Data-driven five-degree-of-freedom overhead crane self-disturbance rejection sliding mode control method and system
Through the data-driven automatic disturbance rejection sliding mode control method of the five-degree-of-freedom crane, the problem of insufficient control accuracy and robustness in the existing technology is solved, and efficient control of the five-degree-of-freedom crane system is achieved, which is suitable for complex applications. engineering applications.
Patent Information
- Application Number
- CN202410635860.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-05-22
- Publication Date
- 2025-01-21
- Estimated Expiration
- 2044-05-22
AI Technical Summary
The prior art is difficult to effectively control the five-degree-of-freedom sky car system, especially when facing complex spatial spherical swings and external disturbances, the control accuracy and robustness are insufficient.
A data-driven five-degree-of-freedom crane automatic disturbance-rejection sliding mode control method is adopted. By establishing a five-degree-of-freedom crane system model, a tracking differentiator and an expanded state observer are constructed, and a sliding mode controller for generalized coupling error signals is designed. Combined with the iterative learning controller, disturbance compensation and control accuracy improvement are achieved.
The control accuracy and robustness of the five-degree-of-freedom crane system are improved, which can effectively suppress load swing and enhance the system's anti-disturbance capability, making it suitable for complex engineering application scenarios.
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Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of five-degree-of-freedom overhead crane systems, and in particular to a data-driven five-degree-of-freedom overhead crane self-disturbance rejection sliding mode control method and system. Background Art
[0002] Overhead crane is a typical under-actuated nonlinear system. At present, there are two main operating modes for overhead cranes, namely manual operation or remote operation, which have the disadvantages of low automation and intelligence, low operating efficiency, poor load swing suppression ability, and long training time for skilled operators. Therefore, it is urgent to design an automatic control method with high precision and strong robustness for the overhead crane system.
[0003] Researchers have designed an effective control method for the overhead crane system. Depending on whether real-time status feedback is required, the existing methods can be roughly divided into two categories: open-loop control methods and closed-loop control methods. Although the open-loop control method has a simple structure and is easy to implement in engineering, it cannot overcome the destructive behavior of external disturbances on the system and may even cause loss of control. The closed-loop control method provides better control performance due to its advantages such as insensitivity to disturbances and real-time feedback adjustment.
[0004] Existing closed-loop methods, mainly including sliding mode control method, model predictive control method, neural network control method, control method based on energy shaping, adaptive control method, etc., are used to enhance the robustness and control quality of the overhead crane system. However, there are still two major shortcomings:
[0005] 1. Most of the control methods currently designed are designed for two-degree-of-freedom (fixed cable length) or three-degree-of-freedom (time-varying cable length) systems. However, in actual applications, the overhead crane usually requires the trolley and bridge to operate synchronously during operation, and the lifting task is completed with the lifting of the cable. In this working mode, the overhead crane has five degrees of freedom, and the load swing is no longer a plane swing, but a more complex spatial spherical swing. Therefore, designing control methods based on two-degree-of-freedom or three-degree-of-freedom systems deviates from actual engineering problems and is difficult to achieve engineering applications.
[0006] 2. Since the five-degree-of-freedom overhead crane system has more complex dynamic characteristics, and the mass of the hook and load, the length of the rope, and the coefficients related to friction are usually unknown or uncertain. In addition, the overhead crane will inevitably encounter some external interference, such as crosswinds, collisions, etc. The existing control method has a complex structure and a fixed control law. It cannot solve the nonlinear problems such as dead zones, saturation, friction, etc. that inevitably exist in many actuators. It is difficult to meet the control requirements and control accuracy of different environments and different tasks, and it is impossible to achieve smooth control. Summary of the invention
[0007] The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a data-driven five-degree-of-freedom overhead crane self-disturbance rejection sliding mode control method.
[0008] The technical solution adopted by the present invention to solve the technical problem is: a five-degree-of-freedom overhead crane self-disturbance rejection sliding mode control method based on data drive comprises the following steps:
[0009] Establish a five-degree-of-freedom overhead crane system model;
[0010] A tracking differentiator is constructed to extract the displacement of the reference trajectory and its differential signal, while expanding the parameter setting range and suppressing the differential signal noise;
[0011] An extended state observer is constructed to estimate the displacement and swing angle of the overhead crane and its total disturbance signal in real time.
[0012] Based on the generalized coupled error signal, a sliding mode controller is designed, and a composite anti-disturbance sliding mode controller is constructed by combining a differentiator and an observer to achieve disturbance compensation.
[0013] Through iterative learning controller, the control input is repeatedly corrected to improve the control accuracy and system robustness;
[0014] The five-degree-of-freedom overhead crane system is controlled based on a data-driven active disturbance rejection sliding mode controller.
[0015] According to the Lagrangian method, the dynamic model of the five-degree-of-freedom overhead crane is as follows:
[0016] Where, m, m x , m y are the load mass, trolley mass and bridge mass respectively; l is the cable length; θ x and θ y are the swing angles in the x and y directions respectively, the x direction is the running direction of the trolley, and the y direction is the running direction of the bridge; f x and f y is the translational driving force, f l is the load suspension force; S x = sin(θ x ), S y = sin(θ y ), C x =cos(θ x ), C y =cos(θ y ).
[0017] Variable x1 = [xyl θ x θ y ] T , The following state space expression is obtained:
[0018]
[0019] Where u = [f x f y f l ] T ,y1 is the system output;
[0020]
[0021] The tracking differentiator is a third-order nonlinear tracking differentiator, which is constructed as follows:
[0022]
[0023] In the above formula, is the output of the third-order nonlinear tracking differentiator, i.e., displacement, is the first-order derivative of the differentiator output, i.e., velocity, To track the second-order derivative of the differentiator output, i.e., acceleration, r i is the target setting value of the trolley, bridge and load, e i To track the deviation between the displacement output by the differentiator and the set displacement value, γ∈R 3×3 >0 is the adjustable parameter of the differentiator.
[0024] The extended state observer includes a displacement observer and an angle observer;
[0025] The displacement observer is designed as follows:
[0026]
[0027] In the above formula, is the displacement of the trolley, bridge and load, is the displacement observer pair The estimated value of is the error between the displacement and the displacement observer, is the displacement observer pair The estimate of the first derivative of is the total displacement disturbance, β 11 , β 12 , β 13 are displacement observer gains, and their values are related to the observation accuracy. is a nonlinear function, α1 and δ1 are both adjustment parameters of the nonlinear function. To control the input adjustable parameters, it determines the strength of disturbance compensation;
[0028] The angle observer is designed as follows:
[0029]
[0030] In the above formula, is the swing angle of the load in space, The angle observer is The estimated value of is the error between the angle and the angle observer, is the displacement observer pair An estimate of the first-order derivative of is the total angular disturbance, β 21 , β 22 , β 23 are angle observer gains, and their values are related to the observation accuracy. is a nonlinear function, α2 and δ2 are both adjustment parameters of the nonlinear function, b j It is an adjustable parameter for controlling input and determines the strength of disturbance compensation.
[0031] To facilitate the gain tuning of the two extended state observers mentioned above, the gain is configured to the bandwidth, and then
[0032]
[0033] Establishing a sliding mode controller based on the generalized coupling error signal includes the following steps:
[0034] Design the generalized coupling error signal σ:
[0035]
[0036] Where, e is the positioning error vector, k θ ∈R 3×2 and ω∈R 2×2 is a positive definite diagonal gain matrix, τ is time, and dτ is the integrand expression;
[0037] The designed integral sliding surface s is:
[0038]
[0039] Where σ is the generalized coupling error signal, c1 and c2 are positive definite diagonal matrices;
[0040] Obtain the first-order derivative of the sliding surface s and derive the sliding mode controller as:
[0041]
[0042] In the formula, u eq is an equivalent control item.
[0043] If the equivalent control term ueq It is completely known that the dynamics of the closed-loop system remains on the sliding surface, and the system error gradually decreases and converges to 0 according to the expected trajectory. However, the system inevitably contains many unknown uncertainties and external disturbances, all of which are regarded as the total disturbance estimated by the observer.
[0044] In order to obtain the ideal equivalent control term, a data-driven anti-disturbance sliding mode control method is proposed, which uses a nonlinear extended state observer to estimate the system state and the total disturbance, and performs disturbance compensation in the feedback link; secondly, in this method, each repeated task is called an iteration, represented by k (k=1,2,3...), and the robust iterative learning controller only needs the data information input of the sliding mode dynamics in the previous iteration to correct the control input signal of the current iteration.
[0045] The overall control law of the data-driven ADRC sliding mode controller is designed as follows:
[0046]
[0047] In the formula, is the sliding mode control term, is the iteration control term, and k is the number of iterations.
[0048] In order to enhance the robustness of the control system and ensure the convergence time, the sliding mode control term Updated to:
[0049] Iteration Control for:
[0050]
[0051] Where k1, k2, k3 are sliding mode control gains, q, β1, β2 are iterative learning control gains, s k is the sliding surface at the kth iteration.
[0052] The system applied to the above method comprises
[0053] Data acquisition module: used to collect status information of the five-degree-of-freedom overhead crane system;
[0054] Storage module: used to store the sliding mode dynamic data information of each iteration and the data information collected by the data acquisition module;
[0055] Microprocessor: used to execute the steps in the data-driven five-degree-of-freedom overhead crane self-disturbance rejection sliding mode control method and issue relevant instructions.
[0056] Compared with the prior art, the present invention has the following beneficial effects:
[0057] 1. This application integrates the advantages of three methods: active disturbance rejection control, sliding mode control, and iterative learning control. Based on the data-driven active disturbance rejection sliding mode controller, the five-degree-of-freedom overhead crane system is positioned and sway-free, which solves the positioning and load suppression problems of the five-degree-of-freedom overhead crane system, ensures that the control input is always within the allowable range, and improves the control accuracy and robustness;
[0058] 2. This application conducts a rigorous theoretical analysis of the stability and iterative convergence of the five-degree-of-freedom overhead crane system without any linearization or approximation processing, and satisfactory performance can be obtained only by adjusting the control gain.
[0059] 3. The third-order nonlinear tracking differentiator of the present application only requires the target position, and does not require the differential signal of the target position, which solves the contradiction between rapidity and overshoot when tracking the reference trajectory, expands the gain setting range, and is convenient for engineering applications.
[0060] 4. This application only includes positioning error and load swing angle. The nonlinear extended state observer estimates the system state and lumped disturbance in real time without relying on the system model. It makes up for the defects of sensors that cannot be measured, cannot be measured accurately, and cannot be measured completely, greatly improving the control accuracy of the overhead crane system.
[0061] 5. The robust iterative learning controller of the present application only requires the data information input of the sliding mode dynamics in the previous iteration to correct the control input signal of the current iteration. It has a simple structure and is suitable for application scenarios of repeated lifting operations of overhead cranes. BRIEF DESCRIPTION OF THE DRAWINGS
[0062] Figure 1 It is a schematic diagram of the five-degree-of-freedom overhead crane system of the present invention;
[0063] Figure 2 A block diagram of the control system proposed for this application;
[0064] Figure 3 This is a flow chart of the control method for this application;
[0065] Figure 4 is the simulation result of the first group of simulations by the method of the present application;
[0066] Figure 5 It is the convergence result of the iterative error in the first group of simulations of the method of the application;
[0067] Figure 6 It is the simulation comparison result of the first set of simulations performed by the method of the present application with the CAC and HSCM control methods;
[0068] Figure 7 is the simulation result of the method of the present application for the second group;
[0069] Figure 8 This is the simulation result of the method of the present application for the third group. DETAILED DESCRIPTION
[0070] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.
[0071] Active disturbance rejection control technology is a method of effectively controlling systems with complex uncertainties and external disturbances without relying on an accurate mathematical model of the controlled object. It mainly includes three parts: a differentiator, an extended state observer, and a nonlinear feedback controller. Each part can be designed independently, has a simple structure, and is easy to implement in engineering.
[0072] Sliding mode variable structure control technology has strong robustness due to its fast response, simple physical implementation, insensitivity to system parameters, and no need for system online identification.
[0073] Iterative learning control is a data-driven, high-precision control method that is mainly used to process control systems with repetitive operation characteristics. It can simulate the human learning process and use the error information and control input information measured in the previous or previous iterations to correct the control input signal of the current iteration. It can then repeat the practice to gradually improve the performance of the control system and enable the repetitive task to be better controlled in the current iteration.
[0074] In order to improve the control accuracy and robustness of the overhead crane system and realize compliant control, the present invention considers a five-degree-of-freedom overhead crane model close to actual engineering applications, combines the above three control methods, and constructs a composite control method that integrates the advantages of the three control methods, enhances the system robustness and anti-interference ability, and has broad application prospects and potential economic benefits.
[0075] Specifically, refer to Figure 1-Figure 8 , the data-driven active disturbance rejection sliding mode control method includes the following steps:
[0076] Firstly, the dynamic model of the five-degree-of-freedom overhead crane system is established;
[0077] Specifically, the present application performs dynamic modeling according to the Lagrangian method, and the dynamic model of the five-degree-of-freedom overhead crane is as follows:
[0078]
[0079] Where, m, m x , m yare the load mass, trolley mass and bridge mass respectively; l is the cable length; θ x and θ y are the swing angles in the x and y directions respectively, the x direction is the running direction of the trolley, and the y direction is the running direction of the bridge; f x and f y is the translational driving force, f l is the load suspension force; S x = sin(θ x ), S y = sin(θ y ), C x =cos(θ x ), C y =cos(θ y ).
[0080] Select the state variable x1 = [xyl θ x θ y ] T , The following state space expression is obtained:
[0081]
[0082] Where u = [f x f y f l ] T , y1 is the system output;
[0083]
[0084] Secondly, a tracking differentiator is constructed to extract the displacement of the reference trajectory and its differential signal, while expanding the parameter setting range and suppressing the differential signal noise;
[0085] The tracking differentiator is a third-order nonlinear tracking differentiator, which is constructed as follows:
[0086]
[0087] In the above formula, is the output of the third-order nonlinear tracking differentiator, i.e., displacement, is the first-order derivative of the differentiator output, i.e., velocity, To track the second-order derivative of the differentiator output, i.e., acceleration, r i is the target setting value of the trolley, bridge and load, e i To track the deviation between the displacement output by the differentiator and the set displacement value, γ∈R 3×3 >0 is the adjustable parameter of the differentiator.
[0088] An extended state observer is constructed to estimate the displacement and swing angle of the overhead crane and its total disturbance signal in real time; the improved nonlinear function in the extended state observer of the present application improves the estimation accuracy and stability. Furthermore, the extended state observer includes a displacement observer and an angle observer;
[0089] Specifically, the displacement observer is designed as follows:
[0090]
[0091] In the above formula, is the displacement of the trolley, bridge and load, is the displacement observer pair The estimated value of is the error between the displacement and the displacement observer, is the displacement observer pair The estimate of the first derivative of is the total displacement disturbance, β 11 , β 12 , β 13 are displacement observer gains, and their values are related to the observation accuracy. is a nonlinear function, α1 and δ1 are both adjustment parameters of the nonlinear function. It is an adjustable parameter for controlling input and determines the strength of disturbance compensation.
[0092] The angle observer is designed as follows:
[0093]
[0094] In the formula, is the swing angle of the load in space, The angle observer is The estimated value of is the error between the angle and the angle observer, is the displacement observer pair The estimate of the first derivative of is the total angular disturbance, β 21 , β 22 , β 23 are angle observer gains, and their values are related to the observation accuracy. is a nonlinear function, α2 and δ2 are both adjustment parameters of the nonlinear function, b j It is an adjustable parameter for controlling input and determines the strength of disturbance compensation.
[0095] In order to facilitate the observer gain tuning, the gain is configured to the bandwidth, then
[0096]
[0097] Subsequently, a sliding mode controller is designed based on the generalized coupling error signal, and a composite active disturbance rejection sliding mode controller is constructed by combining a differentiator and an observer; specifically, this application designs an integral sliding surface based on the generalized coupling error signal, and derives a sliding mode controller based on the system model, and uses it as a nonlinear feedback controller in the active disturbance rejection control technology.
[0098] Specifically, the following steps are included:
[0099] Design the generalized coupling error signal σ:
[0100]
[0101] Where, e is the positioning error vector, k θ ∈R 3×2 and ω∈R 2×2 is a positive definite diagonal gain matrix, τ is time, and dτ is the integrand expression.
[0102] The designed integral sliding surface s is:
[0103]
[0104] Where σ is the generalized coupling error signal, and c1 and c2 are positive definite diagonal matrices.
[0105] Obtain the first-order derivative of the sliding surface s and derive the sliding mode controller as:
[0106]
[0107] In the formula, u eq is an equivalent control item.
[0108] Finally, the control input is iteratively corrected through a data-driven iterative learning controller to generate the final iterative learning self-disturbance rejection sliding mode controller; this application considers the difficulty of total disturbance compensation in the system, proposes a robust iterative learning law, designs an iterative learning controller, and iteratively corrects the control input, thereby improving control accuracy, achieving disturbance compensation, and improving system robustness.
[0109] If the equivalent control term u eq It is completely known that the dynamics of the closed-loop system remains on the sliding surface, and the system error gradually decreases and converges to 0 according to the expected trajectory. However, the system inevitably contains many unknown uncertainties and external disturbances, all of which are regarded as the total disturbance estimated by the observer.
[0110] In order to obtain the ideal equivalent control term, a data-driven anti-disturbance sliding mode control method is proposed, which uses a nonlinear extended state observer to estimate the system state and the total disturbance, and performs disturbance compensation in the feedback link; secondly, in this method, each repeated task is called an iteration, represented by k (k=1,2,3...), and the robust iterative learning controller only needs the data information input of the sliding mode dynamics in the previous iteration to correct the control input signal of the current iteration.
[0111] The overall control law of the data-driven iterative learning ADRC sliding mode controller is designed as follows:
[0112]
[0113] In the formula, is the sliding mode control term, is the iteration control term, and k is the number of iterations.
[0114] In order to enhance the robustness of the control system and ensure the convergence time, the sliding mode control term Updated to:
[0115] Robust iterative learning control law is the iterative control term Designed for:
[0116]
[0117] Where k1, k2, k3 are sliding mode control gains, q, β1, β2 are iterative learning control gains, s k is the sliding surface at the kth iteration.
[0118] The stability analysis of this application is as follows:
[0119] For the five-DOF crane system shown in equation (6), if the anti-disturbance sliding film controller is designed in the form of equation (14), the system tracking error can converge to 0 in a theoretically finite time. The proof is as follows:
[0120] Select the Lyapunov function:
[0121] The first-order derivative is:
[0122]
[0123] After substituting the control law, we can get the following form:
[0124]
[0125] According to the above equation, the convergence time t of sliding mode dynamics can be obtained:s for
[0126]
[0127] In the formula, When system time t ≥ t s When the sliding mode dynamics can converge to s k =0.
[0128] Therefore, the system error equation can be updated as
[0129]
[0130] For the above second-order differential equation, it is obvious that as long as c1>0, c2>0 is guaranteed, the error can converge to 0. In summary, the designed generalized coupling error and sliding mode dynamics are stable.
[0131] The iterative convergence analysis is as follows:
[0132] For the iterative learning term (16), after a finite number of iterative learning, it can converge to the sliding mode surface s k =0. The proof is as follows:
[0133] The energy function of the kth iteration is defined as:
[0134] in, The difference in energy function between the kth iteration and the k-1th iteration is expressed as follows:
[0135]
[0136] The first-order derivative of equation (23) can be calculated by the following formula:
[0137]
[0138] Substituting formula (24) into (23), we get the following results:
[0139]
[0140] Next, the energy function difference between the kth iteration and the k-1th iteration is Defined as:
[0141]
[0142] Calculating the first-order derivative of equation (26), we have the following results:
[0143]
[0144] Substituting formula (27) into (26), we get the following results:
[0145]
[0146] Known results,
[0147]
[0148] Based on formula (29),
[0149]
[0150] Next, the third energy function difference between the kth iteration and the k-1th iteration has the following form:
[0151] Existing relationship
[0152] (ab) T (ab)-(ac) T (ac)=(cb) T [2(ab)+(bc)] (32)
[0153] Available
[0154]
[0155] Furthermore, formula (31) can be written as
[0156]
[0157] According to equations (22)-(34), the error of the energy function can be calculated as follows:
[0158]
[0159] Based on Lyapunov stability theory, when s k ≡0, there is ΔV k ≡0. The proposed controller satisfies the existence and reachability conditions of the sliding surface, and through continuous iterations, the sliding surface will converge to s at any time k =0.
[0160] This application verifies the control performance and robustness of this method through simulation research. Specifically, the numerical simulation is divided into three groups. Among them,
[0161] In the first group, there is no problem of uncertain / unknown system parameters and external disturbances. The designed data-driven iterative learning anti-disturbance control method is compared with the traditional nonlinear coupling control method (CAC) and hierarchical sliding mode control method (HSMC).
[0162] In the second group, the robustness of the proposed method with uncertain / unknown system parameters is further verified.
[0163] In the third group, the anti-disturbance capability of the proposed method under the influence of external disturbances is verified without changing the controller gains.
[0164] Specifically, the system parameters are set as: m = 1kg, m x =6.5kg, m y =10kg, g=9.8m / s 2 .
[0165] The corresponding parameters of the desired trajectory are set as: d =0.6m,y d =0.5m,l d =1m.
[0166] The initial state of the system is set to:
[0167] [x(0) y(0) l(0) θ x (0) θ y (0)] T =[0 0 0.4 0 0] T .
[0168] After careful tuning, the control gains of this method are shown in the following table:
[0169]
[0170]
[0171] In the first group: the system parameters are not changed, no external disturbance is applied, and the iterative control is performed 10 times. By observing the convergence results of the iterative error, it can be found that after the fourth iteration, the control system tends to be stable; secondly, the 10th iterative control result is compared with the CAC method and the HSMC method.
[0172] In the second group: the system parameters and control gains are not changed, no external disturbance is applied, and the iterative control is performed 10 times. The robustness of the designed control method is further verified by changing the initial state of the load. The initial state of the load is set to θ x (0) = θ y (0) = 1°.
[0173] In the third group: without changing the system parameters and control gains, the designed control method is verified to resist disturbances by applying external disturbances to the load. A sinusoidal signal is applied as a disturbance signal between 10s and 11s, and a pulse signal is applied as a disturbance signal between 14s and 15s. The amplitude of the disturbance signal is 1°.
[0174] Finally, the five-degree-of-freedom overhead crane system can be controlled based on a data-driven iterative learning anti-disturbance sliding mode controller.
[0175] A system based on the above data-driven five-degree-of-freedom overhead crane self-disturbance rejection sliding mode control method includes:
[0176] Data acquisition module: used to collect the status information of the five-degree-of-freedom overhead crane system, the status information includes the displacement information of the trolley and the bridge, the cable lifting information, and the load angle swing information. This application collects the said status through an incremental rotary encoder (E6B2-CWZ6CZ5BZ3E) and an angle encoder (Tamagawa TS5705N50 05N250), and the collected data can be stored in a computer-readable storage medium.
[0177] Storage medium: used to store the sliding mode dynamic data information of each iteration and the data information collected by the data acquisition module. The storage medium includes various media that can store program codes, such as USB flash drives, mobile hard disks, read-only memories (ROMs), random access memories (RAMs), and optical disks, and is integrated with the data acquisition module and the microprocessor.
[0178] Microprocessor: used to execute the steps of the data-driven self-disturbance rejection sliding mode control method described in the embodiment and issue related instructions. The microprocessor generates instructions for controlling the translational driving force and load suspension force of the trolley and the bridge according to the steps in the application method based on the input expected displacement and the collected displacement state, and issues them to the corresponding drive motor for execution, so as to realize the attached Figure 3 The functions specified by one or more processes in the application method flowchart.
[0179] The above descriptions are only optional embodiments of the present invention, and are not intended to limit the patent scope of the present invention. All equivalent structural changes made using the contents of the present invention's specification and drawings, or directly / indirectly applied in other related technical fields, are included in the patent protection scope of the present invention.
Claims
1. A data-driven five-degree-of-freedom overhead crane self-disturbance rejection sliding mode control method, characterized in that: The steps include: Establish a dynamic model of the five-degree-of-freedom overhead crane system; perform dynamic modeling according to the Lagrangian method. The dynamic model of the five-degree-of-freedom overhead crane is as follows: Where, m, m x , m y are the load mass, trolley mass and bridge mass respectively; l is the cable length; θ x and θ y are the swing angles in the x and y directions respectively, the x direction is the running direction of the trolley, and the y direction is the running direction of the bridge; f x and f y is the translational driving force, f l is the load suspension force; S x = sin(θ x ), S y = sin(θ y ), C x =cos(θ x ), C y =cos(θ y ); Select the state variable x1 = [xyl θ x θ y ] T , The following state space expression is obtained: Where u = [f x f y f l ] T ; A tracking differentiator is designed to extract the displacement of the reference trajectory and its differential signal; the tracking differentiator is a third-order nonlinear tracking differentiator, and its construction form is as follows: In the above formula, is the output of the third-order nonlinear tracking differentiator, γ∈R 3×3 >0 is an adjustable parameter of the differentiator; an extended state observer is constructed to estimate the displacement and swing angle of the overhead travelling crane and its total disturbance signal in real time; the extended state observer includes a displacement observer and an angle observer; The displacement observer is designed as follows: The angle observer is designed as follows: In the formula, is a nonlinear function, is the total angular disturbance, α2 and δ2 are both adjustment parameters of nonlinear functions, b j To control the input adjustable parameters, it determines the strength of disturbance compensation; Designing a sliding mode controller based on a generalized coupled error signal, and combining a differentiator and an observer to form a composite active disturbance rejection sliding mode controller; Designing a sliding mode controller based on a generalized coupled error signal, and combining a differentiator and an observer to form a composite active disturbance rejection sliding mode controller includes the following steps: Design the generalized coupling error signal σ: Where, e is the positioning error vector, k θ ∈R 3×2 and ω∈R 2×2 is a positive definite diagonal gain matrix; The designed integral sliding surface s is: Where σ is the generalized coupling error signal, c1 and c2 are positive definite diagonal matrices; Obtain the first-order derivative of the sliding surface s and derive the sliding mode controller as: In the formula, u eq is an equivalent control item; The control input is iteratively corrected by a data-driven robust iterative learning controller to generate the final iterative learning anti-disturbance sliding mode controller; The overall control law of the final iterative learning anti-disturbance sliding mode controller is designed as follows: In the formula, is the sliding mode control term, is the iteration control term, k is the number of iterations; Sliding Mode Control Updated to: Iteration Control for: The five-degree-of-freedom overhead crane system is controlled based on a data-driven active disturbance rejection sliding mode controller.
2. A system applied to the data-driven five-degree-of-freedom overhead crane self-disturbance rejection sliding mode control method according to claim 1, characterized in that: include Data acquisition module: used to collect status information of the five-degree-of-freedom overhead crane system; Storage module: used to store the sliding mode dynamic data information of each iteration and the data information collected by the data acquisition module; Microprocessor: used to execute the steps in the data-driven five-degree-of-freedom overhead crane self-disturbance rejection sliding mode control method and issue relevant instructions.
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