Adaptive sliding mode control method for electro-hydraulic servo system based on barrier function

Abstract

The application relates to an adaptive sliding mode control method of an electro-hydraulic servo system based on a barrier function, and comprises the following steps: establishing a nonlinear mathematical model of an electro-hydraulic servo system; constructing a non-singular terminal sliding mode surface according to the nonlinear mathematical model of the electro-hydraulic servo system; constructing an adaptive law according to the non-singular terminal sliding mode surface and by introducing a barrier function; obtaining real-time states of the electro-hydraulic servo system, dynamically adjusting a sliding mode gain through the adaptive law, and realizing sliding mode control. Compared with a traditional sliding mode control method, the application can realize fast response, significantly inhibit the chattering phenomenon of control input, enhance the robustness of the system to unknown disturbances, and has high control precision and industrial application value.

Description

Technical Field

[0001] This invention relates to the field of electro-hydraulic servo system control technology, and in particular to an adaptive sliding mode control method for electro-hydraulic servo systems based on a barrier function. Background Technology

[0002] Electro-hydraulic servo systems (EHS), as the core of industrial drive control, have found irreplaceable applications in aerospace actuators, large-scale engineering machinery, and precision industrial automation equipment due to their significant advantages such as high power density, high dynamic response, and strong load capacity. However, an EHS is inherently a complex dynamic system with highly nonlinear characteristics. In actual operation, the accurate modeling of the system often faces significant challenges due to factors such as flow nonlinearity, control valve dead zone, and hydraulic fluid compressibility. Furthermore, the uncertainties in hydraulic parameters, such as the effective volumetric elastic modulus of the hydraulic fluid fluctuating with temperature, the internal leakage coefficient changing with usage time, and complex viscous damping characteristics, make it difficult for traditional control strategies based on fixed models to maintain ideal performance under all operating conditions.

[0003] In the motion control of electro-hydraulic servo systems, external disturbances are another core bottleneck affecting tracking accuracy. To improve the system's robustness to uncertainties and disturbances, sliding mode control has been widely studied due to its insensitivity to parameter changes and strong disturbance suppression capabilities. However, the application of traditional sliding mode control in the electro-hydraulic servo field is still subject to severe technical limitations. The most prominent contradiction lies in the design of the switching gain: to ensure the system can converge even in the presence of strong disturbances, designers usually have to anticipate the physical upper bound of the disturbance and set a switching gain that is much larger than the actual requirement. While this "over-designed gain" ensures stability, it leads to severe high-frequency chattering in the control input.

[0004] Chattering poses a significant threat to electro-hydraulic servo systems. High-frequency oscillating control signals not only accelerate the wear of hydraulic valve cores and shorten the lifespan of hydraulic components, but also excite unmodeled high-frequency dynamics in the system, leading to drastic fluctuations in position tracking accuracy and even system instability. Furthermore, while traditional linear sliding surfaces are simple in structure, their error convergence speed often exhibits asymptotic characteristics, making it difficult to meet the stringent requirements of "fast convergence within a finite time" in modern high-precision machining. Although terminal sliding mode control, which has emerged in recent years, can accelerate convergence, the singularity problem near the equilibrium point and the overestimation of gain due to the inability to accurately predict the disturbance amplitude remain major obstacles to achieving higher performance in electro-hydraulic servo control systems.

[0005] Therefore, there is an urgent need for a high-performance adaptive control method that can automatically adapt to unknown disturbance changes without needing to predict the upper bound of the disturbance, and can effectively suppress control chattering and ensure finite-time convergence. Summary of the Invention

[0006] The purpose of this invention is to provide an adaptive sliding mode control method for electro-hydraulic servo systems based on barrier functions. By introducing barrier functions to design an adaptive law, the control gain can be dynamically adjusted according to the real-time state of the system, thereby achieving rapid response and high-precision displacement tracking of the hydraulic system while ensuring system stability. This solves the technical problem of large chattering caused by sliding mode control in the prior art.

[0007] To achieve the above objectives, the present invention provides the following solution: An adaptive sliding mode control method for electro-hydraulic servo systems based on barrier functions includes: Establish a nonlinear mathematical model for the electro-hydraulic servo system; Based on the nonlinear mathematical model of the electro-hydraulic servo system, a non-singular terminal sliding surface is constructed. Based on the non-singular terminal sliding surface, an adaptive law is constructed by introducing a barrier function; The real-time status of the electro-hydraulic servo system is acquired, and the sliding mode gain is dynamically adjusted through the adaptive law to achieve sliding mode control.

[0008] Optionally, establishing a nonlinear mathematical model for the electro-hydraulic servo system includes: Based on the unknown external disturbances and the uncertainty of hydraulic parameters, a nonlinear mathematical model of the electro-hydraulic servo system containing parameter uncertainties and unknown external disturbances is constructed, and feedback linearization is performed to obtain the transformed nonlinear mathematical model of the electro-hydraulic servo system.

[0009] Optionally, constructing a non-singular terminal sliding surface includes: Based on the transformed nonlinear mathematical model of the electro-hydraulic servo system, the tracking error and its derivative are obtained. Based on the tracking error and its derivative, a non-singular terminal sliding surface is constructed.

[0010] Optionally, the non-singular terminal sliding surface is: ; in, , , , For exponential parameters, nonlinear functions , Let be the system state vector. For sliding mode variables, To track errors, This is the first derivative of the tracking error.

[0011] Optionally, the adaptive law is: ; ; in, For adaptively adjusted sliding mode gain, For adaptive rate parameters, This is the exponential adjustment coefficient for the adaptive gain. For the current moment, For integration time variable, For sliding mode variables Constraint boundaries, It is a barrier function type continuous control law.

[0012] Optionally, implementing sliding mode control includes: Based on the non-singular terminal sliding surface, a virtual control input is constructed, wherein the virtual control input includes an equivalent control term and a robust control term, and the robust control term is introduced into the sliding gain; Sliding mode control is achieved by adjusting the sliding mode gain.

[0013] Optionally, the virtual control input for: ; ; ; in, and These are equivalent control terms and robust control terms, respectively. The first derivative of the desired trajectory, The second derivative of the desired trajectory. The third derivative of the desired trajectory, This is the second state variable after coordinate transformation. This is the third state variable after coordinate transformation.

[0014] The beneficial effects of this invention are as follows: 1) The adaptive sliding mode control method for electro-hydraulic servo systems based on barrier functions proposed in this invention effectively solves the problems caused by nonlinearity, parameter uncertainty, and external disturbances in electro-hydraulic servo systems. By introducing a non-singular terminal sliding surface, the tracking error of the system is ensured to converge within a finite time. Simultaneously, by designing an adaptive law using the barrier function, the control gain can change according to the disturbance amplitude, avoiding the need for predicting the upper bound of the disturbance. Experimental and simulation results show that this method significantly improves the dynamic performance and robustness of the electro-hydraulic servo system.

[0015] 2) By introducing a barrier function, this invention effectively suppresses control input chattering, a phenomenon that may occur in traditional sliding mode control methods. The adaptive sliding mode control strategy of this invention, through the design of an adaptive law for the barrier function, allows the control gain to be dynamically adjusted according to the system state, without needing to predict the upper bound of the disturbance, thus avoiding the chattering problem caused by overestimation of disturbances in traditional sliding mode control methods. Compared to traditional methods, this invention exhibits stronger adaptability and higher stability when dealing with system uncertainties. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a flowchart of an adaptive sliding mode control method for an electro-hydraulic servo system based on a barrier function, according to an embodiment of the present invention. Figure 2 This is an experimental curve showing the position tracking performance of the hydraulic system according to an embodiment of the present invention. Figure 3 This is a diagram showing the hydraulic cylinder speed and load pressure according to an embodiment of the present invention; Figure 4 This is a diagram of experimental sliding mode variables in an embodiment of the present invention; Figure 5 This is an experimental control voltage diagram of an embodiment of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0020] like Figure 1 As shown, this embodiment proposes an adaptive sliding mode control method for an electro-hydraulic servo system based on a barrier function, including: Establish a nonlinear mathematical model for the electro-hydraulic servo system; Based on the nonlinear mathematical model of the electro-hydraulic servo system, a non-singular terminal sliding surface is constructed. Based on the non-singular terminal sliding surface, an adaptive law is constructed by introducing a barrier function; The real-time status of the electro-hydraulic servo system is acquired, and the sliding mode gain is dynamically adjusted through the adaptive law to achieve sliding mode control.

[0021] Furthermore, the establishment of a nonlinear mathematical model for the electro-hydraulic servo system includes: Based on the unknown external disturbances and the uncertainty of hydraulic parameters, a nonlinear mathematical model of the electro-hydraulic servo system containing parameter uncertainties and unknown external disturbances is constructed, and feedback linearization is performed to obtain the transformed nonlinear mathematical model of the electro-hydraulic servo system.

[0022] Specifically, a dynamic model of an electro-hydraulic servo system with parameter uncertainties is established, and the state vector of the electro-hydraulic servo system is... for ,in, and For the position and speed of the hydraulic cylinder, Let be the cross-sectional area of ​​the hydraulic cylinder. The load pressure of the hydraulic cylinder. Representing the transpose, and considering unknown external disturbances and lumped uncertainties of different hydraulic parameters, the nonlinear mathematical model of this electro-hydraulic servo system with parameter uncertainties and unknown external disturbances is expressed as follows: (1); In the formula: (2); in, , , These represent the positions of the state vectors respectively. ,speed With pressure The derivative, Characterize the effect of the load spring stiffness k on the system. Characterizes the viscous damping effect (motion resistance) of the system. Indicates the mass of the load slider The reciprocal of represents the system's sensitivity to acceleration. and Characterizes the volumetric elasticity of a hydraulic system and the pressure loss effect caused by internal leakage. This represents the nominal value of the gain term in the hydraulic system, characterizing how the servo valve flow affects the acceleration of the hydraulic cylinder, and is influenced by the supply pressure and fluid dynamics. and These represent the nominal values ​​of the load stiffness coefficient and the viscous damping coefficient, respectively. This indicates the effective bulk modulus of hydraulic oil. This represents the leakage coefficient of the hydraulic cylinder. This indicates the flow coefficient of the servo valve. The slope representing the area of ​​the servo valve port. The density of hydraulic oil is indicated by the following nominal values: To represent. Parameters This indicates the electro-hydraulic gain of the servo valve. It is the total volume of the hydraulic cylinder. Indicates the oil supply pressure. It is the input voltage controlled by the servo valve. It is a sign function, that is, when u>0, When u=0, When u < 0, It determines the direction of oil flow.

[0023] express The lumped uncertainty in the electro-hydraulic servo system is caused by factors such as parameter uncertainties, friction, and external load disturbances. express The lumped uncertainty caused by factors such as the dynamic characteristics of the servo valve and pressure fluctuations in the hydraulic system is expressed as: (3); in, This represents the difference in load spring coefficient between the nominal system and the system with lumped uncertainty. This represents the difference in viscous damping coefficient between the nominal system and the system with lumped uncertainty. , express Corresponding Non-nominal value The difference, express Corresponding Non-nominal value The difference.

[0024] To facilitate subsequent feedback linearization and robust controller design, the nonlinear electro-hydraulic servo system in formula (1) can be reformulated as a standard input affine form as follows: (4); in, Represents the system state vector. To control the input, This is the system output.

[0025] Vector Field and and output function As shown below: (5); Based on the Lie derivative framework, the relative order of the system is determined by the output function. Decision. Along the vector field right Find the first-order Lie derivative, along Find the second-order Lie derivative, and along... beg The Lie derivatives are as follows: (6); Within the normal working area, conditions Being satisfied, thus guaranteeing Therefore, the control input is in the output. The explicit appearance of the third derivative indicates that the system has a relative order of third order. Furthermore, due to the control input... Only the third state equation is entered, and its relative order is the same as the system order. Therefore, the necessary condition for exact input-output feedback linearization is satisfied.

[0026] To construct the Brunovsky canonical form, a coordinate transformation is introduced as defined by [definition of the coordinate transformation]. .

[0027] Taking the time derivative of the transformed state, we get: (7); To obtain the linearly controllable standard form, a virtual control input is introduced. Defined as ,in , Considering the uncertainties and the equivalent effects of external disturbances, the other terms are combined into a single disturbance term. .

[0028] Therefore, the transformed system can be rewritten as: (8); Depend on The actual control input can be obtained explicitly. With virtual input Mapping relationship between them: (9).

[0029] Furthermore, constructing the non-singular terminal sliding surface includes: Based on the transformed nonlinear mathematical model of the electro-hydraulic servo system, the tracking error and its derivative are obtained. Based on the tracking error and its derivative, a non-singular terminal sliding surface is constructed.

[0030] Specifically, a non-singular terminal sliding surface is designed to ensure that the system tracking error converges to zero within a finite time. To achieve the desired trajectory For high-precision tracking, the tracking error of the system and its derivative are defined as follows: (10); in, To track errors, This is the first derivative of the tracking error.

[0031] To ensure finite-time convergence and avoid singularities, the following non-singular terminal sliding surface is constructed: (11); in , , The exponential parameter satisfies Nonlinear functions Defined as: (12); For sliding mode variables By taking the derivative and combining it with formula (10), we can obtain: (13); To ensure that the sliding mode variables remain within a preset range, a barrier function is introduced: (14); This function is in As the time approaches infinity, it effectively constrains the sliding mode variables in the control law design. For sliding mode variables The constraint boundary is further defined by introducing a barrier function to design an adaptive law, enabling the control gain to be dynamically adjusted according to the real-time state of the system, thus compensating for uncertainties without needing to know the upper bound of the disturbance.

[0032] Furthermore, implementing sliding mode control includes: Based on the non-singular terminal sliding surface, a virtual control input is constructed, wherein the virtual control input includes an equivalent control term and a robust control term, and the robust control term is introduced into the sliding gain; Sliding mode control is achieved by adjusting the sliding mode gain.

[0033] Specifically, based on the sliding surface structure of formula (11), a virtual control input is constructed: (15); Among them, according to the expression of the derivative of s in equation (13), in order to offset the terms that are dynamically related to the desired trajectory and the known error, the equivalent control term is selected as: (16); The robust control term is designed as follows: (17); in For adaptively adjusted sliding mode gain, The first derivative of the desired trajectory, The second derivative of the desired trajectory. The second state variable after coordinate transformation, i.e., the system output. The first derivative; The third state variable after coordinate transformation, i.e., the system output. The second derivative of .

[0034] To balance rapid arrival and chatter suppression, the following adaptive law is introduced: (18); in For adaptive rate parameters, This is the exponential adjustment coefficient for the adaptive gain. For the current moment, For integration time variable, For sliding mode variables The constraint boundary. The barrier function type continuous control law is defined as: (19); Through the above design, when the system state is far from the sliding surface, the adaptive gain increases rapidly to ensure that it can be reached in a finite time; when the sliding variable enters the boundary layer region, the control input changes continuously and becomes smooth as the error decreases.

[0035] Furthermore, an adaptive sliding mode controller for an electro-hydraulic servo system based on a barrier function is constructed based on Lyapunov stability theory, and the system stability is proven.

[0036] when When, then the sliding mode variable Will arrive at the assembly within a limited time And adaptive sliding mode gain This approach phase remains bounded.

[0037] The specific analysis is as follows: for Sliding mode dynamics can be written as ,in Describes the lumped disturbance and satisfies Let be an unknown constant. Construct the Lyapunov function: (20); in For design constants, To meet . a normal number.

[0038] right Taking the derivative and substituting it into the sliding mode dynamics, we get: (twenty one); use and Furthermore, we can obtain: (twenty two); According to the adaptive law and conditions We can obtain: (twenty three); therefore, Monotonically increasing and satisfying: (twenty four); Therefore, for any given constant There exists a finite time. , so that: (25); Its explicit upper bound is: (26); because ,have Therefore, for all : (27); Applying the comparison lemma to the above differential inequality, we get: (28); therefore, ,Right now Will arrive at the set within a finite time .

[0039] For when At that time, once the system trajectory enters the set The control law based on the barrier function will further reduce the sliding mode variable within a finite time. Drive to ,in To meet Any preset value, and .

[0040] The specific analysis is as follows: Introduce auxiliary variables: (29); This constant specifies a compact neighborhood around the origin.

[0041] for The adaptive gain is determined by a control law based on the barrier function: (30); In particular, when At that time, by the above From the definition, we can obtain: (31); Consider the Lyapunov function: (32); Along the closed-loop dynamic pair Taking the time derivative, we get: (33); use as well as We can obtain: (34); set up To meet An arbitrary preset constant. Because exist The above about Strictly incremental, for all ,have: (35); definition: (36); So, for all ,have: (37); According to the standard finite-time stability lemma To be achieved within a limited time .therefore, Enter the set within a limited time. .

[0042] To further verify the performance of the proposed controller, an experimental platform was built. The electro-hydraulic servo system is powered by an oil pump station (HY-36CC-01 / 11kW), and uses a nozzle-flap servo valve (D633-R04K01M0NSM2) to control the movement of the hydraulic cylinder. The hydraulic cylinder (UG1511R25 / 16-100) drives the disc load. The system integrates a displacement sensor (JHQGA-40) and a pressure sensor (BD-Sensors-DMP-331) to measure the displacement and intracavity pressure of the hydraulic cylinder, respectively. Feedback signals are acquired through an NI data acquisition card (PCI-6221 / 37-pin). The control algorithm was developed and implemented in the MATLAB / Simulink environment on the host computer, and the algorithm code was compiled and downloaded to the target machine for execution. The control cycle was set to 1ms, and the control signal u was output through the NI card to drive the servo valve, thereby regulating the hydraulic flow into the hydraulic cylinder.

[0043] Considering the range of motion of the hydraulic cylinder, the desired trajectory of the hydraulic cylinder position is set as follows: The nominal hydraulic parameters remain consistent with those in the simulation. The controller parameters are selected as follows: , , , , , as well as .

[0044] Experimental results are as follows Figures 2-5 As shown, the actuator displacement rapidly tracks the desired trajectory within approximately 0.15 s and maintains good synchronization during subsequent operations. Experimental error curves indicate that the system's tracking error converges within 0.35 s and remains within ±0.5 mm. Simultaneously, the control input changes smoothly without significant high-frequency chattering. These experimental results verify the finite-time stability of the proposed control strategy and demonstrate its feasibility in practical electro-hydraulic servo systems. In particular, fast and accurate trajectory tracking can still be achieved even with large initial position deviations.

[0045] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. An adaptive sliding mode control method for electro-hydraulic servo systems based on barrier functions, characterized in that, include: Establish a nonlinear mathematical model for the electro-hydraulic servo system; Based on the nonlinear mathematical model of the electro-hydraulic servo system, a non-singular terminal sliding surface is constructed. Based on the non-singular terminal sliding surface, an adaptive law is constructed by introducing a barrier function; The real-time status of the electro-hydraulic servo system is acquired, and the sliding mode gain is dynamically adjusted through the adaptive law to achieve sliding mode control.

2. The adaptive sliding mode control method for an electro-hydraulic servo system based on a barrier function according to claim 1, characterized in that, The establishment of a nonlinear mathematical model for an electro-hydraulic servo system includes: Based on the unknown external disturbances and the uncertainty of hydraulic parameters, a nonlinear mathematical model of the electro-hydraulic servo system containing parameter uncertainties and unknown external disturbances is constructed, and feedback linearization is performed to obtain the transformed nonlinear mathematical model of the electro-hydraulic servo system.

3. The adaptive sliding mode control method for an electro-hydraulic servo system based on a barrier function according to claim 2, characterized in that, Constructing a non-singular terminal sliding surface includes: Based on the transformed nonlinear mathematical model of the electro-hydraulic servo system, the tracking error and its derivative are obtained. Based on the tracking error and its derivative, a non-singular terminal sliding surface is constructed.

4. The adaptive sliding mode control method for an electro-hydraulic servo system based on a barrier function according to claim 3, characterized in that, The non-singular terminal sliding surface is: ； in, , , , For exponential parameters, nonlinear functions , Let be the system state vector. For sliding mode variables, To track errors, This is the first derivative of the tracking error.

5. The adaptive sliding mode control method for an electro-hydraulic servo system based on a barrier function according to claim 4, characterized in that, The adaptive law is: ； ； in, For adaptively adjusted sliding mode gain, For adaptive rate parameters, This is the exponential adjustment coefficient for the adaptive gain. For the current moment, For integration time variable, For sliding mode variables Constraint boundaries, It is a barrier function type continuous control law.

6. The adaptive sliding mode control method for an electro-hydraulic servo system based on a barrier function according to claim 5, characterized in that, Implementing sliding mode control includes: Based on the non-singular terminal sliding surface, a virtual control input is constructed, wherein the virtual control input includes an equivalent control term and a robust control term, and the robust control term is introduced into the sliding gain; Sliding mode control is achieved by adjusting the sliding mode gain.

7. The adaptive sliding mode control method for an electro-hydraulic servo system based on a barrier function according to claim 6, characterized in that, The virtual control input for: ； ； ； in, and These are equivalent control terms and robust control terms, respectively. The first derivative of the desired trajectory, The second derivative of the desired trajectory. The third derivative of the desired trajectory, This is the second state variable after coordinate transformation. This is the third state variable after coordinate transformation.

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