Hydraulic swing joint position servo system and NDOB-SMC control method thereof

Abstract

The present application relates to a kind of hydraulic swing joint position servo system and its NDOB-SMC control method, first design hydraulic swing joint position servo system, servo valve and the cylinder body of hydraulic cylinder are integrated direct connection design in this system, abandon oil pipe connection, not only structure is more compact, and reduce part interference factor;Second, design a kind of sliding mode control strategy based on nonlinear disturbance observer, combine nonlinear disturbance observer and sliding mode control, give full play to respective advantages, improve the tracking accuracy and response speed of hydraulic swing joint;Finally, the component model library of AMEsim platform is rich and the powerful numerical operation ability of Matlab platform, by creating S-Function interface, the joint simulation of two platforms is realized, and the effectiveness and superiority of the proposed control method are verified.

Description

Technical fields:

[0001] This invention relates to the field of hydraulic swing joint control technology, specifically to a hydraulic swing joint position servo system and its NDOB-SMC control method. Background technology:

[0002] Currently, most robot joints are driven by motors, but their output power is low, especially in special tasks such as rescue, exploration, and military applications, where their load capacity is insufficient. Through research and discovery, scholars have found that hydraulic robots driven by electro-hydraulic servo systems have advantages such as high power-to-volume ratio, stable operation, and fast response speed. They are gradually being used in modern industry and military fields, and their control issues are increasingly becoming a focus of attention.

[0003] Electro-hydraulic servo systems are affected by the nonlinearity of servo valve flow, the uncertainty of system parameters and models, and other disturbances, increasing the difficulty of developing high-performance controllers for electro-hydraulic servo systems. Conventional PID control is widely used due to its simple algorithm and relatively independent control parameters, but its positioning control capability is poor in nonlinear domains such as electro-hydraulic servo systems. Therefore, many scholars have proposed various control strategies to address the problems of system nonlinearity, parameter uncertainty, and the impact of external disturbances on system tracking accuracy. These include adaptive control, robust control, fuzzy control, active anti-disturbance control, observer-based control, and sliding mode control. Among these, sliding mode control is less sensitive to changes in system parameters and disturbances, exhibiting good adaptability and robustness, making it widely used in military, aerospace, transportation, and other nonlinear control fields. However, due to the existence of sliding modes, sliding mode control can cause chattering at control inputs. Therefore, how to reduce chattering without affecting the performance of the sliding mode controller is a research topic for many scholars. For example, Rubagotti et al. designed an integral form of sliding surface, which enhances the robustness of the system through integral sliding mode control. The sliding mode controller designed by Xue et al. can bring the position error to zero within a certain time, but it requires no external disturbances, and the controller's output parameters still exhibit chattering. Gao et al. proposed a terminal sliding mode control with faster convergence 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 chattering and achieved better control accuracy by combining multiple control strategies. Therefore, with increasing system complexity and control requirements, many scholars have attempted to combine multiple control methods to achieve optimal performance of the entire control system. Some of these scholars have introduced the disturbance observer method to compensate for the controller input; nonlinear disturbance observers are more effective than linear ones.

[0004] Designing disturbance observers is more challenging, while nonlinear disturbance observers can better eliminate uncertainties and unknown disturbances in nonlinear systems, enabling real-time estimation of disturbances. For example, the disturbance observer used by Zhu et al. successfully suppressed external disturbances and improved the system's accuracy. Bu et al. designed a novel nonlinear disturbance observer based on an improved sliding mode differentiator. This observer effectively suppresses nonlinear disturbances, improves the system's robustness, and its effectiveness was verified through simulation. The paper also simulates the designed observer, showing improved accuracy after the problem of unmeasurable elastic states was solved.

[0005] In simulation experiments, most scholars initially conducted simulations based on a single software platform. This method effectively shortened the development cycle, reduced costs and risks, and ensured good reliability. However, due to the increasing complexity of systems and the ever-increasing demands, the inherent nonlinear behavior and modeling uncertainties of electro-hydraulic servo systems make it extremely difficult to establish accurate mathematical models. Using a single software platform for simulation experiments is far from meeting the current needs of simulation. Therefore, in recent years, some scholars have adopted co-simulation methods for research and experiments on electro-hydraulic servo systems and other related fields. Its application areas mainly involve automotive suspensions, machine tools, and lifting actuators. Regarding co-simulation research, Liu et al. studied the modeling method of virtual prototypes and simplified dynamic systems to replace them, but the model establishment was not accurate. Zhang et al. used the S-function interface to call the AMEsim platform to conduct co-simulation with the AMEsim and Matlab platforms, enhancing the ability to develop control strategies for electro-hydraulic lifting systems and effectively verifying the control accuracy of the proposed observer-sliding mode control strategy. To solve the problem of valve core jamming, Chen et al. used three platforms, Matlab, AMEsim and Fluent, for joint simulation and obtained key flow data of each oil port in the spool valve through experiments.

[0006] Analysis of existing literature reveals that scholars have made significant contributions to sliding mode control, nonlinear disturbance observers, and co-simulation. However, when it comes to hydraulic swing joint position servo systems, especially considering the nonlinearity and model uncertainty of electro-hydraulic position servo systems, achieving high-performance control and verifying control strategies through co-simulation have become new technical challenges.

[0007] It should be noted that the above content falls within the inventor's technical knowledge and does not necessarily constitute prior art. Summary of the Invention:

[0008] The purpose of this invention is to address the problems existing in the prior art and provide a hydraulic swing joint position servo system and its NDOB-SMC control method. First, a hydraulic swing joint position servo system is designed, in which the servo valve and hydraulic cylinder are integrated and directly connected, eliminating the need for oil pipe connections. This not only makes the structure more compact but also reduces some interference factors. Second, a sliding mode control strategy based on a nonlinear disturbance observer is designed, combining the nonlinear disturbance observer and sliding mode control to fully leverage their respective advantages and improve the tracking accuracy and response speed of the hydraulic swing joint. Finally, by combining the rich component model library of the AMEsim platform and the powerful numerical computing capabilities of the Matlab platform, an S-Funcution interface is created to achieve joint simulation of the two platforms, verifying the effectiveness and superiority of the proposed control method.

[0009] The present invention achieves the above objectives by adopting the following technical solutions:

[0010] A hydraulic swing joint position servo system includes a hydraulic swing joint, which includes an upper connecting plate and a swing-type hydraulic cylinder on the upper connecting plate. The piston rod of the swing-type hydraulic cylinder is designed in an arc shape, and a lower connecting plate is provided on the piston rod. The lower connecting plate rotates and swings with the piston rod. An angle sensor is provided at the center of the rotation and swing of the lower connecting plate. A servo valve is provided on the cylinder body of the swing-type 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.

[0011] A hollow shaft is provided at the rotational swing center of the cylinder corresponding to the lower connecting plate. Bearings are provided at both ends of the hollow shaft. A lower connecting plate is provided on each bearing. A bearing baffle is provided on the outer wall of the lower connecting plate. The two lower connecting plates are symmetrically installed on the piston rod.

[0012] The cylinder body adopts a split design, including a symmetrically designed inner cylinder and an 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 set in a hollow shaft. The rotating shaft of the angle sensor is mounted on one of the lower connecting plates, and the rotating shaft is collinear with the rotation swing center of the lower connecting plate.

[0013] A method for controlling an NDOB-SMC hydraulic swing joint position servo system, comprising the hydraulic swing joint position servo system as described above, with the following specific steps:

[0014] S1. Establish a mathematical model for the hydraulic swing joint position servo system, specifically including:

[0015] The load torque balance equation of the hydraulic swing joint position servo system is established, and its expression is as follows:

[0016]

[0017] P L =p1-p2;

[0018] k q =C d w(1 / ρ) 1 / 2

[0019] Where A is the effective area of ​​the piston, P L For flow gain, p1 is the upper chamber pressure, p2 is the lower chamber pressure, and C is the lower chamber pressure. d ρ 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, and T is the flow coefficient. L For external load torque, B p J is the equivalent viscous damping coefficient. L For rotational inertia, This refers to all unmodeled interference items in the system;

[0020] Define state variables:

[0021]

[0022] The state equation of the hydraulic swing joint position servo system is expressed as:

[0023]

[0024] In the formula, α=[α1, α2, α3, α4] T ,α1=B p R 2 / J L d1(t)=[f(t,x1,x2)+T L ] / J L d1(t) represents the combined disturbance of uncertainties in the system mismatch model, and d2(t) = (4ARβ) e / V t J L Q(t) and d2(t) represent the combined disturbances of uncertainties in the system matching model, and α2 = 4ARβ e k t / V t J L α3=4A 2 R 2 β e / V t J L α4=4β e C i / V t , λ1=[p s -x3sign(u) J L / AR] 1 / 2 ,β e V is the elastic modulus of the oil. t Let Q(t) be the total volume of the two cavities, Q(t) be the time-varying modeling error, u be the overall system control law, and k be the total volume of the two cavities. t For the total flow gain, C i C is the internal leakage flow coefficient. e p is the external leakage flow coefficient. s Due to supply pressure;

[0025] S2. Design a superhelical interference observer, specifically including:

[0026] The superspiral disturbance observer for the mismatched model is constructed as follows:

[0027]

[0028] In the formula

[0029]

[0030] Where parameters a1 and a2 are both positive numbers, the disturbance estimate of d1(t) is:

[0031]

[0032] The superspiral disturbance observer of the matching model is constructed, and its expression is as follows:

[0033]

[0034] In the formula,

[0035]

[0036] Where parameters a3 and a4 are both positive numbers, the disturbance estimate of d2(t) is:

[0037]

[0038] S3. Design a sliding mode controller to obtain the overall system control law, specifically including:

[0039] The desired angle signal of the hydraulic swing joint position servo system is set to x. d If the actual angular displacement output signal of the hydraulic swing joint position servo system is x1, then the error vector of the hydraulic swing joint position servo system is as follows:

[0040]

[0041] make The controlled object can then be rewritten as:

[0042]

[0043] Combining this equation with the state equation of the hydraulic swing joint position servo system, we get:

[0044]

[0045] From this transformation, we can obtain:

[0046]

[0047] Take [c1, c2, 1] T If all values ​​are greater than zero, then the switching function for the sliding surface is selected as follows:

[0048] s(x) = c1e1 + c2e2 + e3

[0049] Differentiate both sides of the above equation and then... Substituting the equation, we get:

[0050]

[0051] in:

[0052]

[0053] From the formula Japanese style Compensation control law can be obtained for:

[0054]

[0055] The design method for a sliding mode controller based on the exponentially approaching law is as follows:

[0056]

[0057] The overall control law u of the system is obtained as follows:

[0058]

[0059] In the formula, k1 and k2 are the discontinuous gains of the sliding mode controller, and both are greater than zero;

[0060] The hydraulic swing joint is precisely controlled according to the overall system control law u;

[0061] S4. Conduct joint simulation experiments, specifically including:

[0062] First, the hydraulic swing joint position servo system model was built and its parameters were set on the AMEsim platform. A SimuCosim interface was also established, and the hydraulic swing joint position servo system model was manipulated to generate an S-function and output information including angle, angular velocity, and pressure, for connection with Matlab / Simulink. Second, a sliding mode control model was built and run on the Matlab / Simulink platform, generating an output control signal u to the AMEsim platform for real-time control. Finally, the AMEsim platform fed back information to the Matlab platform, thus achieving co-simulation.

[0063] In step S1, setting 1: the desired angle signal of the hydraulic swing joint position servo system is x. d x d ∈C 3 Under normal operating conditions, the hydraulic swing joint position servo system satisfies the following condition for the swing hydraulic cylinder: 0 < p r <p1<p s , 0 < p r <p2<p s p1 is the pressure in the upper chamber, p2 is the pressure in the lower chamber, p s Due to supply pressure, p r The return oil pressure; and |P L |p s It is small enough to ensure that α2λ1≠0;

[0064] Setting 2: Composite interference d i (t) is bounded, and d i (t) is differentiable.

[0065] In step S1, Lemma 1 states: assuming 1 ≤ i ≤ n, consider the controlled system:

[0066]

[0067] Where x~ i d is a state variable. i (t) represents the composite interference, d i The first derivative of (t) exist;

[0068] Employing a superspiral control law:

[0069] u si (t)=u 1i (t)+u 2i (t);

[0070]

[0071]

[0072] Setting: a i a i+1 It is a positive number and satisfies:

[0073]

[0074] Therefore, we can conclude that:

[0075]

[0076] Therefore, the hydraulic swing joint position servo system is stable, and It converges to zero within a finite amount of time.

[0077] In step S2, the estimation error between the super-helical interference observer and the hydraulic swing joint position servo system is set as follows:

[0078]

[0079] Will and

[0080]

[0081] Subtraction yields:

[0082]

[0083] Combine the above formula with Combining the results, we get:

[0084]

[0085] According to Lemma 1, and It will converge to zero in a finite time, thus the disturbance estimate of d1(t) is obtained as:

[0086]

[0087] Similarly, and

[0088]

[0089] Subtraction yields:

[0090]

[0091] According to Lemma 1, and It will converge to zero in a finite time, thus the disturbance estimate of d2(t) is obtained as:

[0092]

[0093] In step S3, the Lyapunov function of the hydraulic swing joint position servo system is taken as:

[0094]

[0095] Differentiate both sides of the equation and then... as well as

[0096]

[0097] Substituting, we get:

[0098]

[0099] From the formula It can be seen that when (γ-k2) < 0 and k1 > 0, then This holds true consistently, and only when s = 0. Therefore, the closed-loop system is stable.

[0100] The present invention, employing the above-described structure, can bring the following beneficial effects:

[0101] Building upon the research of other scholars, this paper first innovatively designs a hydraulic swing joint position servo system. The biggest improvement of this system lies in directly connecting the servo valve to the cylinder body, eliminating the need for the oil delivery pipeline between the servo valve and the traditional hydraulic cylinder. This significantly improves space utilization, mitigates the nonlinearity of pipeline volume changes caused by oil pressure and temperature, and reduces some interference factors. Based on this, a sliding mode control strategy based on a nonlinear disturbance observer is designed, and a mathematical model of the hydraulic swing joint position servo system is established. Based on this, the uncertainty factors and disturbances of the system are compensated using a disturbance observer method to reduce their impact 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 built using the AMEsim platform, and a sliding mode controller based on a nonlinear disturbance observer is built on the Matlab / Simulink platform. Finally, co-simulation is conducted by calling the AMEsim platform through the S-function interface, verifying the effectiveness and superiority of the proposed control method. Attached image description:

[0102] Figure 1 This is a schematic diagram of the hydraulic swing joint of the present invention;

[0103] Figure 2 This is a schematic diagram of the hydraulic swing joint of the present invention from another perspective;

[0104] Figure 3This is an exploded view of the hydraulic swing joint of the present invention;

[0105] Figure 4 This is an exploded view of the hydraulic swing joint of the present invention from another perspective.

[0106] Figure 5 This is a schematic diagram of the hydraulic swing joint of the present invention installed on a wearable device;

[0107] Figure 6 This is a schematic diagram illustrating the working principle of the hydraulic swing joint position servo system of the present invention.

[0108] Figure 7 This is a schematic diagram of the co-simulation between AMEsim16 and Matlab 2016a in this invention;

[0109] Figure 8 This is a schematic diagram of the hydraulic system model in AMEsim of the present invention;

[0110] Figure 9 This is a schematic diagram of the NDOB-SMC controller in Matlab for this invention;

[0111] Figure 10 This is a simulation result diagram verifying the effectiveness of the constant load of the NDOB-SMC of this invention;

[0112] Figure 11 This is a diagram showing the variable load sub-model and its mass variation curve of the present invention.

[0113] Figure 12 The figure shows the joint simulation results of the present invention using variable load;

[0114] Figure 13 This is a comparison chart of angle errors under the variable amplitude sinusoidal signal of this invention;

[0115] Figure 14 This is a comparison chart of angle tracking curves under the variable amplitude sinusoidal signal of this invention;

[0116] Figure 15 This is a comparison chart of angle tracking curves under the triangular wave signal of this invention;

[0117] Figure 16 This is a comparison chart of angle tracking curves under variable amplitude signals according to the present invention;

[0118] Figure 17 This is a comparison diagram of angle errors under the triangular wave input signal of this invention;

[0119] Figure 18 This is a comparison chart of angle errors under the variable amplitude input signal of this invention;

[0120] In the diagram, 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. Rotary shaft, 5. Servo valve, 6. Hydraulic station, 601. Oil tank, 602. Hydraulic pump, 603. Electric motor, 604. Safety valve, 605. Suction filter, 7. Computer, 8. Hollow shaft, 9. Bearing, 10. Bearing retainer, 11. Wearable device. Detailed implementation method:

[0121] To more clearly illustrate the overall concept of the present invention, a detailed description will be provided below with reference to the accompanying drawings and examples.

[0122] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0123] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0124] Furthermore, the terms “upper,” “lower,” “rotational swing,” “inner,” and “outer” are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the location of the indicated technical feature.

[0125] In this invention, it should be noted that, for ease of description and better understanding of the present application, (n) is set after the formula, where n is a positive integer and (n) only represents the sequence number of the formula.

[0126] In this invention, unless otherwise explicitly specified and limited, the terms "provided with," "set up," and "connected" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection; they can refer to a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0127] like Figure 1-6As shown, a hydraulic swing joint position servo system includes a hydraulic swing joint. The hydraulic swing joint includes an upper connecting plate 1, on which a swing-type hydraulic cylinder 2 is mounted. The piston rod 202 of the swing-type hydraulic cylinder 2 is designed in an arc shape. A lower connecting plate 3 is mounted on the piston rod 202, and the lower connecting plate 3 rotates and swings with the piston rod 202. An angle sensor 4 is located at the center of the rotation and swing of the lower connecting plate 3. A servo valve 5 is mounted on the cylinder body 201 of the swing-type hydraulic cylinder 2. The servo valve 5 is connected to a hydraulic station 6 via an oil circuit. The angle sensor 4 is communicatively connected to a computer 7, and the computer 7 is communicatively connected to the servo valve 5. In hydraulically driven robots, linear telescopic piston cylinders and swing cylinders are the two most common drive modes. Robots using linear telescopic piston cylinder hydraulic drives indirectly realize the movement of robot joints, but their large size and the additional nonlinear problems caused by the structure limit the robot's performance. To address the aforementioned issues, this paper designs a compact hydraulic swing joint integrating a cylinder body and servo valve. The servo valve 5 is mounted on the swing hydraulic cylinder 2, eliminating the need for a separate oil delivery pipeline between the servo valve 5 and the traditional hydraulic cylinder. This significantly improves space utilization, reduces the nonlinearity of pipeline volume changes caused by oil pressure and temperature variations, and minimizes some interference factors. The hydraulic swing joint position servo system operates as follows: First, the oil in the system flows under the action of the hydraulic pump 602 (a component of the hydraulic station 6, driven by an electric motor 603; the entire oil circuit also includes an oil tank 601, a safety valve 604, and a suction filter 605). The flow rate and direction of the oil are controlled by the servo valve 5. Then, the oil is supplied to the swing hydraulic cylinder 2, causing the piston rod 202 in the swing hydraulic cylinder 2 to operate and drive the joint to rotate and swing. 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 degree of the servo valve 5, thereby realizing the angular position control of the hydraulic swing joint. In practical applications, the hydraulic swing joint position servo system of this application needs to be installed on the wearable device 11 to achieve interaction with the human body.

[0128] A hollow shaft 8 is provided at the rotational swing center of the cylinder body 201 corresponding to the lower connecting plate 3. Bearings 9 are provided at both ends of the hollow shaft 8, and each bearing 9 is equipped with one lower connecting plate 3. A bearing baffle 10 is provided on the outer wall of the lower connecting plate 3. The two lower connecting plates 3 are symmetrically mounted on the piston rod 202. By designing the hollow shaft 8 and bearings 9, the rotation of the lower connecting plate 3 can be supported, resulting in better structural strength and rotational swing stability of the lower connecting plate 3.

[0129] The cylinder body 201 adopts a split design, including a symmetrically designed inner cylinder 203 and outer cylinder 204. The inner cylinder 203 and outer cylinder 204 are connected by threads (using bolts, nuts, or other threaded structures; the mounting holes are shown in the diagram). A coil spring 11 is provided between the outer cylinder 204 and the lower connecting plate 3 located on the outer side, and a coil spring 11 is provided between the inner cylinder 203 and the lower connecting plate 3 located on the inner side. A servo valve 5 is provided on the side wall of the outer cylinder 204. The angle sensor 4 is installed inside the hollow shaft 8, and the rotating shaft 401 of the angle sensor 4 is mounted on one of the lower connecting plates 3, with the rotational swing center of the rotating shaft 401 collinear with that of the lower connecting plate 3. The split design of the cylinder body 201 not only facilitates the installation and disassembly of the piston rod 202, but also facilitates the direct machining of the required oil passages on the outer cylinder 204, enabling direct connection with the servo valve 5 (without oil pipe connection).

[0130] like Figure 7-9 As shown, an NDOB-SMC control method for a hydraulic swing joint position servo system includes the hydraulic swing joint position servo system described above, with the following specific steps:

[0131] S1. Establish a mathematical model for the hydraulic swing joint position servo system, specifically including:

[0132] First, the flow equation for servo valve 5 can be expressed as:

[0133]

[0134] Q L =(Q1+Q2) / 2 (2)

[0135] P L =p1-p2 (3)

[0136] k q =C d w(1 / ρ) 1 / 2 (4)

[0137] In the formula, Q L Where Q1 is the flow rate in the high-level chamber, Q2 is the flow rate in the low-level chamber, and X is the load flow rate. v P represents the valve core displacement of the spool valve. s Due to supply pressure, P L For flow gain, C d ρ is the flow coefficient, w is the area gradient of the servo valve, and ρ is the hydraulic oil density.

[0138] Where, sign(X) v It can be described as:

[0139]

[0140] This application uses a high-response servo valve, therefore the control of servo valve 5 is proportional to the displacement of the spool valve, i.e., X v =k v u, where k v Let u be the amplification gain of the servo amplifier and u be the overall system control law. Therefore, formula (1) can be converted to:

[0141]

[0142] k t =k v k q (7)

[0143] Where, k t This represents the total flow gain relative to u.

[0144] The flow continuity equation for a swing-type hydraulic cylinder is:

[0145]

[0146]

[0147] Equations (8) and (9) above can be transformed into pressure dynamic equations for the two chambers of a swing-type hydraulic cylinder:

[0148]

[0149] Where Q(t) is the time-varying modeling error (caused by internal leakage, parameter deviation, unmodeled pressure dynamics, etc.), and C i C is the internal leakage flow coefficient. e V is the external leakage flow coefficient, V1 is the effective volume of the upper cavity, V2 is the effective volume of the lower cavity, and V... t For the total volume of the two cavities, β e This refers to the elastic modulus of the oil.

[0150] The hydraulic swing joint proposed in this paper is based on the mathematical model and control of an arc-shaped hydraulic cylinder. Compared with the load force balance equation of the traditional straight-rod piston hydraulic cylinder, the arc-shaped swing hydraulic cylinder adopts the load moment balance equation. Since the motion characteristics of the hydraulic cylinder's power components are affected by loads, including viscous damping force, inertial 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:

[0151]

[0152] P L =p1-p2 (12)

[0153] k q=C d w(1 / ρ) 1 / 2 (13)

[0154] Where A is the effective area of ​​the piston, p1 is the pressure in the upper chamber, p2 is the pressure in the lower chamber, R is the radius of rotation of the piston rod, and T is the effective area of ​​the piston. L For external load torque, B p J is the equivalent viscous damping coefficient. L For rotational inertia, This refers to all unmodeled interference items in the system;

[0155] Define state variables:

[0156]

[0157] The state equation of the hydraulic swing joint position servo system is expressed as:

[0158]

[0159] In the formula, α=[α1, α2, α3, α4] T ,α1=B p R 2 / J L d1(t)=[f(t,x1,x2)+T L ] / J L d1(t) represents the combined disturbance of uncertainties in the system mismatch model, and d2(t) = (4ARβ) e / V t J L Q(t) and d2(t) represent the combined disturbances of uncertainties in the system matching model, and α2 = 4ARβ e k t / V t J L α3=4A 2 R 2 β e / V t J L α4=4β e C i / V t , λ1=[p s -x3sign(u) J L / AR] 12 .

[0160] Assumption 1: The desired angle signal of the hydraulic swing joint position servo system is x. d x d ∈C 3 Under normal operating conditions, the hydraulic swing joint position servo system satisfies the following condition for the swing hydraulic cylinder: 0 < pr <p1<p s , 0 < p r <p2<p s , where p r The return oil pressure; and |P L |p s It is small enough to ensure that α2λ1≠0;

[0161] Assumption 2: Composite interference d i (t) is bounded, meaning there exists an unknown positive real number ψ. i >0, such that |d i (t)|≤ψ i , at the same time d i (t) is differentiable, that is, it exists.

[0162] Lemma 1: Let 1 ≤ i ≤ n, and consider a controlled system:

[0163]

[0164] in, d is a state variable. i (t) represents the composite interference, d i The first derivative of (t) exist;

[0165] Employing a superspiral control law:

[0166] u si (t)=u 1i (t)+u 2i (t) (17)

[0167]

[0168]

[0169] Setting: a i a i+1 It is a positive number and satisfies:

[0170]

[0171] Therefore, we can conclude that:

[0172]

[0173] Therefore, the hydraulic swing joint position servo system is stable, and It converges to zero within a finite amount of time.

[0174] S2. Design a superhelical interference observer, specifically including:

[0175] Based on formula (15) and under the premises of assumptions 1 and 2, a superspiral disturbance observer for the mismatched model is constructed, and its expression is as follows:

[0176]

[0177] In the formula

[0178]

[0179] Where parameters a1 and a2 are both positive numbers, the disturbance estimate of d1(t) is:

[0180]

[0181] Based on formula (15) and under the premises of assumptions 1 and 2, a superspiral disturbance observer for the matching model is constructed, and its expression is as follows:

[0182]

[0183] In the formula,

[0184]

[0185] Where parameters a3 and a4 are both positive numbers, the disturbance estimate of d2(t) is:

[0186]

[0187] Verification of the above calculations:

[0188] The estimation error between the superhelical interference observer and the system is set as:

[0189]

[0190] In equation (15) Subtracting from equation (22) gives:

[0191]

[0192] Combining equation (23) and equation (29), we get:

[0193]

[0194] According to Lemma 1, and It will converge to zero in a finite time, so the disturbance estimate of d1(t) is obtained as equation (24).

[0195] Similarly, in equation (15) Subtracting from equation (25) yields:

[0196]

[0197] According to Lemma 1, and It will converge to zero in a finite time, so the disturbance estimate of d2(t) is obtained as equation (27).

[0198] S3. Design a sliding mode controller to obtain the overall system control law, specifically including:

[0199] The desired angle signal of the hydraulic swing joint position servo system is set to x. d If the actual angular displacement output signal of the hydraulic swing joint position servo system is x1, then the error vector of the hydraulic swing joint position servo system is as follows:

[0200]

[0201] make The controlled object can then be rewritten as:

[0202]

[0203] Combining this equation with the state equation of the hydraulic swing joint position servo system, we get:

[0204]

[0205] From this transformation, we can obtain:

[0206]

[0207] Take [c1, c2, 1] T If all values ​​are greater than zero, then the switching function for the sliding surface is selected as follows:

[0208] s(x)=c1e1+c2e2+e3 (36)

[0209] Differentiate both sides of the above equation and then... Substituting the equation, we get:

[0210]

[0211] in:

[0212]

[0213] From the formula Japanese style Compensation control law can be obtained for:

[0214]

[0215] The design method for a sliding mode controller based on the exponentially approaching law is as follows:

[0216]

[0217] The overall control law u of the system is obtained as follows:

[0218]

[0219] In equation (41), k1 and k2 are the discontinuous gains of the sliding mode controller, and both are greater than zero;

[0220] The hydraulic swing joint is precisely controlled according to the overall system control law u.

[0221] Stability analysis:

[0222] The Lyapunov function of the system is:

[0223]

[0224] Differentiating both sides of equation (42) and substituting equations (37) and (40) into the equation, we obtain equation (43):

[0225]

[0226] From the formula It can be seen that when (γ-k2) < 0 and k1 > 0, then This holds true consistently, and only when s = 0. Therefore, the closed-loop system is stable.

[0227] S4. Conduct joint simulation experiments, specifically including:

[0228] The nonlinearity and modeling uncertainties of electro-hydraulic servo control systems make it difficult to directly establish accurate mathematical models. However, the AMEsim and Matlab co-simulation platform not only integrates AMEsim's fluid simulation capabilities for mechanical and hydraulic systems but also fully utilizes Matlab's powerful numerical computation capabilities. Therefore, using the S-function interface to call the two platforms, drawing on their respective advantages, achieves perfect complementarity. A co-simulation model was built in Matlab 2016a and AMEsim 16 to verify the effectiveness of the proposed controller.

[0229] First, the hydraulic swing joint position servo system model was built and its parameters were set on the AMEsim platform. A SimuCosim interface was also established, and the hydraulic swing joint position servo system model was manipulated to generate an S-function and output information including angle, angular velocity, and pressure, for connection with Matlab / Simulink. Second, a sliding mode control model was built and run on the Matlab / Simulink platform, generating an output control signal u to the AMEsim platform for real-time control. Finally, the AMEsim platform fed back information to the Matlab platform, thus achieving co-simulation.

[0230] The main parameters of the AMEsim hydraulic system are shown in the table below:

[0231]

[0232] To verify the effectiveness and superiority of the sliding mode control method based on nonlinear disturbance observer proposed in this paper in a hydraulic swing joint position servo system, simulation comparison experiments were conducted on three control schemes: NDOB-SMC, traditional PID, and traditional SMC. This section mainly designs the following two simulation scenarios: (1) Considering the input signal as a sinusoidal signal, the effectiveness analysis of NDOB-SMC control under constant load and variable load conditions. (2) Under the condition of variable load, the superiority analysis of the three control methods is carried out for the input sinusoidal signal, triangular wave signal, and variable amplitude signal.

[0233] (1) Validity analysis

[0234] When the load force is constant, the hydraulic swing joint swings for a time of t = 24s, performing a sinusoidal motion from -20° to 20°. A sinusoidal signal with an amplitude of 20, a frequency of π / 4, and a phase of -π / 2 is given, and the constant load is 15kg. The NDOB-SMC control parameters are k1 = 3.9e3, k2 = 5, c1 = 4e4, and c2 = 400. The disturbance observer parameters are a1 = 5, a2 = 3, a3 = 5, and a4 = 3, with gains of 0.8e-5 and 0.6e-6 respectively. The simulation results are as follows: Figure 10 As shown.

[0235] To better verify the effectiveness of the proposed control, a variable load was used instead of a constant load. However, no suitable sub-model existed in AMEsim. Therefore, the AMEsim set function was used to design a variable load sub-model that varies sinusoidally within the range of 5kg to 25kg. The sub-model design and load variation curve are shown below. Figure 11 As shown. Figure 12 The figure shows the results of the co-simulation using variable load.

[0236] Through the above joint simulation test, it has been proven that NDOB-SMC can stabilize the tracking accuracy within a fixed range under both constant load and variable load operating conditions.

[0237] (2) Advantages Analysis

[0238] To verify the superiority of the proposed control algorithm, this experiment compared it with traditional PID control and traditional SMC control. PID control 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: k3 = 3.9e3, k4 = 5, c3 = 4e4, c4 = 400. A sinusoidal signal with an amplitude of 20, a frequency of π / 4, and a phase of -π / 2 is given. The load remains variable, and its curve is shown below. Figure 10 As shown in the figure. The error curve results of the simulation experiment are as follows. Figure 13 As shown, the angle tracking curve is as follows: Figure 14 As shown.

[0239] from Figure 13 and 14 It can be clearly observed that, under the same sinusoidal desired signal input, the angle error of SMC control is within ±0.15°, while the angle error of traditional PID control reaches ±0.2°. From... Figure 11 The data shows that sliding mode control with added nonlinear disturbance observer can stably control the angle error within ±0.1°, and has better tracking accuracy compared with traditional SMC and traditional PID control.

[0240] To fully verify the superiority and adaptability of the proposed NDOB-SMC control in practical applications of hydraulic swing joint position servo systems, experiments were conducted using a triangular wave signal with a range of ±20° and a sinusoidal signal with a variable amplitude varying from -20° to 90° as the desired signal. The performance of the three controllers was then examined. The simulation results of the triangular wave signal angle tracking are shown below. Figure 15 As shown, the angle tracking results of the variable amplitude sinusoidal signal are as follows: Figure 16 As shown in the figure. The angle errors under the two signals are respectively as follows: Figure 17 , 18 As shown.

[0241] like Figure 15 , 17 As shown, when the desired signal is a triangular wave, NDOB-SMC control, compared with traditional PID control (error ±0.1°) and traditional SMC control (error ±0.15°), can still stabilize the angle error within ±0.05°, despite large fluctuations near the turning point of the triangular wave, enabling the tracking angle to converge quickly and achieving better tracking accuracy.

[0242] like Figure 16 , 18 The results clearly show that when the amplitude is used as the desired signal, the overall angle error of NDOB-SMC can be stably controlled within ±0.5°, exhibiting better tracking accuracy. In contrast, the angle error of traditional PID control fluctuates within ±1°, and the angle error of traditional SMC control fluctuates within ±0.75°, showing poorer tracking performance than NDOB-SMC control. NDOB-SMC control can accept various input signals and adapt well to different load quality variations. These experimental results demonstrate that the proposed control strategy has higher control accuracy and also enables the system to achieve better dynamic performance and a stable state, meeting the needs of practical operating conditions.

[0243] The above specific embodiments should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, any alternative improvements or modifications made to the embodiments of the present invention shall fall within the scope of protection of the present invention.

[0244] Any aspects of this invention not described in detail are well-known to those skilled in the art.

Claims

1. An NDOB-SMC control method for a hydraulic swing joint position servo system, characterized by, The hydraulic swing joint position servo system comprises a hydraulic swing joint, 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 in a circular arc shape, a lower connecting plate is arranged on the piston rod, the lower connecting plate rotates and swings along with the piston rod, an angle sensor is arranged at the center of the rotation and swing of the lower connecting plate, a servo valve is arranged on a cylinder body of the swing hydraulic cylinder, the servo valve is connected with a hydraulic station, the angle sensor is connected with a computer, and the computer is connected with the servo valve; a hollow shaft is arranged at the center of the rotation and swing of the lower connecting plate on the cylinder body, bearings are arranged at two ends of the hollow shaft, one lower connecting plate is arranged on each bearing, bearing stop plates are arranged on outer side walls of the lower connecting plates, and the two lower connecting plates are symmetrically arranged on the piston rod; the cylinder body is designed in a split mode and comprises symmetrically designed inner and outer cylinder barrels, the inner and outer cylinder barrels are connected through threads, the servo valve is arranged on a side wall of the outer cylinder barrel, the angle sensor is arranged in the hollow shaft, a rotating shaft of the angle sensor is arranged on one of the lower connecting plates, and the rotating shaft is collinear with the center of the rotation and swing of the lower connecting plate; The NDOB-SMC control method comprises the following steps: S1, a mathematical model of the hydraulic swing joint position servo system is established, specifically comprising: A load torque balance equation of the hydraulic swing joint position servo system is established, and the expression is as follows: ； ； ； wherein, Aeffis the piston effective area, G is the flow gain, Pupis the upper chamber pressure, Pdownis the lower chamber pressure, C is the flow coefficient, K is the area gradient of the servo valve, rho is the hydraulic oil density, r is the piston rod rotation radius, Tloadis the external load torque, Ceqis the equivalent viscous damping coefficient, J is the moment of inertia, d is all the unmodeled disturbances in the system; The state variable is defined as: ； The state equation of the hydraulic swing joint position servo system is expressed as: ； In the formula, , , , is the compound disturbance of the uncertainty factor of the system mismatch model, , is the compound disturbance of the uncertainty factor of the system matching model, , , , , is the elastic modulus of the oil, is the total volume of the two cavities, is the time-varying modeling error, is the total control law of the system, is the total flow gain, is the internal leakage flow coefficient, is the external leakage flow coefficient, is the supply pressure; S2, an over-helix disturbance observer is designed, specifically comprising: An over-helix disturbance observer of a mismatched model is constructed, and the expression is as follows: ； In the formula ； Among them, parameters , If all are positive numbers, then The interference is estimated as follows: ； An over-helix disturbance observer of a matched model is constructed, and the expression is as follows: ； In the formula, ； Among them, parameters , If all are positive numbers, then The interference is estimated as follows: ； S3, a sliding mode controller is designed to obtain a total control law of the system, specifically comprising: Let the angle desired signal of the hydraulic swing joint position servo system be set as , the actual angle displacement output signal of the hydraulic swing joint position servo system be , then the error vector of the hydraulic swing joint position servo system is as follows: ； Let Then the control object can be rewritten as: ； The formula is combined with the state equation of the hydraulic swing joint position servo system to obtain: ； The formula is converted from the formula to obtain: ； Take If both are greater than zero, the switching function of the sliding surface is selected as: ； Taking the derivative of both sides of the equation above and setting Substituting the equation gives: ； Wherein: ； The compensation control law is obtained as and is ​ ； The sliding mode controller design method of the exponential approach law is selected as: ； The total control law of the system is obtained is: ； wherein , are the discontinuous gains of the sliding mode controller and are both greater than zero; According to the system total control law Precise control of the hydraulic swing joint; S4, a joint simulation experiment is performed, specifically comprising: Firstly, the model of hydraulic swing joint position servo system is built and parameters are set on AMEsim platform, and SimuCosim interface is established. The model of hydraulic swing joint position servo system is operated to generate function and output information including angle, angular velocity and pressure, so as to be connected with Matlab / Simulink. Secondly, the model of sliding mode control is built and run on Matlab / Simulink platform to generate an output control signal to AMEsim platform, so as to realize real-time control of AMEsim platform. Finally, AMEsim platform feeds back information to Matlab platform, so as to realize joint simulation.

2. The NDOB-SMC control method of a hydraulic swing joint position servo system according to claim 1, wherein In step S1, setting 1: the desired angle signal of the hydraulic swing joint position servo system is... , Under normal operating conditions, the hydraulic cylinder of the swing joint position servo system satisfies the following requirements: , , For the upper chamber pressure, The pressure in the lower chamber. Due to supply pressure, This is the return oil pressure; and Compare Small enough to ensure ; Setting 2: Composite Interference bounded, and differentiable.

3. The NDOB-SMC control method of hydraulic swing joint position servo system according to claim 2, wherein, In the step S1, Lemma 1 is: setting , consider the controlled system: ； wherein is a state variable, is a composite disturbance, a first derivative exists; The over-helix control law is adopted: ； ； ； Set: , is positive and satisfies: ； Thus, the following can be obtained: ； Therefore, the hydraulic swing joint position servo system is stable, and 、 converges to zero in a limited time.

4. The NDOB-SMC control method of hydraulic swing joint position servo system according to claim 3, wherein, In the step S2, the estimation error between the over-helix disturbance observer and the hydraulic swing joint position servo system is set as: ， To with ； The following is obtained by subtraction: ； The above formula is combined with gives: ； According to Lemma 1, and will converge to zero in finite time, thus obtaining the interference estimate is ； By analogy, the same applies to and ； The following is obtained by subtraction: ； According to Lemma 1, and will converge to zero in finite time, thus obtaining the interference estimate is 。 5. The NDOB-SMC control method of hydraulic swing joint position servo system according to claim 4, wherein, In the step S3, the Lyapunov function of the hydraulic swing joint position servo system is taken as: ； Taking the derivative of both sides of the equation and setting them equal to each other gives and ； The following is obtained by substitution: ； From the formula it is known that when and then is always true and only when , , so the closed-loop system is stable.

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