Flexible mechanical arm vibration control method and system based on high gain method

Abstract

The invention relates to a flexible mechanical arm vibration control method based on a high-gain method, and the method comprises the following steps: carrying out the modeling of a flexible mechanical arm based on a Lagrange equation and a Hamilton principle, and collecting a boundary state signal of the flexible mechanical arm; according to the collected boundary state information of the flexible mechanical arm and the flexible mechanical arm model design control rate, the flexible mechanical arm is controlled; a boundary high-gain controller is constructed through the control rate, and the actuator outputs a control signal through the boundary high-gain controller; and the gain value range of the boundary high-gain controller is obtained to ensure the stability of the flexible mechanical arm. According to the method provided by the invention, the boundary high-gain controller is adopted to reduce the influence of unknown disturbance on the stability of the flexible mechanical arm, the elastic vibration of the flexible mechanical arm is inhibited, the loss caused by the fact that the flexible mechanical arm is in elastic vibration for a long time is prevented, and the flexible mechanical arm obtains relatively high precision in actual engineering application.

Description

Technical Field

[0001] The present invention relates to the technical field of vibration suppression of flexible mechanical arms, and in particular to a vibration control method and system of a flexible mechanical arm based on a high-gain method. Background Art

[0002] In recent years, with the in-depth research on flexible robotic arm systems and the needs of practical real-world fields, more and more flexible robotic arms have been used in robotics, aerospace, and marine development due to their light weight, low energy consumption, and control speed. However, due to the elastic deformation of flexible robotic arms, elastic vibration of the flexible system will be caused, which is not conducive to the accuracy and stability of the system's motion positioning. Therefore, it is very important to effectively control the flexible robotic arm, and its control problem has become a hot topic of current research.

[0003] In the flexible arm robot system, due to the influence of external disturbances, the stability of the flexible robot may be destroyed, thereby affecting the accuracy of the actual system, and even causing fatigue damage to the system and shortening its service life; in addition, in the actual flexible robot system, in addition to the need to suppress the impact of disturbances on the system, the flexible robot is also required to reach the specified angle as quickly as possible under the action of the controller. Summary of the invention

[0004] In view of this, in order to solve the problem that the elastic vibration of the flexible mechanical arm cannot be controlled in the related art, the present invention provides a flexible mechanical arm vibration control method based on a high gain method, comprising the following steps:

[0005] S1. The flexible manipulator is modeled according to the Lagrange equation and Hamilton principle, and the system equations and boundary conditions in the form of Euler-Bernoulli beam are obtained;

[0006] S2, using sensors to collect boundary state information of the flexible robotic arm;

[0007] S3, the boundary state signal of the flexible mechanical arm is combined with the boundary high gain control rate to control the flexible mechanical arm;

[0008] S4, using the flexible manipulator model to design a control rate to construct a boundary high gain controller, the actuator outputs a control signal through the boundary high gain controller, and obtains a gain value range of the boundary high gain controller;

[0009] Preferably, the system equation expression of the Euler-Bernoulli beam form is:

[0010]

[0011] ω(x,t)=xθ(t)+z(x,t)

[0012] Among them, ω(x, t) represents the lateral displacement of the flexible manipulator, z(x, t) represents the elastic deflection of the flexible manipulator, ρ represents the unit mass per unit length, and E I represents the bending stiffness per unit length, T represents the tension per unit length, c represents the damping coefficient per unit length, I h represents the hub inertia per unit length, L represents the length of the flexible manipulator, θ(t) represents the angular position of the hub, () x represents the derivative with respect to space, () t represents the derivative with respect to time;

[0013] The boundary condition expression is:

[0014]

[0015] Among them, d(t) represents the boundary perturbation, assuming that there is an upper bound satisfying u(t) represents the boundary high gain controller output.

[0016] Preferably, the boundary state information of the flexible manipulator includes boundary displacement ω(L,t), boundary velocity ω t (l,T), boundary curvature ω x (0,t), boundary bending velocity ω xt (0,t) and the angular position θ(t) of the hub.

[0017] Preferably, the expression of the boundary high gain controller output u(t) is:

[0018] U(t)

[0019] r(t)=-k1Tz(L,t)-k1E I ω xx (0,T)+θ t (t)+k2(θ(t)-θ d )

[0020] Among them, k1, k2, k3, k, β, β1, β2 represent gain coefficients and are all positive constants, θ d Represents the target angle after the selected displacement, which is a positive constant;.

[0021] Preferably, obtaining the gain value range of the boundary high gain controller comprises the following steps:

[0022] Select the Lyapunov function, the expression is:

[0023] V(t)=V1(t)+V2(t)+V3(t)+V4(t)

[0024]

[0025] V2(t)=β1ρ∫0 L ω t (x,t)z(x,t)dx

[0026]

[0027] Among them, V1(t) represents the energy term including the kinetic energy and potential energy of the system, V2(t) represents the cross term of stability analysis, V3(t) represents the auxiliary term, and V4(t) represents the error term of the angle;

[0028] Combined with boundary state information and boundary high gain controller, the negative definiteness of the first-order derivative of Lyapunov function with respect to time t is verified, and the gain range of boundary high gain controller is obtained.

[0029] The state of the flexible robotic arm satisfies z(x,t)→0.

[0030] A flexible manipulator vibration control system based on a high gain method, comprising:

[0031] A sensor for collecting boundary state information of the flexible robotic arm;

[0032] A boundary high gain controller outputs a signal to control the actuator according to boundary state information of the flexible manipulator;

[0033] The actuator receives the control signal from the boundary high gain controller and acts on the flexible robotic arm.

[0034] Preferably, the sensor comprises a laser displacement sensor, an inclinometer and a pressure strain gauge.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] The present invention provides a high-gain based flexible robotic arm vibration control method, which adopts a boundary high-gain controller to reduce the influence of unknown disturbances on the stability of the flexible robotic arm, prevents the loss of the flexible robotic arm caused by elastic vibration for a long time, and enables the flexible robotic arm to obtain higher accuracy in actual engineering applications; at the same time, the boundary high-gain controller can make the system state converge quickly by selecting a sufficiently large controller gain, so that the flexible robotic arm can reach the specified angle as quickly as possible under the action of the boundary high-gain controller. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 This is a schematic diagram of the structure of the flexible mechanical arm of the present invention;

[0038] Figure 2 This is a flow chart of boundary control of the present invention;

[0039] Figure 3 This is a vibration displacement diagram of the flexible manipulator when the boundary high gain controller is used under boundary disturbance in the present invention;

[0040] Figure 4 The boundary vibration displacement diagram of the flexible manipulator when the boundary high gain controller is used under boundary disturbance in the present invention;

[0041] Figure 5 It is a structural block diagram of the boundary vibration control system of the flexible manipulator of the present invention. DETAILED DESCRIPTION

[0042] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the specific implementation mode, structure, characteristics and effects of the present invention are described in detail below in combination with the accompanying drawings and preferred embodiments.

[0043] Example 1

[0044] The present invention provides a flexible robotic arm vibration control method based on a high-gain method, which adopts a boundary high-gain controller to reduce the influence of unknown disturbances on the stability of the flexible robotic arm and reduce the loss caused by the flexible robotic arm being in elastic vibration for a long time, so that the flexible robotic arm can obtain higher accuracy in actual engineering applications.

[0045] The present invention provides a flexible mechanical arm vibration control method based on a high gain method, comprising the following steps:

[0046] S1. The flexible manipulator is modeled according to the Lagrange equation and Hamilton principle, and the system equations and boundary conditions in the form of Euler-Bernoulli beam are obtained;

[0047] The system equations in Euler-Bernoulli beam form are expressed as:

[0048]

[0049] Among them, ω(x, t) = xθ(t) + z(x, t), ω(x, t) represents the lateral displacement of the flexible manipulator, z(x, t) represents the elastic deflection of the flexible manipulator, ρ represents the unit mass per unit length, and E I represents the bending stiffness per unit length, T represents the tension per unit length, c represents the damping coefficient per unit length, I h represents the hub inertia per unit length, L represents the length of the flexible manipulator, θ(t) represents the angular position of the hub, () x represents the derivative with respect to space, () t represents the derivative with respect to time;

[0050] The boundary condition expression is:

[0051]

[0052] Among them, d(t) represents the boundary perturbation, assuming that there is an upper bound satisfying u(t) represents the boundary high gain controller output;

[0053] S2. Use sensors to collect boundary state information of the flexible manipulator, including boundary displacement ω(L,t) and boundary velocity ω t (L, t), boundary curvature ω x (0,t), boundary bending velocity ω xt (0,t) and the angular position of the hub θ(t);

[0054] S3, the boundary state signal of the flexible manipulator is combined with the boundary high gain control rate to control the flexible manipulator;

[0055] S4. Using the flexible manipulator model to design a control rate and construct a boundary high gain controller, the actuator outputs a control signal through the boundary high gain controller, and the gain value range of the boundary high gain controller is obtained;

[0056] The expression of the boundary high gain controller output u(t) is:

[0057] u(t)

[0058] r(t)=-k1Tz(L,t)-k1E I ω xx (0,t)+θ t (t)+k2(θ(t)-θ d )

[0059] Among them, k1, k2, k3, k, β, β1, β2 represent gain coefficients and are all positive constants, θ d Indicates the target angle after the selected displacement, which is a positive constant;

[0060] Obtaining the gain range of the boundary high gain controller includes the following steps:

[0061] Select the Lyapunov function, the expression is:

[0062] V(t)=V1(t)+V2(t)+V3(t)+V4(t)

[0063]

[0064] V2(t)=β1ρ∫0 L ω t (x,t)z(x,t)dx

[0065]

[0066] Among them, V1(t) represents the energy term including the kinetic energy and potential energy of the system, V2(t) represents the cross term of stability analysis, V3(t) represents the auxiliary term, and V4(t) represents the error term of the angle;

[0067] The boundary state information and the boundary high gain controller are combined to verify the negative definiteness of the first-order derivative of the Lyapunov function with respect to time t, and the gain range of the boundary high gain controller is obtained to ensure the stability of the flexible manipulator.

[0068] The state of the flexible robotic arm satisfies z(x,t)→0.

[0069] The system parameter settings of the flexible robotic arm in this embodiment are as follows:

[0070] Length of the flexible robotic arm: L = 1m;

[0071] Hub inertia per unit length of the flexible robotic arm: I h =0.5kg / m 2 ;

[0072] Bending stiffness per unit length of the flexible robotic arm: E I =2N·m 2 ;

[0073] Unit mass per unit length of the flexible robotic arm: ρ = 0.2 kg / m;

[0074] Tension per unit length of the flexible robotic arm: T = 2N;

[0075] Damping coefficient per unit length of the flexible manipulator: c = 0.01 N·s / m 2 ;

[0076] Boundary perturbation: d(t) = 0.2 + 0.1 sin(πt) + 0.2 sin(2πt);

[0077] The initial value of the system is: ω(x,0)=z(x,0)=x 2 / 5,ω t (x,0)=z t (x,0)=0,θ d =0.5;

[0078] The controller uses a boundary high gain controller, and the selected controller gain is:

[0079] k=5, k1=0.5, k3=0.5, β=1, β1=0.01,

[0080] like Figure 3 As shown, by using the method provided by the present invention, when a boundary high gain controller is used under boundary disturbance, the vibration suppression effect of the flexible manipulator is better, the displacement state of the flexible manipulator is stable, and the robust performance is better; Figure 4 As shown in the figure, when the boundary high gain controller is used under boundary disturbance, the boundary displacement of the flexible manipulator reaches the desired state after about 1.5 seconds, and the convergence speed is fast.

[0081] The influence of boundary disturbance is effectively reduced by the boundary high gain controller, ensuring that the actuator can well suppress the vibration of the flexible robot arm under boundary disturbance conditions; since the boundary state information used by the designed boundary high gain controller is available, it is feasible in practical applications.

[0082] Example 2

[0083] like Figure 5 As shown, this embodiment provides a flexible manipulator vibration control system based on a high gain method, including:

[0084] Sensors, including laser displacement sensors, inclinometers, and pressure strain gauges, for collecting boundary state information of the flexible manipulator;

[0085] A boundary high gain controller outputs a signal to control the actuator according to boundary state information of the flexible manipulator;

[0086] The actuator receives the control signal from the boundary high gain controller and acts on the flexible robotic arm.

[0087] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment as above, it is not used to limit the present invention. Any technical personnel in this field can make some changes or modify the technical contents disclosed above into equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any brief modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A flexible manipulator vibration control method based on a high gain method, characterized in that: The following steps are involved: S1. The flexible manipulator is modeled according to the Lagrange equation and Hamilton principle, and the system equations and boundary conditions in the form of Euler-Bernoulli beam are obtained; S2, using sensors to collect boundary state information of the flexible robotic arm; S3, the boundary state signal of the flexible mechanical arm is combined with the boundary high gain control rate to control the flexible mechanical arm; S4. Using the flexible manipulator model to design a control rate and construct a boundary high gain controller, the actuator outputs a control signal through the boundary high gain controller to obtain a gain value range of the boundary high gain controller.

2. A flexible manipulator vibration control method based on a high gain method according to claim 1, characterized in that: The system equations in the Euler-Bernoulli beam form are expressed as: ω(x,t)=xθ(t)+z(x,t) Among them, ω(x, t) represents the lateral displacement of the flexible manipulator, z(x, t) represents the elastic deflection of the flexible manipulator, ρ represents the unit mass per unit length, and E I represents the bending stiffness per unit length, T represents the tension per unit length, c represents the damping coefficient per unit length, I h represents the hub inertia per unit length, L represents the length of the flexible manipulator, θ(t) represents the angular position of the hub, () x represents the derivative with respect to space, () t represents the derivative with respect to time; The boundary condition expression is: Among them, d(t) represents the boundary perturbation, assuming that there is an upper bound satisfying u(t) represents the boundary high gain controller output.

3. The flexible manipulator vibration control method based on the high gain method according to claim 1 is characterized in that: The boundary state information of the flexible manipulator includes boundary displacement ω(L,t), boundary velocity ω t (L, t), boundary curvature ω x (0,t), boundary bending velocity ω xt (0,t) and the angular position θ(t) of the hub.

4. The flexible manipulator vibration control method based on the high gain method according to claim 2 is characterized in that: The expression of the boundary high gain controller output u(t) is: r(t)=-k1Tz(L,t)-k1E I oh xx (0,t)+θ t (t)+k2(θ(t)-θ d ) Among them, k1, k2, k3, k, β, β1, β2 represent gain coefficients and are all positive constants, θ d Represents the target angle after the selected displacement, which is a positive constant;.

5. The flexible manipulator vibration control method based on the high gain method according to claim 1, characterized in that: Obtaining the gain value range of the boundary high gain controller comprises the following steps: Select the Lyapunov function, the expression is: V(t)=V1(t)+V2(t)+V3(t)+V4(t) Among them, V1(t) represents the energy term including the kinetic energy and potential energy of the system, V2(t) represents the cross term of stability analysis, V3(t) represents the auxiliary term, and V4(t) represents the error term of the angle; Combined with boundary state information and boundary high gain controller, the negative definiteness of the first-order derivative of Lyapunov function with respect to time t is verified, and the gain range of boundary high gain controller is obtained. The state of the flexible robotic arm satisfies z(x,t)→0.

6. A flexible manipulator vibration control system based on a high gain method, characterized in that: include: A sensor for collecting boundary state information of the flexible robotic arm; A boundary high gain controller outputs a signal to control the actuator according to boundary state information of the flexible manipulator; The actuator receives the control signal from the boundary high gain controller and acts on the flexible robotic arm.

7. A flexible manipulator vibration control system based on a high gain method according to claim 6, characterized in that: The sensor includes a laser displacement sensor, an inclinometer and a pressure strain gauge.

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