An actuator parameter unknown axial conveyor belt adaptive constraint control method

Abstract

The application provides an axial conveyor belt adaptive constraint control method with unknown actuator parameters, and relates to the technical field of conveyor belt control.The application adopts state feedback and an adaptive control method to design a controller.Firstly, a dynamic model of an axial conveyor belt system is established based on physical structure characteristics and an extended Hamilton principle, and then a mathematical model of boundary vibration constraint is established.Then, a parameter adaptive law and a controller are designed in combination with a logarithmic type barrier Lyapunov function and an energy function of the system to compensate for the influence of actuator parameter uncertainty and achieve the vibration suppression purpose of the system.Finally, the system is analyzed for stability according to Lyapunov stability theory, and it is proved that all signals of the closed-loop system are bounded.Simulation experiments are conducted by using MATLAB, and the simulation experiment results show that the adaptive boundary controller based on the barrier Lyapunov function designed has good control effect.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of conveyor belt control, and in particular to an axial conveyor belt adaptive constraint control method with unknown actuator parameters. BACKGROUND

[0002] An axial conveyor belt system is a highly efficient, reliable, flexible and suitable for various logistics scenarios automated transportation equipment system, not only can large-scale automation logistics transportation process, reduce human operation, but also can improve logistics efficiency and accuracy. In the logistics warehouse, the axial conveyor belt system can be used for the conveying and sorting of goods in the warehouse, speeding up the logistics process and improving transportation efficiency; in the industrial production line, the axial conveyor belt can transport raw materials, semi-finished products and finished products through the production line to different work areas, improve production efficiency, and reduce manual operation; in the sea shipping container, the axial conveyor belt can be used in the container terminal loading and unloading system, which can move external goods from the terminal to the ship or warehouse. In short, the axial conveyor belt system has been widely used in various logistics and production fields, making outstanding contributions to improving efficiency, reducing cost and improving productivity for enterprises. However, most of the existing research results on the axial conveyor belt system are to model its dynamics as ordinary differential equations only related to time variables and design control schemes based on this. In fact, due to the flexible structure of the conveyor belt system material, the dynamics of the system during transportation operation is not only related to the time variable but also related to the spatial position change variable. Therefore, many scholars have turned to study the axial conveyor belt system modeled by partial differential equations to achieve more accurate control effect.

[0003] With the development of various control technologies, the stability research of the axial conveyor belt system has made many important achievements. It is worth noting that most of the results are obtained under ideal control input conditions. When the control input meets the theoretical requirements, many existing control methods can guarantee the performance of the system. However, in practical applications, due to the influence of friction and external disturbances, additional vibrations and slow changes in actuator parameters often occur, where additional vibrations not only produce a lot of noise but also endanger the safe operation of the system, and the actuator parameter is a key factor in designing the control scheme. Therefore, it is necessary to design a suitable control scheme to suppress additional vibrations and offset the impact of unknown actuator parameters. Especially when the axial conveyor belt is used in complex operating environments such as large airports and coal mines, reasonable handling of the additional vibrations of the system not only can reduce noise and optimize control, but also can improve the robustness of the system.

[0004] In addition, in order to keep the transient performance of the system output, such as boundary vibration and speed, within the constraint limit, a corresponding constant constraint model is introduced, so that the system state not only runs within the constraint limit, but also ensures the boundedness of the closed-loop system signal. Further, in order to meet the actual engineering requirements, the system is also considered to be subjected to unknown distributed disturbances. SUMMARY

[0005] In view of the deficiencies of the prior art, the present application provides an actuator parameter unknown axial conveyor belt adaptive constraint control method. For an axial conveyor belt system with unknown actuator parameters and boundary vibration constraints, an adaptive control scheme is designed based on state feedback, which not only fits the actual application, but also effectively improves the steering stability and operation safety of the axial conveyor belt system.

[0006] An actuator parameter unknown axial conveyor belt adaptive constraint control method, comprising the following steps:

[0007] Step 1: According to the physical structure of the axial conveyor belt system, combined with the Hamilton principle, the following dynamic equation is established:

[0008] ρy tt (h,t)+(ρa+c)y h (h,t)+2ρvy ht (h,t)

[0009] +(ρv 2 -T)y hh (h,t)+c s y t (h,t)-f(h,t)=0 (1)

[0010]

[0011] In the formula, y(h,t) is the additional vibration of the system; S is the controllable region of the system; ρ is the mass per unit length; c s is the viscous damping coefficient of the system; T is the tension of the system; v is the running speed of the system; a represents acceleration; u(t) is the control input; S' is the uncontrollable region of the system, and its influence on the system is regarded as boundary disturbance d(t); f(h,t) is the distributed disturbance received by the system; M is the mass of the actuator; c is the damping coefficient of the actuator (the present application studies the case where the actuator parameters M and c are unknown). In addition, since the power provided by the actuator is limited, there are normal numbers q1, q2, and q3, satisfying |v|≤q1, |a|≤q2, |f(h,t)|≤q3.

[0012] Define auxiliary signals z1 and z2 as

[0013]

[0014] In the formula, k1>0 is a constant.

[0015] Step 2: Establish a logarithmic boundary vibration constraint model:

[0016]

[0017] where l0is the constraint bound of the boundary vibration, and the initial state of the auxiliary signal z1satisfies z1(0) < l0.

[0018] Step 3: Design the controller based on the boundary state information of the system;

[0019] Step 3.1: Design the controller: select the Lyapunov function as follows:

[0020] V(t) = V a (t) + V b (t) + V c (t) (5)

[0021] where

[0022]

[0023]

[0024]

[0025] In the formula, γ, λ > 0 are design parameters.

[0026] Taking the time t derivative of V(t), we get

[0027] V t (t) = V at (t) + V bt (t) + V ct (t) (9)

[0028] where

[0029]

[0030]

[0031]

[0032] Combining formula (2) and formula (3), we get

[0033]

[0034] Substituting formula (10), formula (11) and formula (13) into formula (9), we get

[0035]

[0036] The control input u(t) is designed as:

[0037]

[0038] where k3>0 is a constant, and are the estimates of the actuator mass M and damping coefficient c, respectively. Substituting equation (15) into equation (14) gives

[0039]

[0040] Step 3.2: Adaptive law selection and stability verification for the axial conveyor system:

[0041] According to the actuator parameter estimation error, the following Lyapunov function is further selected:

[0042] V0(t) = V(t) + V d (t) (17)

[0043] where

[0044]

[0045] In the formula,

[0046] Taking the time derivative of V0(t) gives

[0047] V 0t (t) = V t (t) + V dt (t) (19)

[0048] where

[0049]

[0050] The adaptive laws of the design parameters and are respectively:

[0051]

[0052]

[0053] In the formula, k4, k5>0 are constants.

[0054] Substituting equations (16), (21) and (22) into equation (19) gives

[0055]

[0056] In the formula, k6, k7 and k8>0 are constants.

[0057] The parameters γ, λ and k iwhere i = 1, …, 8, satisfy the following conditions

[0058]

[0059] Further, get

[0060]

[0061] In the formula:

[0062]

[0063]

[0064]

[0065]

[0066] According to Lyapunov criterion, from formula (25), the axial conveyor belt system is stable.

[0067] Step 4: Adjust the parameters of the control input and the adaptive law to achieve the final control goal:

[0068] By adjusting the controller and adaptive law parameters, the axial conveyor belt system can still achieve vibration suppression effect under unknown actuator parameters.

[0069] The beneficial effects produced by the above technical solutions are:

[0070] The application provides an axial conveyor belt adaptive constraint control method with unknown actuator parameters. The application combines the ideas of parameter adaptive control and output state constraint control, improves the robustness and control accuracy of the axial conveyor belt system, further improves the steady-state performance and transient performance of the axial conveyor belt system, and enhances the steering stability of the conveyor belt and improves the safety of its production operation. The control method of the application first analyzes the force of the axial conveyor belt system, establishes its dynamic equation, and then defines an auxiliary signal to represent the output constraint state of the system. In addition, a logarithmic function model is used in the application to constrain the boundary vibration of the system. The controller and adaptive law designed in the application have certain reference significance for the controller design of other axial conveyor belt systems and the vibration suppression problem of the conveyor belt system under actuator parameter uncertainty and external disturbance.

[0071] The application applies the ideas of parameter adaptive control and output state constraint control to the controller design of the axial conveyor belt system, improves the control performance of the system. In addition, compared with the control scheme assuming that the actuator parameters are known in the past research, the application has wider practical application value. The proposed control algorithm ensures the operation safety and steering stability of the axial conveyor belt. Attached Figure Description

[0072] Figure 1 This is a flowchart of the axial conveyor belt adaptive constraint control method in an embodiment of the present invention;

[0073] Figure 2 This is a three-dimensional schematic diagram of the additional vibration of the system within 10 seconds in an embodiment of the present invention;

[0074] Figure 3 This refers to the vibration change at the system boundary within 10 seconds in this embodiment of the invention.

[0075] Figure 4 This is the trajectory of the control input u(t) within 10 seconds in this embodiment of the invention;

[0076] Figure 5 This is the response curve of the actuator parameter adaptive law within 10 seconds in an embodiment of the present invention. Detailed Implementation

[0077] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0078] An adaptive constraint control method for axial conveyor belts with unknown actuator parameters, such as Figure 1 As shown, it includes the following steps:

[0079] Step 1: Based on the physical structure of the axial conveyor belt system and Hamilton's principle, the following dynamic equations are established:

[0080] ρy tt (h,t)+(ρa+c)y h (h,t)+2ρvy ht (h,t)

[0081] +(ρv 2 -T)y hh (h,t)+c s y t (h,t)-f(h,t)=0 (26)

[0082]

[0083] In the formula, y(h,t) is the additional vibration of the system; S is the controllable region of the system; ρ is the mass per unit length; c sis the viscous damping coefficient of the system; T is the tension of the system; v is the running speed of the system; a represents acceleration; u(t) is the control input; S' is the uncontrollable region of the system, and its influence on the system is regarded as a boundary disturbance d(t); f(h, t) is the distributed bounded disturbance suffered by the system; M is the mass of the actuator; c is the damping coefficient of the actuator (in the present application, the cases where the parameters M and c of the actuator are unknown are studied). In addition, since the power provided by the actuator is limited, there exist positive numbers q1, q2, and q3, satisfying |v|≤q1, |a|≤q2, |f(h, t)|≤q3. Figure 2 is a three-dimensional variation diagram of the extra vibration of the system within 10 seconds in the embodiment of the present application; wherein the horizontal axis represents position, the vertical axis represents time, and the vertical axis represents extra vibration;

[0084] The auxiliary signals z1 and z2 are defined as

[0085]

[0086] wherein k1>0 is a constant.

[0087] Step 2: Establish a logarithmic boundary vibration constraint model:

[0088]

[0089] wherein l0 is the constraint boundary of the boundary vibration, and the initial state of the auxiliary signal z1 satisfies z1(0)<l0.

[0090] Figure 3 is the vibration variation of the system at the boundary within 10 seconds in the embodiment of the present application; wherein the horizontal axis represents time, and the vertical axis represents vibration. The dotted line and the dashed line represent the constraint boundary, and the solid line represents the actual boundary vibration variation curve;

[0091] Step 3: Design a controller based on the boundary state information of the system;

[0092] Step 3.1: Design a controller: select a Lyapunov function of the following form:

[0093] V(t)=V a (t)+V b (t)+V c (t) (30)

[0094] wherein

[0095]

[0096]

[0097]

[0098] where γ, λ > 0 are design parameters.

[0099] Taking the derivative of V(t) with respect to time t, we have

[0100] V t (t) = V at (t) + V bt (t) + V ct (t) (34)

[0101] where

[0102]

[0103]

[0104]

[0105] Combining equation (2) and equation (3), we have

[0106]

[0107] Substituting equation (10), equation (11) and equation (13) into equation (9), we have

[0108]

[0109] The control input u(t) is designed as:

[0110]

[0111] where k3 > 0 is a constant, and are the estimates of the actuator mass M and damping coefficient c, respectively. Figure 4 is the trajectory of the control input u(t) in 10 seconds in the embodiment of the present application; where the horizontal axis represents time, and the vertical axis represents force. The solid line represents the response curve of the input u(t) under the control scheme;

[0112] Substituting equation (15) into equation (14), we have:

[0113]

[0114] Step 3.2: Adaptive law selection and stability verification for the axial conveyor belt system:

[0115] According to the actuator parameter estimation error, the following Lyapunov function is further selected:

[0116] V0(t) = V(t) + V d (t) (42)

[0117] wherein

[0118]

[0119] wherein

[0120] Taking the time derivative of V0(t), we have

[0121] V 0t (t) = V t (t) + V dt (t) (44)

[0122] wherein

[0123]

[0124] Design parameters and The adaptive laws of and are respectively:

[0125]

[0126]

[0127] wherein k4, k5>0 are constants.

[0128] Substituting equation (16), equation (21) and equation (22) into equation (19), we have

[0129]

[0130] wherein k6, k7 and k8>0 are constants.

[0131] The parameters γ, λ and k i wherein i = 1, …, 8, satisfy the following conditions

[0132]

[0133] Further, we have

[0134]

[0135] wherein:

[0136]

[0137]

[0138]

[0139]

[0140] According to Lyapunov criterion, it is obtained from formula (25) that the axial conveyor belt system is stable.

[0141] Figure 5 The response curve of the adaptive law of the actuator parameter in 10 seconds in the embodiment of the application; wherein the horizontal axis represents time. The solid line represents The response curve under the control scheme, and the dashed line represents The response curve under the control scheme.

[0142] Step 4: Adjust the parameters of the control input and the adaptive law to achieve the final control goal:

[0143] By adjusting the parameters of the controller and the adaptive law, the axial conveyor belt system can still achieve the vibration suppression effect under the condition that the parameters of the actuator are unknown.

[0144] In the embodiment of the application, the length S of the axial conveyor belt system is selected as 10 m, the mass per unit length p is 1.0 kg / m, the viscous damping coefficient c s = 1.0 Ns / m, the tension T is 4900 N, g = 9.8 N / kg, the acceleration a a = a d = 3.5g. The mass of the actuator M is 5.0 kg, and the damping coefficient of the actuator c is 1.0 Ns / m 2 . The boundary vibration constraint boundary is l0 = 0.011. The boundary disturbance and the distributed disturbance of the system are respectively

[0145] In the embodiment of the application, the main design parameters are k1 = 100, k2 = 100, k3 = 100, k4 = 10 and k5 = 10. In addition, in the application, the interval of the running time is set as [t a ,t b ,t c ,t d ,t e ,t f ,t g ] = [1, 2, 3, 7, 8, 9, 10] s, and the initial state is v0 = y t (h, 0) = 0, y(h, 0) = h / 10000,

[0146] Through the simulation experiment, it can be found that although the axial conveyor belt system is affected by the uncertainty of the parameters of the actuator, the additional vibration of the system can still be well suppressed after the adaptive control scheme is implemented, and it is further concluded that the control scheme has good performance.

[0147] The above description is merely that of the preferred embodiments of the present disclosure and a description of the technical principles of the present disclosure. It should be understood by those skilled in the art that the inventive scope of the embodiments of the present disclosure is not limited to the technical solutions formed by the specific combinations of the above technical features, and should also cover other technical solutions formed by the combinations of the above technical features or equivalent features without departing from the above inventive concept. For example, the technical solutions formed by the mutual replacement of the above features and the technical features with similar functions disclosed in the embodiments of the present disclosure (but not limited to) form the technical solutions.

Claims

1. An axial conveyor belt adaptive constraint control method with unknown actuator parameters, characterized in that, The method comprises the following steps: Step 1: according to the physical structure of the axial conveyor belt system, combining Hamilton principle, a dynamic equation is established; Step 2: a logarithmic boundary vibration constraint model is established; Step 3: a controller is designed based on the boundary state information of the system; Step 4: the parameters of the control input and the adaptive law are adjusted to achieve the final control target, so that the axial conveyor belt system can still achieve vibration suppression effect under the condition that the actuator parameters are unknown; The dynamic equation in step 1 is as follows: （1） （2） where is the additional vibration of the system; is the controllable region of the system; is the mass per unit length; is the viscous damping coefficient of the system; is the tension of the system; is the running speed of the system; denotes the acceleration; is the control input; is the uncontrollable region of the system, whose influence on the system is regarded as a boundary disturbance ; is the distributed bounded disturbance suffered by the system; is the mass of the actuator; is the damping coefficient of the actuator; in addition, since the power provided by the actuator is limited, there exists a positive constant , , and , satisfying , , , ; Defining an auxiliary signal and is: （3） wherein is a constant; The logarithmic boundary vibration constraint model in step 2 is as follows: （4） wherein, is the constraint boundary of the boundary vibration, and the auxiliary signal satisfies ; The step 3 specifically comprises the following steps: Step 3.1: design the controller: select the Lyapunov function in the following form: （5） Wherein: （6） （7） （8） wherein , are design parameters; For Taking the derivative of time t, we get: （9） Wherein: （10） （11） （12） According to formula (2) and formula (3), the following formula is obtained: （13） Substitute formula (10), formula (11) and formula (13) into formula (9), and the following formula is obtained: （14） Design control input Is: （15） wherein, is a constant, and are estimates of the actuator mass and damping coefficient respectively; Substitute formula (15) into formula (14), and the following formula is obtained: （16） Step 3.2: adaptive law selection and stability verification of the axial conveyor belt system: According to the actuator parameter estimation error, the following Lyapunov function is further selected: （17） Wherein: （18） In the formulae, , ; For Taking the derivative with respect to time, we get: （19） Wherein: （20） Design parameters and The adaptive laws for and are respectively: （21） （22） wherein , is a constant; Substitute formula (16), formula (21) and formula (22) into formula (19), and the following formula is obtained: （23） wherein , and are constants; Selection parameters , and wherein satisfy the following conditions: （24） Further, the following formula is obtained: （25） In the formula: ， ， ， ； According to the Lyapunov criterion, it is obtained from formula (25) that the axial conveyor belt system is stable.

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