A control method for flexible gantry crane system under unknown disturbance based on sliding mode control

Abstract

The present invention relates to a control method for a flexible gantry crane system under unknown disturbances based on sliding mode control, and belongs to the technical field of position control and vibration suppression of flexible gantry crane systems. The method uses a sliding mode control method to perform boundary control on a flexible gantry crane system described by a partial differential equation, that is, only applying a control force at the trolley end, and designs a disturbance observer to weaken the controller jitter problem caused by a sign function. And through Lyapunov stability analysis, it is proved that the flexible gantry crane system can achieve the control goal of position control vibration suppression. The control method provided by an embodiment of the present invention can effectively overcome the influence of unknown disturbances in the system, and at the same time can weaken the jitter problem of the system, and the proposed boundary controller is suitable for practical engineering applications.

Description

Technical Field

[0001] The invention relates to a control method for a flexible gantry crane system under unknown disturbance based on sliding mode control, and belongs to the technical field of position control and vibration suppression of flexible gantry crane systems. Background Art

[0002] Gantry crane systems are now widely used in factories, ports and other places to transport heavy or dangerous goods, which can not only reduce labor and labor intensity of workers but also improve production capacity. The flexible gantry crane system consists of a trolley that can move left and right on the guide rail, a flexible rope and a load. The trolley is driven by a motor to transport the load to the specified location. The flexible rope made of flexible materials has the advantages of light weight and strong shock absorption. However, in the process of transporting the load, the flexible material is prone to vibration, which makes it difficult to accurately position the load to the specified position and causes the system performance to deteriorate. In addition, in the actual system, the influence of unknown disturbances (such as wind disturbances, etc.) will also bring certain difficulties to the vibration suppression of the flexible crane system. Therefore, effective control measures are needed to suppress this vibration.

[0003] Among general control methods, sliding mode control is an effective control strategy for systems affected by disturbances, and it has strong robustness to external disturbances. However, when dealing with disturbances, sliding mode control will set the controller gain based on the maximum value of the disturbance for the sake of conservatism, that is, the switching gain before the sign function will be large, causing the controller to experience severe jitter after the system becomes stable, that is, the amplitude of the system jitter is large. This large amplitude jitter will not only affect the control accuracy, but also increase energy consumption and even cause system instability.

[0004] In addition, the flexible gantry crane system is usually modeled as a partial differential equation system in order to accurately describe the system. Boundary control is an easy-to-implement control method in the partial differential equation control method. The reason is that the control force is only applied at the boundary of the system. However, this infinite-dimensional characteristic of the system brings certain difficulties to the design of the boundary controller. Summary of the invention

[0005] In order to solve the system jitter problem caused by the introduction of sign function in the existing sliding mode control into the flexible gantry crane system, the present invention provides a control method for a flexible gantry crane system under unknown disturbance based on sliding mode control. The method uses the sliding mode control method to perform boundary control on the flexible gantry crane system described by partial differential equations, that is, only applying control force at the trolley end, and designing a disturbance observer to weaken the controller jitter problem caused by the sign function.

[0006] A control method for a flexible gantry crane system under unknown disturbance based on sliding mode control, the method comprising:

[0007] Step S1, obtaining a boundary state signal of the flexible gantry crane system, wherein the boundary state signal includes a boundary curvature y of the flexible rope x (0,t), the boundary angular velocity y of the flexible rope xt (0,t), the car position y(0,t) and the car speed y t (0, t); x represents the spatial position, t represents the time;

[0008] Step S2, designing an integral sliding mode function and constructing a disturbance observer according to the acquired boundary state signal;

[0009] Step S3, constructing a boundary sliding mode controller using the designed integral sliding mode function, disturbance observer and the acquired boundary state signal;

[0010] Step S4, using the constructed boundary sliding mode controller to control the flexible gantry crane system under unknown disturbances.

[0011] Optionally, the method further comprises: modeling the flexible gantry crane system under unknown disturbance to obtain the main control equation and boundary conditions of the flexible gantry crane system under unknown disturbance;

[0012] The main control equation of the flexible gantry crane system under unknown disturbance is:

[0013]

[0014] The boundary conditions of the flexible gantry crane system under unknown disturbance are as follows:

[0015]

[0016] Where y(x,t)∈R is the lateral position of the flexible rope at the spatial position x and the time t, and R represents the real number space; y t (x,t) and y x (x, t) are the first-order partial derivatives of the lateral position y(x, t) of the flexible rope with respect to the time variable t and the space variable x respectively; y tt (x, t) represents the second-order partial derivative of the lateral position y(x, t) of the flexible rope with respect to the time variable t; ρ, L, M and m represent the unit length mass of the flexible rope, the rope length, the trolley mass and the bottom load mass respectively; u(t) is the boundary sliding mode controller to be designed that acts only on the trolley end, d(t) is the unknown disturbance at the boundary of the system, and it is assumed that the unknown disturbance d(t) and its derivative are bounded and satisfy and and are all real numbers greater than 0, indicating the corresponding upper bounds; P(x)=g[m+ρ(Lx)] is the tension of the flexible rope at the spatial position x, where g is the acceleration due to gravity.

[0017] Optionally, the integral sliding mode function designed in step S2 is:

[0018]

[0019] Among them, τ is the integral variable, k2 and k3 are constants greater than 0, y d is the desired position of the car, φ(t) is an auxiliary function, and its expression is φ(t) = y t (0,t)-y x (0,t).

[0020] Optionally, the disturbance observer expression constructed in step S2 is:

[0021]

[0022] Among them, k d is a constant greater than 0, is an auxiliary variable, is an estimate of the unknown disturbance d(t).

[0023] Optionally, the boundary sliding mode controller expression constructed in step S3 is:

[0024]

[0025] Where k1, k2, k3 and k4 are controller gain parameters, which are constants greater than 0; sgn(·) is the sign function; y xt (0,t) is the boundary angular velocity of the flexible rope.

[0026] Optionally, step S4 includes:

[0027] Real-time acquisition of the boundary state signal of the flexible gantry crane system, where the boundary curvature y of the flexible rope x (0,t) is measured by the inclinometer, and the boundary angular velocity y xt (0,t) is based on the measured boundary curvature y x (0, t) is obtained by reverse difference calculation, the car position y(0, t) and the car speed y t (0, t) is measured by the motor encoder at the trolley end;

[0028] The boundary state signal obtained in real time is input into the constructed boundary sliding mode controller to calculate the corresponding control force;

[0029] The corresponding control force is applied to the trolley of the flexible gantry crane system to achieve real-time control of the system.

[0030] Optionally, the boundary sliding mode controller gains k1=10, k2=0.01, k3=10, k4=0.1, and the disturbance observer k d =100.

[0031] The present application also provides a control system for a flexible gantry crane system under unknown disturbance based on sliding mode control, wherein the system controls the flexible gantry crane system under unknown disturbance according to the above method, and the system comprises: a boundary sensor, a boundary sliding mode controller and an actuator;

[0032] The boundary sensor is used to obtain the boundary state signal of the flexible gantry crane system: the boundary curvature y of the flexible rope x (0,t), the boundary angular velocity y of the flexible rope xt (0,t), the car position y(0,t) and the car speed y t (0,t);

[0033] The boundary sliding mode controller is used to calculate the magnitude of the control force according to the boundary state signal obtained by the boundary sensor, and send the calculation result to the actuator in the system;

[0034] The actuator is used to control the system by acting on the flexible crane system trolley according to the magnitude of the received control force.

[0035] Optionally, the boundary sensor includes a motor encoder and an inclinometer.

[0036] The beneficial effects of the present invention are:

[0037] By using the designed integral sliding mode function, disturbance observer and the obtained boundary state signal to construct a boundary sliding mode controller, and through Lyapunov stability analysis, it is proved that the flexible gantry crane system can achieve the control goal of position control vibration suppression. The vibration suppression method provided in the embodiment of the present invention can effectively overcome the influence of unknown disturbances in the system and weaken the jitter problem of the system. The proposed boundary controller is suitable for practical engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0039] Figure 1A flow chart of a method for controlling a flexible gantry crane system under unknown disturbances based on sliding mode control provided by the present invention.

[0040] Figure 2 This is a schematic diagram of the structure of the flexible gantry crane system.

[0041] Figure 3 This is a three-dimensional simulation diagram of the lateral position of the flexible rope under control using the boundary sliding mode controller designed in this application.

[0042] Figure 4 This is a three-dimensional simulation diagram of the lateral offset of the flexible rope under control using the boundary sliding mode controller designed in this application.

[0043] Figure 5 This is a load position simulation diagram under the control of the boundary sliding mode controller designed in this application.

[0044] Figure 6 This is a sliding mode function diagram under control using the boundary sliding mode controller designed in this application.

[0045] Figure 7 The disturbance observer designed for this application Comparison diagram of the perturbation d(t).

[0046] Figure 8 This is a voltage output simulation diagram of the boundary sliding mode controller provided in this application.

[0047] Fig. 9 This is a structural block diagram of the control system of the flexible gantry crane system under unknown disturbance based on sliding mode control provided in this application. DETAILED DESCRIPTION

[0048] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0049] Embodiment 1:

[0050] This embodiment provides a control method for a flexible gantry crane system under unknown disturbance based on sliding mode control, the method comprising:

[0051] Step S1, obtaining a boundary state signal of the flexible gantry crane system, wherein the boundary state signal includes a boundary curvature y of the flexible rope x (0,t), the boundary angular velocity y of the flexible rope xt (0,t), the car position y(0,t) and the car speed y t (0, t); x represents the spatial position, t represents the time;

[0052] Step S2, designing an integral sliding mode function and constructing a disturbance observer according to the acquired boundary state signal;

[0053] Step S3, constructing a boundary sliding mode controller using the designed integral sliding mode function, disturbance observer and the acquired boundary state signal;

[0054] Step S4, using the constructed boundary sliding mode controller to control the flexible gantry crane system under unknown disturbances.

[0055] Embodiment 2:

[0056] This embodiment provides a control method for a flexible gantry crane system under unknown disturbances based on sliding mode control, and verifies the performance of the system under the control method. Figure 1 , the method comprising:

[0057] S110, Model the flexible gantry crane system with unknown disturbances, such as Figure 2 The figure shows the structure diagram of the flexible gantry crane system;

[0058] S120, obtaining a boundary state signal of the flexible gantry crane system;

[0059] S130, designing an integral sliding mode function according to the acquired boundary state signal;

[0060] S140, constructing a disturbance observer to weaken the system chattering phenomenon caused by the sign function;

[0061] S150, constructing a boundary sliding mode controller using the designed integral sliding mode function, disturbance observer and the acquired boundary state signal;

[0062] The above steps are the process of constructing a boundary sliding mode controller. To verify the effectiveness of this method, the system performance under the above controller is verified in this embodiment:

[0063] S160. Based on Lyapunov stability analysis, prove the stability of disturbance observer;

[0064] S170. Prove that under the action of the proposed controller, the system state can reach the sliding surface in a finite time;

[0065] S180. Based on Lyapunov stability analysis, it is proved that the system state is stable on the sliding surface.

[0066] The embodiment of the present invention provides a control method for a flexible gantry crane system under unknown disturbances based on sliding mode control. The boundary sliding mode controller is constructed by using the designed integral sliding mode function, disturbance observer and acquired boundary state signal. Through Lyapunov stability analysis, it is proved that the flexible gantry crane system can achieve the control goal of position control vibration suppression. The vibration suppression method provided by the embodiment of the present invention can effectively overcome the influence of unknown disturbances in the system, and at the same time can weaken the system jitter problem caused by the sign function. The proposed boundary controller is suitable for practical engineering applications.

[0067] Specifically, the control method of the flexible gantry crane system under unknown disturbance based on sliding mode control includes:

[0068] Modeling of flexible gantry crane systems with unknown disturbances, including:

[0069] The Hamilton principle is used to model the flexible gantry crane system with unknown disturbances, and the main control equation of the system is obtained as follows:

[0070]

[0071] The boundary conditions of the system are as follows:

[0072]

[0073] Where y(x,t)∈R is the lateral position of the flexible rope at the spatial position x and the time t, and R represents the real space; y t (x,t) and y x (x, t) are the first-order partial derivatives of the lateral position y(x, t) of the flexible rope with respect to the time variable t and the space variable x respectively; y tt (x, t) represents the second-order partial derivative of the lateral position y(x, t) of the flexible rope with respect to the time variable t; ρ, L, M and m represent the unit length mass of the flexible rope, the rope length, the trolley mass and the bottom load mass, respectively; u(t) is the boundary sliding mode controller to be designed that acts only on the trolley end (end 0); d(t) is the unknown disturbance at the boundary of the system. Assume that the disturbance d(t) and its derivative are bounded and satisfy and and are all real numbers greater than 0, indicating the corresponding upper bounds. And P(x)=g[m+ρ(Lx)] is the tension of the flexible rope at the spatial position x, where g is the acceleration due to gravity.

[0074] Furthermore, the acquisition of the boundary state signal of the flexible gantry crane system includes: the boundary curvature y of the flexible rope x(0,t), the boundary angular velocity y of the flexible rope xt (0,t), the car position y(0,t) and the car speed y t (0,t).

[0075] The boundary signal is easy to obtain in the actual system. The boundary curvature y of the flexible rope is x (0,t) can be measured by the inclinometer, and the boundary angular velocity y xt (0,t) can be based on the measured y x (0, t) is obtained by reverse difference calculation, the car position y(0, t) and the car speed y t (0,t) can be measured by the motor encoder at the trolley end.

[0076] Furthermore, the integral sliding mode function expression is as follows:

[0077]

[0078] In the formula, k2 and k3 are constants greater than 0, y d is the expected position and τ is the integration variable.

[0079] φ(t) is an auxiliary function, which is expressed as follows:

[0080] φ(t)=y t (0,t)-y x (0,t)

[0081] Furthermore, the expression of constructing the disturbance observer is as follows:

[0082]

[0083] In the formula, k d is a constant greater than 0, is an auxiliary variable, is an estimate of the unknown disturbance d(t).

[0084] Furthermore, the constructed boundary sliding mode controller expression is as follows:

[0085]

[0086] In the formula, k1, k2, k3 and k4 are controller gain parameters, which are constants greater than 0, sgn(·) is the sign function; y xt (0,t) is the boundary angular velocity of the edge flexible rope.

[0087] The performance of the flexible gantry crane system under the control of the boundary sliding mode controller constructed above is demonstrated below:

[0088] First, the stability of the designed disturbance observer is proved, including:

[0089] Select the Lyapunov candidate function V d (t) are as follows:

[0090]

[0091] In the formula, is the disturbance error term;

[0092] Ask for V d The first-order derivative of (t) with respect to time t, using the perturbation d(t) and its derivative in the assumption

[0093] is bounded, we get:

[0094]

[0095] In the formula,

[0096] Furthermore, there must be a finite time Among them, μ d > 0. When Sometimes, there is

[0097] Furthermore, under the action of the proposed controller, the system state can reach the sliding surface within a finite time, including:

[0098] Construct Lyapunov candidate function V s (t) are as follows:

[0099]

[0100] Combining the boundary conditions of the flexible gantry crane system and the boundary controller designed above, we can get V s The first-order derivative of (t) with respect to time t is as follows:

[0101]

[0102] If you select Among them, ∈1>0, we get:

[0103]

[0104] Among them, the reaching law is Further calculation shows that the time when the system state reaches the sliding surface is:

[0105]

[0106] Furthermore, the Lyapunov stability analysis is used to prove that the system state is stable on the sliding surface. The specific steps include:

[0107] The Lyapunov function is constructed as follows:

[0108] V(t)=V1(t)+V2(t)+V3(t)

[0109] In the formula,

[0110]

[0111] In the formula, ∈ v and α are both positive constants;

[0112] Verifying that the Lyapunov function is positive definite, we obtain:

[0113] 0≤(1-ξ1)(V1(t)+V2(t))≤V(t)≤(1+ξ1)(V1(t)+V2(t))

[0114] Where, 0<ξ1=max(α(L+∈ v ),

[0115] The first-order derivative of the Lyapunov function at time t is obtained, combined with the boundary conditions, the boundary controller and the sliding surface s(t)=0, and the following is obtained:

[0116]

[0117] In the formula,

[0118] Furthermore, the system state ω(x,t) satisfies:

[0119]

[0120] The above formula shows that the lateral deflection ω(x,t) of the flexible rope is stable.

[0121] In addition, since y(x,t)=ω(x,t)+y(0,t), its state y(0,t)→y d , when t→∞, then y(x,t)→y d , when t→∞.

[0122] From the above derivation, it can be seen that the state of the system is stable under the proposed sliding surface and controller.

[0123] At this point, the position control and vibration suppression are completed, and the system chattering phenomenon caused by the sign function is weakened.

[0124] The effectiveness of the proposed method is illustrated below with specific parameters and accompanying drawings.

[0125] Firstly, the parameters of the flexible gantry crane system are selected as follows: L = 1m, g = 9.8N / kg, M = 2.1kg, m = 10kg, ρ = 0.2kg / m, disturbance d(t) = sin(3t) + cos(5t) + 0.5.

[0126] The initial values ​​of the system are set as follows: the initial position of the car y(x,0) = 0.1m, the initial speed of the car y t (x,0) = 0 m / s, the boundary curvature y of the flexible rope x (0,0) = 0rad, the desired position of the car is y d =0.5m.

[0127] Secondly, the boundary sliding mode controller designed above is adopted, and its controller gains are set as follows: k1 = 10, k2 = 0.01, k3 = 10, k4 = 0.1, and k in the disturbance observer d =100.

[0128] Figure 3 This is a three-dimensional simulation diagram of the lateral position of the flexible rope under control using the boundary sliding mode controller designed in this application. It can be seen from the figure that y(x,t)→y d , the x position of any point on the rope eventually tends to the desired position, that is, the position control goal is achieved.

[0129] Figure 4 This is a three-dimensional simulation diagram of the lateral offset of the flexible rope under control using the boundary sliding mode controller designed in this application. It can be seen from the figure that after t=6s, the lateral offset ω(x,t) is limited to a smaller area near 0, achieving the vibration suppression goal.

[0130] Figure 5 This is a load position simulation diagram under the control of the boundary sliding mode controller designed in this application. It can be seen from the figure that the load is finally transported to the specified position y d =0.5m.

[0131] Figure 6 This is a sliding mode function diagram under the control of the boundary sliding mode controller designed in the present application. It can be seen from the figure that the system reaches the sliding mode surface, that is, s(t)=0, at about t=0.5s.

[0132] Figure 7 Disturbance observer designed for the present invention The comparison chart of the actual disturbance value d(t) and the disturbance d(t) shows that the actual disturbance value d(t) is represented by "*" and the estimated disturbance value Indicated by “—.”, the two lines overlap well, indicating that the designed disturbance observer can observe the unknown disturbance d(t) well.

[0133] Figure 8 This is a voltage output simulation diagram of the boundary sliding mode controller provided by the present invention. It can be seen from the figure that the switching amplitude of the controller designed by the present application is less than the upper limit of the disturbance of 2.5.

[0134] Embodiment three:

[0135] This embodiment provides a control system for a flexible gantry crane system under unknown disturbances based on sliding mode control. Fig. 9 As shown, including:

[0136] (1) Boundary sensor: including motor encoder and inclinometer, mainly used to obtain the boundary state signal y of the flexible gantry crane system x (0,t),y xt (0,t),y(0,t),y t (0, t), these signals are the signals of the system car end, which are easy to measure and calculate in the actual system;

[0137] (2) Boundary sliding mode controller: mainly used to calculate the magnitude of the control force according to the designed boundary sliding mode controller using the boundary state signal obtained above, and send the calculation result to the actuator part in the system;

[0138] Specifically, it is used to calculate the control force u(t) applied to the car.

[0139] (3) Actuator: mainly used to receive the magnitude of the control force calculated by the boundary controller and apply the control force to the flexible crane system.

[0140] The control method and control system of the flexible gantry crane system under unknown disturbance based on sliding mode control provided by the embodiment of the present invention designs a boundary sliding mode controller by using the designed sliding mode function, disturbance observer and acquired boundary state signal, and proves by using Lyapunov stability theory that the system can reach the sliding mode surface within a finite time and the system state is stable on the sliding mode surface, thereby achieving the position control and vibration suppression goals of the flexible gantry crane system and weakening the system jitter phenomenon caused by the sign function. Moreover, the boundary controller designed in the method shown in the present invention only uses the boundary state signal in the system, which is easy to obtain. Therefore, the present invention has theoretical and practical application value.

[0141] It is to be understood that the above embodiments are merely exemplary embodiments used to illustrate the principles of the present invention, but the present invention is not limited thereto. For those of ordinary skill in the art, various modifications and improvements can be made without departing from the spirit and essence of the present invention, and these modifications and improvements are also considered to be within the scope of protection of the present invention.

[0142] Some steps in the embodiments of the present invention may be implemented using software, and the corresponding software program may be stored in a readable storage medium, such as a CD or a hard disk.

[0143] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A control method for a flexible gantry crane system under unknown disturbance based on sliding mode control, characterized in that: The method comprises: Step S1, obtaining a boundary state signal of the flexible gantry crane system, wherein the boundary state signal includes a boundary curvature y of the flexible rope x (0,t), the boundary angular velocity y of the flexible rope xt (0,t), the car position y(0,t) and the car speed y t (0, t); x represents the spatial position, t represents the time; Step S2, designing an integral sliding mode function and constructing a disturbance observer according to the acquired boundary state signal; Step S3, constructing a boundary sliding mode controller using the designed integral sliding mode function, disturbance observer and the acquired boundary state signal; Step S4, using the constructed boundary sliding mode controller to control the flexible gantry crane system under unknown disturbance; The method further comprises: modeling the flexible gantry crane system under unknown disturbance to obtain the main control equation and boundary conditions of the flexible gantry crane system under unknown disturbance; The main control equation of the flexible gantry crane system under unknown disturbance is: The boundary conditions of the flexible gantry crane system under unknown disturbance are as follows: Where y(x,t)∈R is the lateral position of the flexible rope at the spatial position x and the time t, and R represents the real number space; y t (x,t) and y x (x, t) are the first-order partial derivatives of the lateral position y(x, t) of the flexible rope with respect to the time variable t and the space variable x respectively; y tt (x, t) represents the second-order partial derivative of the lateral position y(x, t) of the flexible rope with respect to the time variable t; ρ, L, M and m represent the unit length mass of the flexible rope, the rope length, the trolley mass and the bottom load mass respectively; u(t) is the boundary sliding mode controller to be designed that acts only on the trolley end, d(t) is the unknown disturbance at the boundary of the system, and it is assumed that the unknown disturbance d(t) and its derivative are bounded and satisfy and and are all real numbers greater than 0, indicating the corresponding upper bounds; P(x)=g[m+ρ(Lx)] is the tension of the flexible rope at the spatial position x, where g is the acceleration due to gravity; The integral sliding mode function designed in step S2 is: Among them, τ is the integral variable, k2 and k3 are constants greater than 0, y d is the desired position of the car, φ(t) is an auxiliary function, and its expression is φ(t) = y t (0,t)-y x (0,t); The disturbance observer expression constructed in step S2 is: Among them, k d is a constant greater than 0, is an auxiliary variable, is the estimated value of the unknown disturbance d(t); The boundary sliding mode controller expression constructed in step S3 is: Where k1, k2, k3 and k4 are controller gain parameters, which are constants greater than 0; sgn(·) is the sign function; y xt (0, t) is the boundary angular velocity of the flexible rope; The step S4 comprises: Real-time acquisition of the boundary state signal of the flexible gantry crane system, where the boundary curvature y of the flexible rope x (0,t) is measured by the inclinometer, and the boundary angular velocity y xt (0,t) is based on the measured boundary curvature y x (0, t) is obtained by reverse difference calculation, the car position y(0, t) and the car speed y t (0, t) is measured by the motor encoder at the trolley end; The boundary state signal obtained in real time is input into the constructed boundary sliding mode controller to calculate the corresponding control force; The corresponding control force is applied to the trolley of the flexible gantry crane system to achieve real-time control of the system.

2. The method according to claim 1, characterized in that The boundary sliding mode controller gains k1 = 10, k2 = 0.01, k3 = 10, k4 = 0.1, and the disturbance observer k d =100.

3. A control system for a flexible gantry crane system under unknown disturbance based on sliding mode control, characterized in that: The system controls the flexible gantry crane system under unknown disturbance according to the method described in claim 1 or 2, and the system comprises: a boundary sensor, a boundary sliding mode controller and an actuator; The boundary sensor is used to obtain the boundary state signal of the flexible gantry crane system: the boundary curvature y of the flexible rope x (0,t), the boundary angular velocity y of the flexible rope xt (0,t), the car position y(0,t) and the car speed y t (0,t); The boundary sliding mode controller is used to calculate the magnitude of the control force according to the boundary state signal obtained by the boundary sensor, and send the calculation result to the actuator in the system; The actuator is used to control the system by acting on the flexible crane system trolley according to the magnitude of the received control force.

4. The system according to claim 3, characterized in that The boundary sensors include a motor encoder and an inclinometer.

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