its expression is as follows: In the formula Where, parameters a ₁ and a ₂ are both positive numbers, and the interference estimate of d ₁ (t) is: The superhelical interference observer of the matching model is constructed, and its expression is as follows: In the formula, Wherein, the parameters a ₃ and a ₄ are both positive numbers, and the interference estimate of d ₂ (t) is: S3. Design a sliding mode controller to obtain the overall control law of the system, which includes: Assuming the angle expected signal of the hydraulic swing joint position servo system is x _d , and the actual angular displacement output signal of the hydraulic swing joint position servo system is x ₁ , the error vector of the hydraulic swing joint position servo system is as follows: make Then the control object can be rewritten as: Combining this formula with the state equation of the hydraulic swing joint position servo system, we get: From this conversion formula we can get: If [c ₁ ,c ₂ ,1] ^T are all greater than zero, the switching function of the sliding surface is: s(x)＝c ₁ e ₁ +c ₂ e ₂ +e ₃ Derivative both sides of the above equation and Substituting the equation into the equation, we get: in: By Japanese style The compensation control law can be obtained for: The design method of sliding mode controller with exponential reaching law is: The overall control law u of the system is obtained as: Where, k ₁ and k ₂ are discontinuous gains of the sliding mode controller, and both are greater than zero; The hydraulic swing joint is precisely controlled according to the system's overall control law u; S4. Conduct joint simulation experiments, including: Firstly, the construction and parameter setting of the hydraulic swing joint position servo system model are completed on the AMEsim platform, and the SimuCosim interface is established. The hydraulic swing joint position servo system model is operated to generate the S function and output information including angle, angular velocity, and pressure to connect with Matlab/Simulink; secondly, the sliding mode control model is established and run on the Matlab/Simulink platform to generate an output control signal u to the AMEsim platform to realize real-time control of the AMEsim platform; finally, the AMEsim platform feeds back the information to the Matlab platform to realize joint simulation. 5. The NDOB-SMC control method of a hydraulic swing joint position servo system according to claim 4, characterized in that, in the step S1, setting 1: the angle expected signal of the hydraulic swing joint position servo system is x _d , x _d ∈ C ³ , and when the hydraulic swing joint position servo system works normally, the swing hydraulic cylinder satisfies: 0＜ _pr ＜p ₁ ＜ _ps , 0＜ _pr ＜p ₂ ＜ _ps , p ₁ is the upper chamber pressure, p ₂ is the lower chamber pressure, p _s is the supply pressure, and p _r is the return oil pressure; and | _PL | is sufficiently smaller than p _s to ensure that α ₂ λ ₁ ≠0; Setting 2: The composite disturbance d _i (t) is bounded and d _i (t) is differentiable. 6. The NDOB-SMC control method of a hydraulic swing joint position servo system according to claim 5, characterized in that in the step S1, Lemma 1 is: assuming 1≤i≤n, considering the controlled system: in, is the state variable, d _i (t) is the composite disturbance, and the first-order derivative of d _i (t) is exist; Using super-helical control law: u _si (t)=u _1i (t)+u _2i (t); Assume that a _i and a _i+1 are positive numbers and satisfy: From this we can get: Therefore, the hydraulic swing joint position servo system is stable and converges to zero in finite time. 7. The NDOB-SMC control method of a hydraulic swing joint position servo system according to claim 6, characterized in that in step S2, the estimated error between the super helical disturbance observer and the hydraulic swing joint position servo system is set to: Will and Subtracting: Combine the above formula with Combined to get: According to Lemma 1, and will converge to zero in a finite time, so the interference estimate of d ₁ (t) is: Similarly, and Subtracting them gives: According to Lemma 1, and will converge to zero in a finite time, so the interference estimate of d ₂ (t) is: 8. The NDOB-SMC control method of a hydraulic swing joint position servo system according to claim 7, characterized in that in step S3, the Lyapunov function of the hydraulic swing joint position servo system is: Take the derivative of both sides of the equation and as well as Substituting in, we get: By It can be seen that when (γ-k ₂ )＜0 and k ₁ ＞0, then Always holds, and only when s＝0, Therefore, the closed-loop system is stable.