An improved position control method for a direct-drive electrostatic hydraulic actuator

Abstract

The present invention provides an improved position control method for a direct-drive electrostatic-hydraulic actuator, and belongs to the field of control. The method comprises: firstly, considering the nonlinear characteristics of the direct-drive electrostatic-hydraulic actuator system, establishing a state space model of the system, and reasonably simplifying it into a strict feedback form, wherein the power unit of the direct-drive electrostatic-hydraulic actuator system is a permanent magnet synchronous motor, and the hydraulic pump is a gear pump. Secondly, the obstacle Lyapunov function is combined with the backstepping controller, and the constraint boundary is introduced to ensure the output constraint performance of the system. Finally, the adaptive rate of the uncertain parameters is established to adjust the parameter disturbance in real time online and perform stability analysis. The present invention can solve the problem of system parameter uncertainty in the position control process of the direct-drive electrostatic-hydraulic actuator, and improve the control accuracy and robustness of the direct-drive electrostatic-hydraulic actuator control system.

Description

Technical Field

[0001] The present invention mainly relates to the field of control-related technology, and in particular to an improved position control method for a direct-drive electrostatic hydraulic actuator. Background Art

[0002] Conventional electrostatic hydraulic actuators achieve displacement control of the hydraulic actuator cylinder by controlling the pressure and flow output by the rotary motor driving the swash plate piston pump, while direct-drive electrostatic hydraulic actuators directly drive the bidirectional gear pump to output pressure and flow through a rotary motor. They have no mechanical motion conversion mechanism and have advantages such as simple structure and fast response. Therefore, direct-drive electrostatic hydraulic actuators have become an important research hotspot. In recent years, domestic and foreign scholars have conducted relevant research on the high-precision position control of electrostatic hydraulic actuators.

[0003] The direct-drive electrostatic hydraulic actuator system is a typical uncertain nonlinear system with many nonlinear characteristics and model uncertainties. At present, in order to solve the problems caused by transient parameter time-varying and nonlinear factors, researchers at home and abroad mainly use sliding mode control, adaptive control, neural network control and backstepping control. Although sliding mode control has good robustness to parameter changes, it often causes chattering in practical applications, which affects the control accuracy and smoothness of the system. In addition, the sliding mode controller requires accurate modeling of the system and has difficulty in dealing with high-frequency chattering. Adaptive control can handle system parameter changes, but its performance may be limited when facing complex system dynamics and unmodeled disturbances. The neural network control method relies on a large amount of data training, and the network structure design is complex. Although it has strong self-learning ability, it may take a long time to train when dealing with nonlinear characteristics.

[0004] Backstepping control has strong robustness and adaptability. Combining backstepping control with adaptive control can effectively handle complex nonlinear systems. The industrial field requires electrostatic hydraulic actuators to have fast response and stable capabilities. However, due to the uncertainty of system parameters in the position control process of direct-drive electrostatic hydraulic actuators, backstepping control still needs to be further improved in the position control of direct-drive electrostatic hydraulic actuators. Summary of the invention

[0005] In order to solve the shortcomings of the current technology, the present invention combines the existing technology and starts from practical application to provide an improved position control method for a direct-drive electrostatic hydraulic actuator, which combines backstepping control with adaptive control. It can effectively handle complex nonlinear systems, cope with model uncertainties and parameter changes, and dynamically adjust the control strategy through an adaptive mechanism to improve the robustness of the system. In the adaptive backstepping control, the obstacle Lyapunov function is used to introduce constraint boundaries to ensure the output constraint performance of the system.

[0006] The technical solution of the present invention is as follows:

[0007] An improved position control method for a direct-drive electrostatic hydraulic actuator, wherein the power unit of the direct-drive electrostatic hydraulic actuator system is a permanent magnet synchronous motor, and the hydraulic pump is a gear pump. The control method comprises the following steps:

[0008] S1. Based on the nonlinear characteristics of the direct-drive electrostatic hydraulic actuator system, the state space model of the system is established and simplified into a strict feedback form;

[0009] S2. Based on the established system state space model, a backstepping controller combined with the barrier Lyapunov function is designed, and the constraint boundary is introduced to obtain the expression of the actual control rate of the controller;

[0010] S3. Based on the backstepping controller, the adaptive rate of the uncertain parameters is established to adjust the parameter disturbance online in real time.

[0011] Further, in step S1, establishing a state space model of the system includes the following steps:

[0012] Based on the open-loop transfer function of the position servo of the direct-drive electrostatic hydraulic actuator and the state vector of the position control system of the direct-drive electrostatic hydraulic actuator, the state space model expression of the system is obtained.

[0013] Furthermore, the position servo open-loop transfer function expression of the direct-drive electrostatic hydraulic actuator is as follows:

[0014] ,

[0015] The state vector expression of the direct-drive electrostatic hydraulic actuator position control system is as follows:

[0016] ,

[0017] The state space model expression of the system is as follows:

[0018] ,

[0019] in, , , is the control variable, is the viscous damping coefficient, is the Laplace transform, is the controller control rate, is the effective action area of ​​the piston of the hydraulic cylinder; is the displacement of the hydraulic cylinder piston rod; is the total leakage coefficient of the hydraulic cylinder; is the total compression volume of the hydraulic cylinder; is the effective bulk elastic modulus of hydraulic oil; is the total load mass of the piston rod and its fixed part; is the load spring stiffness; is the external disturbance force, is the rated displacement of the gear pump; is the gear pump angular velocity; is the gear pump leakage coefficient; is the load pressure, is the load disturbance and , , , , .

[0020] Further, in step S2, the backstepping controller is established as follows:

[0021] The state tracking error vector of the direct-drive electrostatic hydraulic actuator system is defined as follows:

[0022] ,

[0023] In the formula, is the system output displacement tracking error, , The state error defined for the system; is the system tracking error limit and ; is the expected value of the system displacement; and Two virtual control quantities designed for the controller;

[0024] Select the barrier Lyapunov function:

[0025] ,

[0026] Get virtual control amount for:

[0027] ,

[0028] In the above formula, is a positive real number;

[0029] By differentiating the obstacle Lyapunov function, we can obtain:

[0030] ,

[0031] right Take the time derivative:

[0032] ,

[0033] because It is not a constrained term, and the quadratic Lyapunov function is chosen:

[0034] ,

[0035] Get virtual control amount for:

[0036] ,

[0037] By differentiating the quadratic Lyapunov function, we can obtain:

[0038] ,

[0039] Defining parameter errors ,in For parameters The estimated value ( ), for the error Taking the derivative, it can be expressed as:

[0040] ,

[0041] Define the third candidate Lyapunov function:

[0042] ,

[0043] In the above formula, , , are all positive real numbers;

[0044] Derivative the third candidate Lyapunov function of the formula yields:

[0045] ,

[0046] In the above formula, is a positive real number;

[0047] According to the above formula, the actual control variable is derived:

[0048] ,

[0049] In the above formula, is a positive real number, is the disturbance estimate and .

[0050] Further, in step S3, the expression of the uncertain parameter adaptation rate is as follows:

[0051] .

[0052] . Further, the control method also includes: step S4, using Lyapunov function to analyze the stability of the system.

[0053] Further, step S4 specifically includes:

[0054] Define the Lyapunov function as:

[0055] ,

[0056] Its derivative with respect to time is obtained as:

[0057] ,

[0058] The above formula can be rewritten as:

[0059] .

[0060] When the parameter adaptation rate of step S3 is taken:

[0061] .

[0062] Satisfy the Lyapunov stability condition and control and Stable at the equilibrium point, when the state error While gradually converging to 0, the system output error It also gradually converges to 0, ensuring that the final output position error of the direct-drive electrostatic hydraulic actuator system gradually converges to 0.

[0063] Beneficial effects of the present invention:

[0064] The improved position control method of the direct-drive electrostatic hydraulic actuator of the present invention proposes a nonlinear adaptive backstepping control method based on the barrier Lyapunov function to solve the problem of system parameter uncertainty in the position control process of the direct-drive electrostatic hydraulic actuator. Firstly, the nonlinear characteristics of the direct-drive electrostatic hydraulic actuator system are considered, and the state space model of the system is established and reasonably simplified into a strict feedback form; secondly, the barrier Lyapunov function is combined with the backstepping controller, and the constraint boundary is introduced to ensure the output constraint performance of the system; finally, the adaptive rate of the uncertain parameters is established to adjust the parameter disturbance online in real time and perform stability analysis;

[0065] Practice has proved that the adaptive backstepping controller designed in the present invention updates system parameters in real time through the adaptive law, and its performance is significantly better than that of the direct backstepping controller and the traditional PI controller, and can significantly improve the tracking accuracy of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1This is a block diagram of the working principle of the system of the present invention;

[0067] Figure 2 This is a comparison diagram of the step tracking experiment of the control method of the present invention;

[0068] Figure 3 This is a comparison diagram of the sinusoidal tracking experiment of the control method of the present invention; Figure 3 (a) is a comparison of the sinusoidal tracking experimental results of three controllers; Figure 3 (b) is a schematic diagram of the speed curve result of the adaptive backstepping controller; Figure 3 (c) is a comparison chart of tracking errors of three controllers;

[0069] Figure 4 This is a control block diagram of the control method of the present invention. DETAILED DESCRIPTION

[0070] The present invention will be further described with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art may make various changes or modifications to the present invention, and these equivalent forms also fall within the scope limited by the application.

[0071] This embodiment provides an improved position control method for a direct-drive electrostatic hydraulic actuator. Figure 1 The control method provided in this embodiment mainly includes establishing a state space model of the system, designing a backstepping controller based on an obstacle Lyapunov function, designing an adaptive rate based on the backstepping controller, and using the Lyapunov function to prove the stability of the system.

[0072] Among them, considering the nonlinear characteristics of the direct-drive electrostatic hydraulic actuator system, the state space model of the system is established and reasonably simplified into a strict feedback form as follows:

[0073] The direct-drive electrostatic hydraulic actuator system is mainly composed of a power unit, a gear pump, a hydraulic cylinder and a control system. The power unit is directly connected to the gear pump and drives the gear pump to rotate.

[0074] The power unit of the direct-drive electrostatic hydraulic actuator system is a permanent magnet synchronous motor. The surface-mounted permanent magnet synchronous motor is selected as the research object. The mathematical model of the permanent magnet synchronous motor is as follows:

[0075] (1),

[0076] In the formula, , They are Axis and stator voltage on the shaft; , They are Axis and stator current on the shaft; is the stator resistance; is the stator inductance; is the rotor flux; is the pole pair number; is the load torque; is the mechanical speed; is the mechanical inertia; is the electrical angular velocity; is the electromagnetic torque; is the viscous friction coefficient. The motor simulation model can be directly established according to the above equation.

[0077] When a bidirectional quantitative gear pump is working, there will be internal and external leakage. The flow output equation of the gear pump can be expressed as:

[0078] (2),

[0079] In the formula, Output flow of the gear pump; is the rated displacement of the gear pump; is the gear pump angular velocity; is the gear pump leakage coefficient; is the load pressure.

[0080] The hydraulic cylinder is the actuator of the direct-drive electrostatic hydraulic actuator, and its flow continuity equation is:

[0081] (3),

[0082] Therefore, the force balance equation for the hydraulic cylinder and the load is:

[0083] (4),

[0084] In the formula, is the system flow; is the effective action area of ​​the piston of the hydraulic cylinder; is the displacement of the hydraulic cylinder piston rod; is the total leakage coefficient of the hydraulic cylinder; is the total compression volume of the hydraulic cylinder; is the effective bulk elastic modulus of hydraulic oil. is the total load mass of the piston rod and its fixed part; is the load spring stiffness; For external interference force.

[0085] From the above formula, the position servo open-loop transfer function of the direct-drive electrostatic hydraulic actuator can be derived as:

[0086] (5),

[0087] The state vector of the direct-drive electrostatic hydraulic actuator position control system can be expressed as:

[0088] (6),

[0089] Therefore, the state space of the nonlinear model of the direct-drive electrostatic hydraulic actuator system can be expressed as:

[0090] (7),

[0091] In the above formula is the controller control rate, is the load disturbance and , , , , .

[0092] After the state space model of the direct-drive electrostatic hydraulic actuator is established through the above steps, a backstepping controller is designed based on the obstacle Lyapunov function on the basis of the model. The design form of the backstepping controller is as follows:

[0093] The state tracking error vector of the direct-drive electrostatic hydraulic actuator system is defined as follows:

[0094] (8),

[0095] In the formula, is the system output displacement tracking error, , The state error defined for the system; is the system tracking error limit and ; is the expected value of the system displacement; and Two virtual controlled variables designed for the controller.

[0096] First, select the barrier Lyapunov function:

[0097] (9),

[0098] Get virtual control amount for:

[0099] (10),

[0100] In the above formula, is a positive real number.

[0101] By taking the derivative of formula (9), we can get:

[0102] (11),

[0103] right Take the time derivative:

[0104] (12),

[0105] because It is not a constrained term, so the quadratic Lyapunov function is chosen:

[0106] (13),

[0107] Get virtual control amount for:

[0108] (14),

[0109] In the above formula, is a positive real number.

[0110] By taking the derivative of formula (13), we can get:

[0111] (15),

[0112] Defining parameter errors ,in For parameters The estimated value ( ), so the error Taking the derivative, it can be expressed as:

[0113] (16),

[0114] After that, define the third candidate Lyapunov function:

[0115] (17),

[0116] In the above formula, , , are all positive real numbers.

[0117] By taking the derivative of formula (17), we can get:

[0118] (18),

[0119] According to the above formula, the actual control variable can be derived:

[0120] (19),

[0121] In the above formula, , and are greater than 0, is the disturbance estimate and .

[0122] Through the above method, the mathematical equation of the backstepping controller is established, the obstacle Lyapunov function is combined with the backstepping controller, and the constraint boundary is introduced to ensure the output constraint performance of the system. Then the adaptive rate based on the backstepping controller is designed. The adaptive rate is as follows:

[0123] By rearranging formula (18), we can obtain:

[0124] (20),

[0125] After eliminating the last three items, the parameter adaptation rate can be obtained as follows:

[0126] (twenty one).

[0127] By establishing the adaptive rate of uncertain parameters to adjust parameter disturbances online in real time, the stability of the system is finally proved by using the Lyapunov function, as follows:

[0128] Define the Lyapunov function as:

[0129] (twenty two),

[0130] Its derivative with respect to time can be obtained as:

[0131] (twenty three),

[0132] Based on the above formula, it can be rewritten as:

[0133] (twenty four),

[0134] When the parameter adaptation rate of formula (21) is taken:

[0135] (25),

[0136] Satisfy the Lyapunov stability condition and control and The rebalance point is stable. According to Barbalat's lemma, when the state error While gradually converging to 0, the system output error It also gradually converges to 0. Therefore, it can be ensured that the final output position error of the direct-drive electrostatic hydraulic actuator system gradually converges to 0.

[0137] As shown in the following table, the values ​​of control parameters related to the direct-drive electrostatic hydraulic actuator in the improved position control method based on the direct-drive electrostatic hydraulic actuator provided in this embodiment are shown.

[0138] Table 1 Main parameters of the system

[0139] .

[0140] Figure 2 This is a step tracking experiment comparison of a direct-drive electrostatic hydraulic actuator of the present invention. The three controllers used for comparison are PI controller, direct backstepping controller and adaptive backstepping controller. In order to verify the response speed capability of the control algorithm proposed in this embodiment and other control methods, experiments are conducted on the centralized control method. The traditional PI control reaches the given expected value in 2.3s, and the tracking error reaches 0.7mm after stabilization; the direct backstepping control reaches the given expected value in 2.1s, and the tracking error reaches 0.4mm after stabilization; the adaptive backstepping controller based on the obstacle Lyapunov function has strong robustness, reaches the given expected value in 1.87s, and the tracking error is less than 0.25mm after stabilization. The designed adaptive backstepping controller updates the system parameters in real time according to its adaptive law, and its performance is significantly better than that of the direct backstepping controller and the traditional PI controller.

[0141] In order to verify the sinusoidal response tracking capability of the control algorithm provided in this embodiment, this control algorithm is compared with other control algorithms under sinusoidal tracking response. Figure 3 As shown. This control algorithm uses an adaptive backstepping controller, and the other two control algorithms use a PI controller and a direct backstepping controller respectively. In the comparative experiment, the frequency of the sinusoidal signal is 0.05Hz. It can be seen from the experimental figure that the traditional PI control and direct backstepping controller can make the system output run according to the reference trajectory, but cannot guarantee that the tracking error of the system is less than kb=1.5mm. The adaptive backstepping controller based on the barrier Lyapunov function has strong robustness and ensures that the tracking error of the system is less than kb=1.5mm. The designed adaptive backstepping controller can update the system parameters in real time, improve the tracking accuracy of the system, and verify the performance of the controller.

Claims

1. An improved position control method for a direct-drive electrostatic hydraulic actuator, wherein the power unit of the direct-drive electrostatic hydraulic actuator system is a permanent magnet synchronous motor, and the hydraulic pump is a gear pump, characterized in that: The control method comprises the following steps: S1. Based on the nonlinear characteristics of the direct-drive electrostatic hydraulic actuator system, the state space model of the system is established and simplified into a strict feedback form; S2. Based on the established system state space model, a backstepping controller combined with the barrier Lyapunov function is designed, and the constraint boundary is introduced to obtain the expression of the actual control rate of the controller; S3, establishing the adaptive rate of uncertain parameters based on the backstepping controller to adjust the parameter disturbance in real time online; In step S1, establishing a state space model of the system includes the following steps: Based on the direct-drive electrostatic hydraulic actuator position servo open-loop transfer function and combined with the direct-drive electrostatic hydraulic actuator position control system state vector, the state space model expression of the system is obtained. The direct-drive electrostatic hydraulic actuator position servo open-loop transfer function expression is as follows: ； The state vector expression of the direct-drive electrostatic hydraulic actuator position control system is as follows: ； The state space model expression of the system is as follows: ； in, , , is the control variable, is the viscous damping coefficient, is the Laplace transform, is the controller control rate, is the effective action area of ​​the piston of the hydraulic cylinder; is the displacement of the hydraulic cylinder piston rod; is the total leakage coefficient of the hydraulic cylinder; is the total compression volume of the hydraulic cylinder; is the effective bulk elastic modulus of hydraulic oil; is the total load mass of the piston rod and its fixed part; is the load spring stiffness; is the external disturbance force, is the rated displacement of the gear pump; is the gear pump angular velocity; is the gear pump leakage coefficient; is the load pressure, is the load disturbance and the estimated value , , , , ; In step S2, the backstepping controller is established as follows: The state tracking error vector of the direct-drive electrostatic hydraulic actuator system is defined as follows: ， In the formula, is the system output displacement tracking error, , The state error defined for the system; is the system tracking error limit, and ; is the expected value of the system displacement; and Two virtual control quantities designed for the controller; Select the barrier Lyapunov function: ； Get virtual control amount for: ； In the above formula, is a positive real number; By differentiating the obstacle Lyapunov function, we can obtain: ； right Take the time derivative: ； because It is not a constrained term, and the quadratic Lyapunov function is chosen: ； Get virtual control amount for: ； By differentiating the quadratic Lyapunov function, we can obtain: ； Defining parameter errors ,in For parameters The estimated value ( =1,2,3,4), for error Taking the derivative, it can be expressed as: ； Define the third candidate Lyapunov function: ； In the above formula, , , are all positive real numbers; Derivative the third candidate Lyapunov function of the formula yields: ； In the above formula, is a positive real number; According to the above formula, the actual control variable is derived: ； In the above formula, is a positive real number, is the interference estimate, and .

2. The improved position control method for a direct-drive electrostatic hydraulic actuator according to claim 1, characterized in that: In step S3, the expression of the uncertain parameter adaptation rate is as follows: 。 3. The improved position control method for a direct-drive electrostatic hydraulic actuator according to claim 2, characterized in that: The control method further includes: step S4, using Lyapunov function to analyze the stability of the system.

4. The improved position control method for a direct-drive electrostatic hydraulic actuator according to claim 3, characterized in that: Step S4 specifically includes: Define the Lyapunov function as: ； Its derivative with respect to time is obtained as: ； The above formula can be rewritten as: ； When the parameter adaptation rate of step S3 is taken: ； Satisfy the Lyapunov stability condition and control and Stable at the equilibrium point, when the state error While gradually converging to 0, the system output error It also gradually converges to 0, ensuring that the final output position error of the direct-drive electrostatic hydraulic actuator system gradually converges to 0.

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