A safe and robust control method, system, device and medium for smooth startup

Abstract

The present invention discloses a safe and robust control method, system, device, and medium for smooth startup. The method comprises obtaining parameters of a target position and the current state of a bridge crane system; constructing an adaptive law, inputting the parameters into the adaptive law, and obtaining an estimated value of the parameters output by the adaptive law; constructing an adaptive coupling signal model, inputting the parameters and their estimated values ​​into the adaptive coupling signal model, and obtaining a coupled signal output by the adaptive coupling signal model; calculating an error signal between the coupled signal and the target position; constructing a time-varying function, and constructing a time-varying sliding surface based on the error signal and the time-varying function; constructing an adaptive time-varying sliding mode controller based on the time-varying sliding surface and the estimated values ​​of the parameters; and obtaining a driving force through the adaptive time-varying sliding mode controller, which drives the bridge crane system to the target position. The present invention can ensure global robustness and achieve smooth startup and operation of the bridge crane.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge crane control, and in particular to a safe and robust control method, system, equipment and medium for smooth startup. Background Art

[0002] Bridge cranes are a type of multi-degree-of-freedom underactuated mechanical system with widespread engineering applications. Studying their control issues has both theoretical and practical value. In terms of theoretical research, bridge crane systems share common characteristics with underactuated mechanical systems, such as a positive definite symmetric inertia matrix and the presence of dynamic nonholonomic constraints. Therefore, studying bridge crane control issues can contribute to the development of control theory for underactuated mechanical systems. With the development of the national economy, various types of bridge cranes, such as those in workshops, docks, and foundry cranes in the metallurgical industry, have become increasingly important, placing increasing demands on crane control. Load swing can make it difficult for the crane system to lower the load at the target location and can cause collisions between the load and other equipment during transportation, resulting in unnecessary losses and reduced efficiency. Anti-sway control is particularly important when loading liquids. Therefore, it is crucial to ensure that the load is lifted from its initial position to the target location within a short period of time, and that load swing is minimized throughout the entire transport process and upon reaching the target location. Furthermore, wind and other uncertainties (such as unknown friction coefficients, trolley mass, load mass, and rope length) can affect crane performance. Failure to properly control load swing not only reduces work efficiency but can also damage the transported goods or surrounding objects. According to research, each load fixation consumes at least 30% more transport time. To date, due to the lack of automated control methods suitable for industrial sites, most industrial cranes are still manually operated by skilled workers. The trolley's positioning performance and the ability to suppress load swing rely entirely on the operator's experience.

[0003] While existing bridge crane controllers have made significant improvements in addressing external interference, there is still room for improvement in addressing issues such as bridge crane system parameter perturbations and unmodeled dynamics. For example, existing methods do not consider the adaptive coupling relationship between load mass and rope length, which may cause the control method to be sensitive to changes in rope length. Some existing technologies can only reduce the initial driving force and cannot ensure that the force increases slowly from zero, making it impossible to smoothly start and operate the bridge crane. Summary of the Invention

[0004] The present invention aims to solve at least one of the technical problems existing in the prior art. To this end, the present invention provides a safe and robust control method, system, device and medium for smooth startup, which can ensure global robustness and achieve smooth startup and operation of a bridge crane.

[0005] In a first aspect, an embodiment of the present invention provides a safe and robust control method for smooth startup, the method comprising:

[0006] Obtain the parameters of the target position and the current state of the bridge crane system;

[0007] constructing an adaptive law, inputting the parameter into the adaptive law, and obtaining an estimated value of the parameter output by the adaptive law;

[0008] constructing an adaptive coupling signal model, inputting the parameter and the estimated value of the parameter into the adaptive coupling signal model, and obtaining a coupling signal output by the adaptive coupling signal model;

[0009] calculating an error signal between the coupled signal and the target position;

[0010] constructing a time-varying function, and constructing a time-varying sliding surface based on the error signal and the time-varying function;

[0011] constructing an adaptive time-varying sliding mode controller based on the time-varying sliding mode surface and the estimated values ​​of the parameters;

[0012] A driving force is obtained by the adaptive time-varying sliding mode controller, and the bridge crane system is driven by the driving force to reach a target position.

[0013] Compared with the prior art, the first aspect of the present invention has the following beneficial effects:

[0014] This method constructs an adaptive coupling signal model, inputs the parameters and the estimated values ​​of the parameters into the adaptive coupling signal model, and obtains a coupling signal output by the adaptive coupling signal model; the coupling gain can be dynamically adjusted to further improve the transient performance of the system; this method constructs a time-varying sliding surface based on the error signal and the time-varying function by constructing a time-varying function; based on the time-varying sliding surface and the estimated values ​​of the parameters, an adaptive time-varying sliding mode controller is constructed; based on the time-varying sliding surface, an adaptive time-varying sliding mode controller is used to achieve smooth startup control and operation of the crane system, which is simpler to implement and does not require a reference trajectory to be planned in advance. It is easier to obtain good control effects in engineering applications and can self-adjust the coupling relationship of multiple system parameters, so that this method not only has better robustness to parameter perturbations, friction disturbances and unmodeled dynamics, but also ensures global robustness.

[0015] According to some embodiments of the present invention, before acquiring the parameters of the target position and the current state of the bridge crane system, the safe and robust control method for smooth startup further includes the steps of:

[0016] A kinetic equation is constructed, wherein the kinetic equation includes:

[0017]

[0018]

[0019] Among them, m t Indicates the mass of the trolley, m p represents the load mass, l represents the length of the suspension rope, θ represents the load swing angle, x represents the displacement of the trolley, F represents the driving force of the trolley in the horizontal direction, and f represents the friction between the trolley and the track. f r ,δ,k rx represents the friction parameter, g represents the acceleration due to gravity;

[0020] Linearize the following formula:

[0021]

[0022] Will Substitution The following formula is obtained from the formula:

[0023]

[0024] Among them, m t 、m p 、m p g、m p l、f r and k rx Represents the system parameters, which are written in vector form as follows:

[0025] Γ=[m t m p m p gm p lf r k rx ] T =[Γ1 Γ2 Γ3 Γ4 Γ5 Γ6] T .

[0026] According to some embodiments of the present invention, the adaptive coupled signal model includes:

[0027] ε=x-σ

[0028] Where ε represents the adaptive coupling signal, σ represents an auxiliary variable, represents the estimated value of Γ4, Γ4 represents the system parameters;

[0029] The first-order derivative of the adaptive coupling signal with respect to time is taken, and the first-order derivative function is obtained by the following formula:

[0030]

[0031] in, represents the first-order derivative function,

[0032] The second-order derivative of the first-order derivative function is taken with respect to time, and the second-order derivative function is obtained by the following formula:

[0033]

[0034] in, represents the second-order derivative function,

[0035] According to some embodiments of the present invention, the calculating an error signal between the coupled signal and the target position includes:

[0036] definition is the control target of the bridge crane system, which is to move the trolley displacement x to the target position x d And eliminate the load swing angle θ to 0;

[0037] According to the adaptive coupling signal and the target position, the adaptive error signal e is constructed by the following formula: ξ :

[0038]

[0039] Among them, e ε The error signal representing the displacement, x d -ε represents the adaptive coupling signal ε and the target position x d Make a difference.

[0040] According to some embodiments of the present invention, constructing the time-varying function, and constructing the time-varying sliding mode surface based on the error signal and the time-varying function, includes:

[0041] A first time-varying function is constructed, wherein the formula of the first time-varying function α(t) is as follows:

[0042]

[0043] A second time-varying function is constructed, wherein the formula of the second time-varying function g(t) is as follows:

[0044]

[0045] Among them, c t 、k α and k g represents a positive parameter of a time-varying function;

[0046] Constructing the time-varying sliding mode surface, the time-varying sliding mode surface includes:

[0047]

[0048] Where t represents time, Represents the error signal e ε The first derivative of , β and λ represent the positive parameters of the sliding surface;

[0049] The second time-varying function g(t) satisfies: and g(∞)=0;

[0050] The first-order derivative of the time-varying sliding surface is obtained to obtain the first-order derivative function: in, u represents an auxiliary function.

[0051] According to some embodiments of the present invention, constructing an adaptive time-varying sliding mode controller based on the time-varying sliding mode surface and the estimated value of the parameter includes:

[0052] The adaptive time-varying sliding mode controller is constructed as follows:

[0053]

[0054] Among them, G(θ) represents the auxiliary function, G(θ)=(Γ1+Γ2sin 2 θ);

[0055] Based on the adaptive time-varying sliding mode controller, the first Lyapunov function is constructed as follows:

[0056]

[0057] Where s represents the time-varying sliding surface, and the first derivative of the first Lyapunov function is obtained as follows:

[0058]

[0059] The control law is constructed as follows:

[0060]

[0061] Among them, k represents the sliding surface gain, μ represents the switching term gain, and both k and μ are positive values. represents the estimated value of the system parameter Γ, It is q and vector, The specific form is as follows:

[0062]

[0063] According to some embodiments of the present invention, the adaptive law is constructed as follows:

[0064] Construct the second Lyapunov function as shown below:

[0065]

[0066] in, Denotes the estimated error of Γ, γ = diag[γ1, γ2, γ3, γ4, γ5, γ6] represents a diagonal positive definite gain matrix, and the estimated error is as follows:

[0067]

[0068] The first-order derivative of the estimated error is:

[0069]

[0070] The first Lyapunov function and the second Lyapunov function are added together using the following formula to obtain an addition function:

[0071]

[0072] The first-order derivative of V(t) is obtained, and the expression of the adaptive time-varying sliding mode controller and the control law are substituted into the first-order derivative of V(t):

[0073]

[0074] Based on the sum function, the adaptive law is constructed as follows:

[0075]

[0076] In a second aspect, an embodiment of the present invention further provides a safe and robust control system for smooth startup, the system comprising:

[0077] A data acquisition unit, used to obtain parameters of a target position and a current state of the bridge crane system;

[0078] An estimated value obtaining unit, configured to construct an adaptive law, input the parameter into the adaptive law, and obtain an estimated value of the parameter output by the adaptive law;

[0079] a coupling signal acquisition unit, configured to construct an adaptive coupling signal model, input the parameter and the estimated value of the parameter into the adaptive coupling signal model, and obtain a coupling signal output by the adaptive coupling signal model;

[0080] an error signal calculation unit, configured to calculate an error signal between the coupling signal and the target position;

[0081] A sliding surface construction unit, configured to construct a time-varying function, and to construct a time-varying sliding surface based on the error signal and the time-varying function;

[0082] A controller construction unit, configured to construct an adaptive time-varying sliding mode controller based on the time-varying sliding mode surface and the estimated values ​​of the parameters;

[0083] A driving control unit is used to obtain a driving force through the adaptive time-varying sliding mode controller, and drive the bridge crane system to a target position through the driving force.

[0084] In a third aspect, an embodiment of the present invention provides a safe and robust control device for smooth startup, comprising at least one control processor and a memory for communicating with the at least one control processor; the memory stores instructions that can be executed by the at least one control processor, and the instructions are executed by the at least one control processor to enable the at least one control processor to execute a safe and robust control method for smooth startup as described above.

[0085] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer-executable instructions, and the computer-executable instructions are used to enable a computer to execute the above-mentioned safe and robust control method for smooth startup.

[0086] It can be understood that the beneficial effects of the above-mentioned second to fourth aspects compared with the relevant technologies are the same as the beneficial effects of the above-mentioned first aspect compared with the relevant technologies. Please refer to the relevant description in the above-mentioned first aspect and will not be repeated here. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments with reference to the following drawings, in which:

[0088] Figure 1 This is a flow chart of a safe and robust control method for smooth startup according to an embodiment of the present invention;

[0089] Figure 2 is a schematic diagram of a dynamic model of a bridge crane according to an embodiment of the present invention;

[0090] Figure 3 is a control block diagram of an adaptive time-varying sliding mode controller according to an embodiment of the present invention;

[0091] Figure 4 This is a comparison diagram of displacement test results according to an embodiment of the present invention;

[0092] Figure 5 This is a comparison chart of load swing angle test results according to an embodiment of the present invention;

[0093] Figure 6 This is a comparison chart of control force experimental results according to an embodiment of the present invention;

[0094] Figure 7 This is a comparison chart of speed test results of an embodiment of the present invention;

[0095] Figure 8 is a diagram of experimental results of parameter perturbation of another embodiment of the present invention;

[0096] Figure 9 is a diagram showing experimental results of non-zero initial interference according to another embodiment of the present invention;

[0097] Figure 10 is a diagram showing experimental results of external interference according to another embodiment of the present invention;

[0098] Figure 11 It is a structural diagram of a safe and robust control system for smooth startup according to another embodiment of the present invention. DETAILED DESCRIPTION

[0099] The following describes embodiments of the present invention in detail. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended only to explain the present invention and are not to be construed as limiting the present invention.

[0100] In the description of the present invention, if there is a description of first, second, etc., it is only for the purpose of distinguishing technical features, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features or implicitly indicating the order of the indicated technical features.

[0101] In the description of the present invention, it should be understood that descriptions involving orientation, such as the orientation or positional relationship indicated by up, down, etc., are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0102] In the description of the present invention, it should be noted that, unless otherwise clearly defined, terms such as setting, installing, and connecting should be understood in a broad sense, and technicians in the relevant technical field can reasonably determine the specific meanings of the above terms in the present invention based on the specific content of the technical solution.

[0103] Bridge cranes are a type of multi-degree-of-freedom underactuated mechanical system with widespread engineering applications. Studying their control issues has both theoretical and practical value. In terms of theoretical research, bridge crane systems share common characteristics with underactuated mechanical systems, such as a positive definite symmetric inertia matrix and the presence of dynamic nonholonomic constraints. Therefore, studying bridge crane control issues can contribute to the development of control theory for underactuated mechanical systems. With the development of the national economy, various types of bridge cranes, such as those in workshops, docks, and foundry cranes in the metallurgical industry, have become increasingly important, placing increasing demands on crane control. Load swing can make it difficult for the crane system to lower the load at the target location and can cause collisions between the load and other equipment during transportation, resulting in unnecessary losses and reduced efficiency. Anti-sway control is particularly important when loading liquids. Therefore, it is crucial to ensure that the load is lifted from its initial position to the target location within a short period of time, and that load swing is minimized throughout the entire transport process and upon reaching the target location. Furthermore, wind and other uncertainties (such as unknown friction coefficients, trolley mass, load mass, and rope length) can affect crane performance. Failure to properly control load swing not only reduces work efficiency but can also damage the transported goods or surrounding objects. According to research, each load fixation consumes at least 30% more transport time. To date, due to the lack of automated control methods suitable for industrial sites, most industrial cranes are still manually operated by skilled workers. The trolley's positioning performance and the ability to suppress load swing rely entirely on the operator's experience.

[0104] While existing bridge crane controllers have made significant improvements in addressing external interference, there is still room for improvement in addressing issues such as bridge crane system parameter perturbations and unmodeled dynamics. For example, existing methods do not consider the adaptive coupling relationship between load mass and rope length, which may cause the control method to be sensitive to changes in rope length. Some existing technologies can only reduce the initial driving force and cannot ensure that the force increases slowly from zero, making it impossible to smoothly start and operate the bridge crane.

[0105] To solve the above problems, the present invention constructs an adaptive coupling signal model, inputs the parameters and the estimated values ​​of the parameters into the adaptive coupling signal model, and obtains a coupling signal output by the adaptive coupling signal model; the coupling gain can be dynamically adjusted to further improve the transient performance of the system; the present invention constructs a time-varying sliding surface based on the error signal and the time-varying function by constructing a time-varying function; based on the time-varying sliding surface and the estimated values ​​of the parameters, an adaptive time-varying sliding mode controller is constructed; based on the time-varying sliding surface, an adaptive time-varying sliding mode controller is used to realize smooth startup control and operation of the crane system, and the implementation method is simpler, does not require a reference trajectory to be planned in advance, and is easier to obtain good control effects in engineering applications. The coupling relationship of multiple system parameters can be self-adjusted, so that the present invention not only has better robustness to parameter perturbations, friction disturbances and unmodeled dynamics, but also ensures global robustness.

[0106] Reference Figure 1 , an embodiment of the present invention provides a safe and robust control method for smooth startup, the method comprising:

[0107] Step S100: Acquire parameters of the target position and the current state of the bridge crane system.

[0108] Specifically, refer to Figure 2 Before obtaining the parameters of the target position and the current state of the bridge crane system, the dynamic equation is constructed. The dynamic equation includes:

[0109]

[0110]

[0111] Among them, m t Indicates the mass of the trolley, m p represents the load mass, l represents the length of the suspension rope, θ represents the load swing angle, x represents the displacement of the trolley, F represents the driving force of the trolley in the horizontal direction, and f represents the friction between the trolley and the track. f r ,δ,k rx represents the friction parameter, and g represents the acceleration due to gravity.

[0112] Analyze the above formula and write it into the following matrix form:

[0113]

[0114] Where M(q)∈R 2×2 represents the positive definite mass inertia matrix, represents the Coriolis force matrix, G(q)∈R 2×1 represents the gravity vector, F∈R 2×1represents the driving force vector, g = [x, θ] T is the state vector, and these matrices / vectors are defined as follows:

[0115]

[0116]

[0117] For the underactuated bridge crane dynamics system, the following properties hold true:

[0118] Property 1: M(q) is a symmetric positive definite matrix;

[0119] Property 2: is an antisymmetric matrix.

[0120] The assumptions of the bridge crane system are described as follows:

[0121] Assumption 1: During operation, the load swing angle θ of the bridge crane is always maintained between -π / 2 and π / 2, that is:

[0122]

[0123] In this embodiment, the crane will not normally exceed this swing angle range during actual operation.

[0124] Since the dynamic equation cannot be completely linearized, the linearization formula is as follows:

[0125]

[0126] Will Substitution The following formula is obtained from the formula:

[0127]

[0128] Among them, m t 、m p 、m p g、m p l、f r and k rx Represents the system parameters, which can be written as vectors:

[0129] Γ=[m t m p m p gm p lf r k rx ] T =[Γ1 Γ2 Γ3 Γ4 Γ5 Γ6] T .

[0130] Based on the above steps, refer to Figure 3 , get the target position x in this embodiment d (i.e. the target position to which the crane needs to move from its current position), and obtain the parameters of the current state of the bridge crane system (i.e. the trolley displacement x and the load swing angle θ at the current moment).

[0131] Step S200: construct an adaptive law, input parameters into the adaptive law, and obtain estimated values ​​of the parameters output by the adaptive law.

[0132] Specifically, the adaptive law is constructed as follows:

[0133] Construct the second Lyapunov function as shown below:

[0134]

[0135] in, represents the estimated error of Γ, γ = diag[γ1,γ2,γ3,γ4,γ5,γ6] represents a diagonal positive definite gain matrix, and the estimated error is as follows:

[0136]

[0137] The first-order derivative of the estimated error is:

[0138]

[0139] The summation function is obtained by adding the first Lyapunov function to the second Lyapunov function using the following formula:

[0140]

[0141] Calculate the first-order derivative of V(t), and substitute the expression and control law of the adaptive time-varying sliding mode controller into the first-order derivative of V(t):

[0142]

[0143] Based on the addition function, the adaptive law is constructed as follows:

[0144]

[0145] In this embodiment, referring to Figure 3 , input the current trolley displacement x and load swing angle θ to the adaptive law (i.e. Figure 3 In the adaptive mechanism in the adaptive law, the estimated value of the system parameters output by the adaptive law can be obtained.

[0146] Step S300: construct an adaptive coupling signal model, input parameters and estimated values ​​of the parameters into the adaptive coupling signal model, and obtain a coupling signal output by the adaptive coupling signal model.

[0147] Specifically, in order to improve the control performance of the bridge crane system, the coupling between the trolley displacement x and the load swing angle θ is enhanced, and an adaptive coupling signal model is designed. The adaptive coupling signal model includes:

[0148] ε=x-σ

[0149] Where ε represents the adaptive coupling signal, σ represents an auxiliary variable, represents the estimated value of Γ4, and Γ4 represents the system parameters.

[0150] By calculating the current trolley displacement x, load swing angle θ and the estimated value of the parameters By inputting it into the adaptive coupling signal model, the coupling signal ε output by the adaptive coupling signal model can be obtained.

[0151] In order to facilitate the subsequent construction of the adaptive time-varying sliding mode controller, the first-order derivative of the adaptive coupling signal with respect to time is taken, and the first-order derivative function is obtained by the following formula:

[0152]

[0153] in, represents the first-order derivative function,

[0154] The second-order derivative of the first-order derivative function with respect to time is obtained by the following formula:

[0155]

[0156] in, represents the second-order derivative function,

[0157] Step S400: Calculate the error signal between the coupling signal and the target position.

[0158] Specific, definition is the control target of the bridge crane system, which is to move the trolley displacement x to the target position x d And eliminate the load swing angle θ to 0;

[0159] According to the adaptive coupling signal and the target position, the adaptive error signal e is constructed by the following formula ξ :

[0160]

[0161] Among them, e ε The error signal representing the displacement, x d -ε represents the adaptive coupling signal ε and the target position x d Make a difference.

[0162] Step S500: construct a time-varying function, and construct a time-varying sliding mode surface based on the error signal and the time-varying function.

[0163] Specifically, the first time-varying function is constructed. The formula of the first time-varying function α(t) is as follows:

[0164]

[0165] Construct the second time-varying function. The formula of the second time-varying function g(t) is as follows:

[0166]

[0167] Among them, c t 、k α and k g represents a positive parameter of a time-varying function;

[0168] Construct a time-varying sliding surface, which includes:

[0169]

[0170] Where t represents time, Represents the error signal e ε The first derivative of , β and λ represent the positive parameters of the sliding surface;

[0171] The second time-varying function g(t) satisfies: and g(∞)=0;

[0172] In order to facilitate the subsequent construction of the adaptive time-varying sliding mode controller, the time-varying sliding mode surface is first-order derived to obtain the first-order derivative function: in, u represents an auxiliary function.

[0173] Step S600: construct an adaptive time-varying sliding mode controller based on the time-varying sliding mode surface and the estimated values ​​of the parameters.

[0174] Specifically, the adaptive time-varying sliding mode controller is constructed as follows:

[0175]

[0176] Where G(θ) represents the auxiliary function, G(θ) = (Γ1+Γ2sin2θ);

[0177] The first Lyapunov function is constructed based on the adaptive time-varying sliding mode controller as shown below:

[0178]

[0179] Where s represents the time-varying sliding surface, and the first derivative of the first Lyapunov function is obtained as follows:

[0180]

[0181] In order to make the adaptive time-varying sliding mode controller satisfy the Lyapunov asymptotic stability, this embodiment constructs the control law in the following way:

[0182]

[0183] Among them, k represents the sliding surface gain, μ represents the switching term gain, and both k and μ are positive values. represents the estimated value of the system parameter Γ, It is q and vector, The specific form is as follows:

[0184]

[0185] Step S700: Acquire driving force through an adaptive time-varying sliding mode controller, and drive the bridge crane system to a target position through the driving force.

[0186] Specifically, the driving force F is obtained by the adaptive time-varying sliding mode controller, and the bridge crane system is driven by the driving force F to reach the target position x d .

[0187] This embodiment constructs an adaptive coupling signal model, inputs parameters and parameter estimates into the adaptive coupling signal model, and obtains a coupling signal output by the adaptive coupling signal model; the coupling gain can be dynamically adjusted to further improve the transient performance of the system; this embodiment constructs a time-varying sliding surface based on the error signal and the time-varying function by constructing a time-varying function; based on the time-varying sliding surface and the parameter estimates, an adaptive time-varying sliding mode controller is constructed; based on the time-varying sliding surface, an adaptive time-varying sliding mode controller is used to achieve smooth startup control and operation of the crane system. The implementation method is simpler and does not require pre-planning of a reference trajectory. It is easier to obtain good control effects in engineering applications. The coupling relationship of multiple system parameters can be self-adjusted, so that this embodiment not only has better robustness to parameter perturbations, friction disturbances and unmodeled dynamics, but also ensures global robustness.

[0188] For better explanation, this embodiment carries out the following theoretical analysis and experimental analysis:

[0189] Theorem 1: For a bridge crane system, a time-varying sliding surface is designed. Sliding mode control can be divided into two phases: the first phase is the arrival phase, when the system reaches the sliding surface with s = 0 from the initial state; the second phase is the sliding phase (sliding phase), when the system slides on the sliding surface with s = 0 to the equilibrium point. Sliding mode control is not robust during the arrival phase. Therefore, if the system's initial state is on the sliding surface with s = 0, then the sliding mode control becomes globally robust.

[0190] The time-varying sliding surface designed in this embodiment eliminates the arrival phase of the sliding surface, ensuring the global robustness of the sliding mode control. It is also a necessary condition for smooth startup, as shown in the following equation:

[0191] s(0)=0.

[0192] To prove Theorem 1, we can get the following reasoning:

[0193]

[0194] When t=0, e0=1, so:

[0195] s(0)=0.

[0196] Therefore, Theorem 1 is proved.

[0197] Theorem 2: For the bridge crane system, under the adaptive time-varying sliding mode controller constructed in this embodiment, the system will converge to an equilibrium state, that is:

[0198]

[0199] To prove Theorem 2, this embodiment constructs the Lyapunov function, namely: Next, we take the first-order derivative with respect to time, and we can get it by the following reasoning:

[0200]

[0201] because So there is Therefore, three situations can be considered:

[0202] Case 1: When s>0, then therefore

[0203] Case 2: When s=0, then therefore

[0204] Case 3: When s<0, then therefore

[0205] Therefore, Theorem 2 is proved.

[0206] The rationality of this embodiment is analyzed based on Theorem 1 and Theorem 2 above, and the advantages of this embodiment over the prior art are analyzed through the following experiments:

[0207] In this embodiment, two sets of numerical simulation experiments are carried out on MATLAB / Simulink to verify the superior performance of the adaptive time-varying sliding mode controller.

[0208] In the first set of experiments, the adaptive time-varying sliding mode controller of this embodiment is compared with the LQR controller and the global sliding mode controller (GSMC). In the second set of experiments, the robustness of the system to parameter changes and external disturbances is verified.

[0209] The system parameters and target position of the adaptive time-varying sliding mode controller in this experiment are set as follows:

[0210] M=3.139kg, m=2kg, l=0.75m, g=9.8m / s2, f r =3,δ=0.01,k rx =0.25,x d =0.5m;

[0211] And the control parameters in the control law are set as follows:

[0212] k α =0.61, k g =0.45, c t =6, λ=5.5, β=0.9, k=18.5, μ=15.6, n=2.8, γ1=4.95, γ2=3.34, γ3=40, γ4=40, γ5=6.43, γ6=5.9.

[0213] Will The initial value of is set to zero, that is:

[0214]

[0215] (1) In the first set of experiments, a performance comparison experiment simulation was conducted.

[0216] This embodiment verifies the control performance of the adaptive time-varying sliding mode controller of this embodiment by comparing it with the prior art LQR controller and global sliding mode controller. To ensure the integrity of the document, the expressions of the LQR controller and global sliding mode controller are as follows:

[0217] LQR Controller:

[0218]

[0219] The control parameters of the LQR controller are set as: k1 = 19, k2 = 11.2, k3 = 200, k4 = 0.009.

[0220] Global sliding mode controller:

[0221]

[0222] The control parameters of the global sliding mode controller are set as follows: α = 1.13, β = 1.7, k = 0.05, w = 1.5524, k g =1.8.

[0223] Performance comparison experiment simulation results are as follows Figures 4 to 7 As shown in the figure, ATVSMC represents the adaptive time-varying sliding mode controller in this embodiment. Figures 4 to 7 As can be seen from the graph, when the three controllers achieve similar times for the trolley to reach its target position, the adaptive time-varying sliding mode controller of this embodiment achieves a smaller load swing than the LQR and GSMC controllers. For the adaptive time-varying sliding mode controller, there is almost no residual load swing when the crane stops moving, while for the LQR controller, there is a larger residual swing. Furthermore, the driving force of the adaptive time-varying sliding mode controller of this embodiment starts from zero and gradually increases, ensuring a smooth start-up of the crane. The overall driving force of the adaptive time-varying sliding mode controller of this embodiment is lower than that of the LQR and GSMC controllers.

[0224] (2) In the first set of experiments, robust experimental simulations were performed.

[0225] To verify the robustness of the adaptive time-varying sliding mode controller of this embodiment to changes in friction parameters, rope length, mass, and external disturbances, the following three simulations are performed (the parameters of the adaptive time-varying sliding mode controller remain unchanged):

[0226] Case 1: Parameter perturbation. The friction parameter is modified to f r =3.5,δ=0.01,k rx =3.25; the load mass is changed to 3kg and the rope length is changed to l=1m.

[0227] Case 2: Non-zero initial disturbance: An initial swing angle disturbance (about 2°) is applied to the load.

[0228] Case 3: External disturbance: A 2-degree pulse disturbance is added to the load between 8 and 8.5 seconds, and a 2-degree sinusoidal disturbance is added between 15 and 16 seconds.

[0229] Robust experimental simulation results are as follows Figures 8 to 10 As shown. Figure 8It can be clearly seen that even with some parameter uncertainties, the adaptive time-varying sliding mode controller of this embodiment can still successfully position the load accurately and eliminate load swing. Figure 9 It can be concluded that the adaptive time-varying sliding mode controller of this embodiment is insensitive to the initial swing disturbance. Figure 10 The crane reacts quickly to the sudden external disturbance shown, effectively damping and ultimately eliminating the resulting load swing within approximately 5 seconds. Therefore, the adaptive time-varying sliding mode controller of this embodiment performs well in all three cases, demonstrating its robustness.

[0230] Reference Figure 11 The embodiment of the present invention further provides a safe and robust control system for smooth startup, the system comprising:

[0231] The data acquisition unit 100 is used to obtain parameters of the target position and the current state of the bridge crane system;

[0232] The estimated value obtaining unit 200 is used to construct an adaptive law, input parameters into the adaptive law, and obtain an estimated value of the parameter output by the adaptive law;

[0233] The coupling signal acquisition unit 300 is used to construct an adaptive coupling signal model, input parameters and estimated values ​​of the parameters into the adaptive coupling signal model, and obtain a coupling signal output by the adaptive coupling signal model;

[0234] an error signal calculation unit 400, configured to calculate an error signal between the coupled signal and the target position;

[0235] A sliding surface construction unit 500 is used to construct a time-varying function, and to construct a time-varying sliding surface based on the error signal and the time-varying function;

[0236] A controller construction unit 600 is used to construct an adaptive time-varying sliding mode controller based on the time-varying sliding mode surface and the estimated values ​​of the parameters;

[0237] The driving control unit 700 is used to obtain the control force through an adaptive time-varying sliding mode controller, and drive the bridge crane system to reach the target position through the control force.

[0238] It should be noted that since the smooth start safety robust control system in this embodiment and the above-mentioned smooth start safety robust control method are based on the same inventive concept, the corresponding contents in the method embodiment are also applicable to the system embodiment and will not be described in detail here.

[0239] An embodiment of the present invention further provides a safe and robust control device for smooth startup, comprising: at least one control processor and a memory for communicating with the at least one control processor.

[0240] The memory, as a non-transient computer-readable storage medium, can be used to store non-transient software programs and non-transient computer executable programs. In addition, the memory may include a high-speed random access memory and may also include a non-transient memory, such as at least one disk storage device, a flash memory device, or other non-transient solid-state storage device. In some embodiments, the memory may optionally include a memory remotely arranged relative to the processor, and these remote memories may be connected to the processor via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0241] The non-transient software program and instructions required to implement the above embodiment of a safe and robust control method for smooth startup are stored in the memory. When executed by the processor, the above embodiment of a safe and robust control method for smooth startup is executed, for example, the above described Figure 1 Method steps S100 to S700.

[0242] The system embodiment described above is merely illustrative, wherein the units described as separate components may or may not be physically separate, i.e., they may be located in one place or distributed across multiple network units. Some or all of these units may be selected based on actual needs to achieve the objectives of this embodiment.

[0243] The embodiment of the present invention further provides a computer-readable storage medium, which stores computer-executable instructions. The computer-executable instructions are executed by one or more control processors, which can enable the one or more control processors to execute a safe and robust control method for smooth startup in the above method embodiment, for example, to execute the above described Figure 1 The functions of method steps S100 to S700 in the embodiment of the present invention are as follows:

[0244] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a general hardware platform. Those skilled in the art can understand that all or part of the processes in the above embodiment methods can be completed by instructing the relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above method. Among them, the storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM), etc.

[0245] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the above embodiments. Various changes can be made within the scope of knowledge possessed by ordinary technicians in the relevant technical field without departing from the scope of the present invention.

Claims

1. A safe and robust control method for smooth startup, characterized in that: The method comprises: Get the target position and the current status of the bridge crane system parameters, including: A kinetic equation is constructed, wherein the kinetic equation includes: in, Indicates the mass of the trolley, Indicates the load mass, Indicates the length of the lifting rope. represents the load swing angle, represents the trolley displacement, Indicates the driving force of the trolley in the horizontal direction, represents the friction between the trolley and the track, , 、 、 represents the friction parameter, represents the acceleration due to gravity; Linearize the following formula: Will Substitution The following formula is obtained from the formula: in, 、 、 、 、 and Represents the system parameters, which are written in vector form as follows: ； constructing an adaptive law, inputting the parameter into the adaptive law, and obtaining an estimated value of the parameter output by the adaptive law; An adaptive coupling signal model is constructed, and the parameters and the estimated values ​​of the parameters are input into the adaptive coupling signal model to obtain a coupling signal output by the adaptive coupling signal model, wherein the adaptive coupling signal model includes: in, represents the adaptive coupling signal, , represents auxiliary variables, express The estimated value of Indicates system parameters; The first-order derivative of the adaptive coupling signal with respect to time is taken, and the first-order derivative function is obtained by the following formula: in, represents the first-order derivative function, ; The second-order derivative of the first-order derivative function is taken with respect to time, and the second-order derivative function is obtained by the following formula: in, represents the second-order derivative function, ; Calculating an error signal between the coupled signal and the target position, comprising: definition is the control target of the bridge crane system, and the control target is to move the trolley Move to the target location and the load swing angle Eliminate the swing to 0; According to the adaptive coupling signal and the target position, an adaptive error signal is constructed by the following formula: : in, The error signal representing the displacement, , Represents the adaptive coupling signal With the target location to make a mistake; A time-varying function is constructed, and a time-varying sliding mode surface is constructed based on the error signal and the time-varying function, wherein: Construct a first time-varying function, wherein the first time-varying function The formula is as follows: ； Construct a second time-varying function, the second time-varying function The formula is as follows: ； in, 、 and represents a positive parameter of a time-varying function; Constructing the time-varying sliding mode surface, the time-varying sliding mode surface includes: in, Indicates time, Indicates the error signal The first derivative of 、 represents the positive parameter of the sliding surface; The second time-varying function satisfy: and ; The first-order derivative of the time-varying sliding surface is obtained to obtain the first-order derivative function: ; in, , u Represents auxiliary functions; constructing an adaptive time-varying sliding mode controller based on the time-varying sliding mode surface and the estimated values ​​of the parameters; A driving force is obtained by the adaptive time-varying sliding mode controller, and the bridge crane system is driven by the driving force to reach a target position.

2. The safe and robust control method for smooth startup according to claim 1, characterized in that: The step of constructing an adaptive time-varying sliding mode controller based on the time-varying sliding mode surface and the estimated values ​​of the parameters includes: The adaptive time-varying sliding mode controller is constructed as follows: in, Represents an auxiliary function, ; Based on the adaptive time-varying sliding mode controller, the first Lyapunov function is constructed as follows: in, Denotes the time-varying sliding surface, and the first derivative of the first Lyapunov function is obtained as follows: The control law is constructed as follows: in, represents the sliding surface gain, represents the switching term gain, and are all positive values, Indicates the system parameters The estimated value of yes and vector, The specific form is as follows: 。 3. The safe and robust control method for smooth startup according to claim 2, characterized in that: The adaptive law is constructed as follows: Construct the second Lyapunov function as shown below: in, express The estimated error, Representing a diagonal positive definite gain matrix, the estimated error is as follows: The first-order derivative of the estimated error is: The first Lyapunov function and the second Lyapunov function are added together using the following formula to obtain an addition function: right Obtain the first-order derivative and substitute the expression of the adaptive time-varying sliding mode controller and the control law into the The first derivative of is: Based on the sum function, the adaptive law is constructed as follows: 。 4. A safe and robust control system with smooth start, characterized in that: The system comprises: The data acquisition unit is used to obtain parameters of the target position and the current state of the bridge crane system, including: A kinetic equation is constructed, wherein the kinetic equation includes: in, Indicates the mass of the trolley, Indicates the load mass, Indicates the length of the lifting rope. represents the load swing angle, represents the trolley displacement, Indicates the driving force of the trolley in the horizontal direction, represents the friction between the trolley and the track, , 、 、 represents the friction parameter, represents the acceleration due to gravity; Linearize the following formula: Will Substitution The following formula is obtained from the formula: in, 、 、 、 、 and Represents the system parameters, which are written in vector form as follows: ； An estimated value obtaining unit, configured to construct an adaptive law, input the parameter into the adaptive law, and obtain an estimated value of the parameter output by the adaptive law; a coupling signal acquisition unit, configured to construct an adaptive coupling signal model, input the parameter and the estimated value of the parameter into the adaptive coupling signal model, and obtain a coupling signal output by the adaptive coupling signal model, wherein the adaptive coupling signal model includes: in, represents the adaptive coupling signal, , represents auxiliary variables, express The estimated value of Indicates system parameters; The first-order derivative of the adaptive coupling signal with respect to time is taken, and the first-order derivative function is obtained by the following formula: in, represents the first-order derivative function, ; The second-order derivative of the first-order derivative function is taken with respect to time, and the second-order derivative function is obtained by the following formula: in, represents the second-order derivative function, ; an error signal calculation unit, configured to calculate an error signal between the coupling signal and the target position, comprising: definition is the control target of the bridge crane system, and the control target is to move the trolley Move to the target location and the load swing angle Eliminate the swing to 0; According to the adaptive coupling signal and the target position, an adaptive error signal is constructed by the following formula: : in, The error signal representing the displacement, , Represents the adaptive coupling signal With the target location to make a mistake; A sliding surface construction unit is configured to construct a time-varying function, and to construct a time-varying sliding surface based on the error signal and the time-varying function, wherein: Construct a first time-varying function, wherein the first time-varying function The formula is as follows: ； Construct a second time-varying function, the second time-varying function The formula is as follows: ； in, 、 and represents a positive parameter of a time-varying function; Constructing the time-varying sliding mode surface, the time-varying sliding mode surface includes: in, Indicates time, Indicates the error signal The first derivative of 、 represents the positive parameter of the sliding surface; The second time-varying function satisfy: and ; The first-order derivative of the time-varying sliding surface is obtained to obtain the first-order derivative function: ; in, , u Represents auxiliary functions; A controller construction unit, configured to construct an adaptive time-varying sliding mode controller based on the time-varying sliding mode surface and the estimated values ​​of the parameters; A driving control unit is used to obtain a driving force through the adaptive time-varying sliding mode controller, and drive the bridge crane system to a target position through the driving force.

5. A safe and robust control device for smooth startup, characterized in that: It includes at least one control processor and a memory for communicating with the at least one control processor; the memory stores instructions that can be executed by the at least one control processor, and the instructions are executed by the at least one control processor to enable the at least one control processor to execute the safe and robust control method for smooth startup as described in any one of claims 1 to 3.

6. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer-executable instructions, and the computer-executable instructions are used to enable a computer to execute the safe and robust control method for smooth startup according to any one of claims 1 to 3.

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