Fuzzy PID (Proportion Integration Differentiation) control method for variable-stiffness flexible joint mechanical arm

Abstract

The invention provides a fuzzy PID (Proportion Integration Differentiation) control method for a variable-stiffness flexible joint mechanical arm, which relates to the technical field of PID control and comprises the following steps of: establishing a dynamic model of the variable-stiffness flexible joint mechanical arm; designing a fuzzy rule of the fuzzy PID control method; a fuzzy rule is applied to real-time adjustment of PID parameters of a system, the variable stiffness and flexibility characteristics of the system are fully considered, and a fuzzy PID control method is applied to the variable stiffness flexible joint mechanical arm; the Matlab Simulink software is used for dynamically simulating the system, the rotating frequency and the torque curve of the system are output, and it is proved that the method has the advantages that the response speed is high, the overshoot is small, and the vibration effect of the vibration suppression system is obvious and stable.

Description

Technical Field

[0001] The invention relates to the technical field of PID control, and in particular to a fuzzy PID control method for a variable-rigidity flexible joint mechanical arm. Background Art

[0002] Industrial robotic arms are widely used in aerospace and other fields of mechanical processing and manufacturing. In order to adapt to work situations with high processing precision and complex working conditions, industrial robotic arms with higher flexibility are often selected as manufacturing equipment. The variable stiffness flexible joints with highly nonlinear characteristics in such industrial robotic arms, and the precise dynamic modeling and intelligent control of such variable stiffness flexible joint robotic arms are the key to reducing processing errors and improving work precision and work efficiency.

[0003] The traditional PID control method is simple and easy to operate, and is widely used in servo systems. However, the traditional PID control method has certain limitations. The control parameters cannot be adjusted as the external environment changes. Obviously, fixed PID parameters cannot achieve precise control of the system. In order to improve the working performance of variable stiffness flexible joint robotic arms, combining traditional PID with other intelligent control methods has become a research hotspot today. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention provides a fuzzy PID control method for a variable stiffness flexible joint robotic arm, aiming to solve the problems in the prior art that the variable stiffness flexible joint robotic arm system is highly nonlinear, difficult to establish a mathematical model and is greatly affected by external disturbances.

[0005] A fuzzy PID control method for a variable stiffness flexible joint mechanical arm comprises the following steps:

[0006] Step 1: Establish the dynamic model of the variable stiffness flexible joint robot system:

[0007]

[0008] Wherein, formula (1) represents the state equation of the variable stiffness flexible joint manipulator system, J m Represents the motor’s moment of inertia, T m Represents the torque output by the motor, θ m Indicates the motor rotation angle, Represents θ m The partial derivative of m Indicates the angular velocity of the motor. Represents ω m The partial derivative of s Indicates the moment of inertia of the load, T s represents the load torque, θ s Indicates the load rotation angle, ωs represents the angular velocity of the load, k s Represents the elastic coefficient of the flexible joint.

[0009] Step 2: Establish the transfer function between load speed and motor torque:

[0010]

[0011] Step 3: Set up the fuzzy PID controller;

[0012] Step 3.1: Take the load speed error E and the error change rate EC as input variables; perform fuzzy reasoning through fuzzy rules to obtain the fuzzy result ΔK p , ΔK i and ΔK d As the output variable, ΔK p Indicates the proportional gain adjustment, ΔK i Indicates the integral gain adjustment, ΔK d Indicates the differential gain adjustment amount; Gauss-type function is used to set seven language values ​​for the input and output of the fuzzy PID controller; the domains of input error and error change rate are set to [-6, 6], and the domain of the actual output controller is set to [-0.6, 0.6];

[0013] Step 3.2: Establish a fuzzy rule table based on the joint deviation of the robot arm to determine the control rules between input and output;

[0014] Step 3.3: Defuzzify the output fuzzy language to realize fuzzy PID control of the variable stiffness flexible joint robot arm.

[0015] The fuzzy rule table is as follows:

[0016] Table 1

[0017]

[0018] Table 2

[0019]

[0020] Table 3

[0021]

[0022] In the table, PB represents positive large, PM represents positive middle, PS represents positive small, NB represents negative large, NM represents negative middle, NS represents negative small, and ZO represents zero; e represents error, and ec represents the error change rate.

[0023] The beneficial effects of adopting the above technical solution are:

[0024] The present invention provides a fuzzy PID control method for a variable stiffness flexible joint robot arm, which solves the technical problem that it is difficult to balance response speed and stability in the flexible joint control in the prior art. Compared with the existing traditional PID control method, it has the following improvements:

[0025] 1. Dynamic performance improvement

[0026] By introducing the fuzzy PID control method, the control parameters (K p , K i and K d ), the control gain can be quickly optimized according to the changes in the system state. Compared with the traditional fixed parameter PID control, this technical solution can significantly improve the dynamic response speed and system stability when the flexible joint is subjected to complex disturbances. It can adapt to complex nonlinear and dynamic environments, shorten the system response time, and reduce overshoot.

[0027] 2. Combination of stiffness adjustment and flexibility control

[0028] The technical solution combines the stiffness modeling and real-time adjustment mechanism of the flexible joint, so that the robot arm can dynamically adjust the stiffness according to the task requirements, realizing the control characteristics of "rigidity and flexibility". Traditional technologies usually use fixed stiffness design, which cannot adapt to different tasks and external disturbances. Improve the adaptability of the flexible robot arm and make it suitable for a variety of complex task scenarios. Improve the accuracy and robustness of control and reduce the impact of environmental disturbances on performance.

[0029] 3. Error adaptive adjustment

[0030] Through the fuzzy reasoning mechanism, the solution can adjust the control parameters in real time according to the error (such as position deviation and error change rate). This method effectively overcomes the failure problem of traditional PID control when the error is large or the system is highly dynamic. It reduces the steady-state error of the system and improves the control accuracy. It also improves the anti-interference ability, especially in a dynamically changing environment.

[0031] 4. Enhanced control capabilities of nonlinear complex systems

[0032] Traditional PID control shows insufficient control performance in nonlinear and strongly coupled systems such as flexible robotic arms. Fuzzy PID combines the characteristics of fuzzy logic in processing uncertainty, significantly enhancing the control capability of complex systems, coping with the nonlinear characteristics and coupling effects in flexible robotic arm control, and providing more stable and reliable control output.

[0033] 5. Simulation experiment verifies significant results

[0034] The simulation experiment was verified by Matlab Simulink software, and the technical solution is superior to the traditional PID control method in multiple indicators such as dynamic response time, stability, and anti-interference ability. The simulation experiment results show that the fuzzy PID control method can effectively improve the overall performance of the system. The present invention verifies the practical feasibility and advantages of the solution, and provides a more efficient control method for the industrial application of flexible robotic arms. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is the system output torque of the embodiment of the present invention;

[0036] Figure 2 The system output rotation frequency of the embodiment of the present invention;

[0037] Figure 3 It is a block diagram of traditional PID and fuzzy PID control in an embodiment of the present invention;

[0038] Figure 4 It is a simulation block diagram of the fuzzy PID program of an embodiment of the present invention. DETAILED DESCRIPTION

[0039] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0040] A fuzzy PID control method for a variable stiffness flexible joint mechanical arm comprises the following steps:

[0041] Step 1: Use mechanical modeling and variable stiffness theory to build a stiffness model of the flexible joint to describe the relationship between joint deformation and external force. By adjusting the stiffness parameters of the flexible joint, the stiffness adaptation of the robot arm under different task conditions can be achieved. This process relies on the dynamic calculation of the driving torque and the real-time correction of the joint modal coordinates.

[0042] Establish the dynamic model of the variable stiffness flexible joint robot system:

[0043]

[0044] Wherein, formula (1) represents the state equation of the variable stiffness flexible joint manipulator system, J m Represents the motor’s moment of inertia, T m Represents the torque output by the motor, θ m Indicates the motor rotation angle, Represents θ m The partial derivative of m Indicates the angular velocity of the motor. Represents ω m The partial derivative of sIndicates the moment of inertia of the load, T s represents the load torque, θ s Indicates the load rotation angle, ω s represents the angular velocity of the load, k s Represents the elastic coefficient of the flexible joint.

[0045] Step 2: Establish the transfer function between load speed and motor torque:

[0046]

[0047] Step 3: Set up the fuzzy PID controller;

[0048] Based on the combination of fuzzy control theory and PID controller, a fuzzy PID control system is designed to deal with the uncertainty in nonlinear complex systems. In the controller, the fuzzy rule base is used to adjust the PID parameters (K p , K i and K d ), and generate incremental parameters (ΔK p , ΔK i and ΔK d ), optimize the dynamic performance of the control system.

[0049] Step 3.1: Take the load speed error E and the error change rate EC as input variables; perform fuzzy reasoning through fuzzy rules to obtain the fuzzy result ΔK p , ΔK i and ΔK d As the output variable, ΔK p Indicates the proportional gain adjustment, ΔK i Indicates the integral gain adjustment, ΔK d Indicates the differential gain adjustment amount; Gauss-type function is used to set seven language values ​​for the input and output of the fuzzy PID controller; the domains of input error and error change rate are set to [-6, 6], and the domain of the actual output controller is set to [-0.6, 0.6];

[0050] Step 3.2: Establish a fuzzy rule table based on the joint deviation of the robot arm to determine the control rules between input and output;

[0051] The fuzzy rule table is constructed based on the joint deviations of the robot arm (such as displacement error and error change rate). Using the fuzzy inference mechanism, the control gain is dynamically adjusted according to the real-time error and error change rate to improve the system response speed and stability.

[0052] Step 3.3: Defuzzify the output fuzzy language to realize fuzzy PID control of the variable stiffness flexible joint robot arm.

[0053] The fuzzy rule table is as follows:

[0054] Table 1

[0055]

[0056] Table 2

[0057]

[0058] Table 3

[0059]

[0060] In the table, PB represents positive large, PM represents positive middle, PS represents positive small, NB represents negative large, NM represents negative middle, NS represents negative small, and ZO represents zero; e represents error, and ec represents the error change rate.

[0061] A flexible joint robot control simulation experimental platform is constructed to verify the effectiveness of the fuzzy PID control method. The dynamic simulation verification scheme effect in this embodiment is as follows:

[0062] In order to verify the effectiveness of the method of the present invention, a simulation model was established through simulink, and conventional PID dynamic simulation was performed on the variable stiffness flexible joint robot arm, and the PID parameters were preliminarily adjusted using the empirical method. Figure 3 and Figure 4 It can be seen that the overshoot and regulation of the traditional PID control method are not ideal, the oscillation and instability of the system are obvious, and there is room for further optimization.

[0063] Using the fuzzy PID control method, a simulation model was established through simulink to perform conventional PID dynamic simulation on the variable stiffness flexible joint robot arm. Figure 1 and Figure 2 In the comparison with the traditional PID control method, it can be seen that the use of fuzzy PID control method effectively reduces the system angle error and torque fluctuation, making the system run faster and more stable, and achieving the expected effect. Compared with the traditional PID controller, the simulation experimental results show that this method has significant advantages in dynamic response, steady-state accuracy and anti-interference performance.

[0064] The above description is only a preferred embodiment of the present disclosure and an explanation of the technical principles used. Those skilled in the art should understand that the scope of the invention involved in the embodiments of the present disclosure is not limited to the technical solutions formed by a specific combination of the above-mentioned technical features, but should also cover other technical solutions formed by any combination of the above-mentioned technical features or their equivalent features without departing from the above-mentioned inventive concept. For example, the above-mentioned features are replaced with the technical features with similar functions disclosed in the embodiments of the present disclosure (but not limited to) to form a technical solution.

Claims

1. A fuzzy PID control method for a variable stiffness flexible joint robot arm, characterized in that: The following steps are involved: Step 1: Establish a dynamic model of the variable stiffness flexible joint robot system; Step 2: Establish the transfer function between load speed and motor torque; Step 3: Set up the fuzzy PID controller.

2. The fuzzy PID control method for a variable stiffness flexible joint mechanical arm according to claim 1, characterized in that: The dynamic model of the variable stiffness flexible joint manipulator system described in step 1 is as follows: Wherein, formula (1) represents the state equation of the variable stiffness flexible joint manipulator system, J m Represents the motor’s moment of inertia, T m Represents the torque output by the motor, θ m Indicates the motor rotation angle, Represents θ m The partial derivative of m Indicates the angular velocity of the motor. Represents ω m The partial derivative of s Indicates the moment of inertia of the load, T s represents the load torque, θ s Indicates the load rotation angle, ω s represents the angular velocity of the load, k s Represents the elastic coefficient of the flexible joint.

3. The fuzzy PID control method for a variable stiffness flexible joint mechanical arm according to claim 2, characterized in that: The transfer function described in step 2 is as follows:

4. The fuzzy PID control method for a variable stiffness flexible joint robot arm according to claim 1, characterized in that: The step 3 specifically comprises the following steps: Step 3.1: Take the load speed error E and the error change rate EC as input variables; perform fuzzy reasoning through fuzzy rules to obtain the fuzzy result ΔK p , ΔK i and ΔK d As the output variable, ΔK p Indicates the proportional gain adjustment, ΔK i Indicates the integral gain adjustment, ΔK d Indicates the differential gain adjustment amount; Gauss-type function is used to set seven language values ​​for the input and output of the fuzzy PID controller; the domains of input error and error change rate are set to [-6, 6], and the domain of the actual output controller is set to [-0.6, 0.6]; Step 3.2: Establish a fuzzy rule table based on the joint deviation of the robot arm to determine the control rules between input and output; Step 3.3: Defuzzify the output fuzzy language to realize fuzzy PID control of the variable stiffness flexible joint robot arm.

5. The fuzzy PID control method for a variable stiffness flexible joint mechanical arm according to claim 4, characterized in that: The fuzzy rule table described in step 3.2 is as follows: Table 1 Table 2 Table 3 In the table, PB represents positive large, PM represents positive middle, PS represents positive small, NB represents negative large, NM represents negative middle, NS represents negative small, and ZO represents zero; e represents error, and ec represents the error change rate.

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