Improved global sliding mode control method for wire harness winding manipulator

Abstract

The invention discloses an improved global sliding mode control method for a wire harness winding manipulator. The method comprises the following steps: step 1, designing a global sliding mode switching function, saving the response time of an approaching mode by omitting the approaching mode, and accelerating the convergence speed of a system; 2, an improved global sliding mode controller is designed, and the response speed of the system is increased; 3, solving a control law of the global sliding mode controller improved based on the constant-speed reaching law by adopting the constant-speed reaching law; and 4, the controller designed in the step 3 is applied to the wire harness winding manipulator for numerical simulation analysis. According to the design of the improved controller, swinging and shaking of the system can be better restrained, the tracking precision and robustness of the system are improved on the premise that the stability of the system is guaranteed, and the method is simple, easy to apply, low in cost and capable of being widely applied to the control application fields such as wire harness winding manipulators.

Description

Technical Field

[0001] The present invention specifically relates to an improved global sliding mode control method for a wire harness winding robot. Background Art

[0002] With the continuous development of science and technology and the continuous changes in market demand, the types and classifications of wire harness tape winding equipment at home and abroad are also constantly increasing and updating. Classification is based on different technical principles, materials used, etc. For example, according to the control method of the winding machine, it can be divided into manual control and automatic control; according to the materials used by the winding machine, it can be divided into plastic winding machines and paper winding machines. Wire harness winding tape is divided into handheld tape winding machines, desktop tape winding machines and floor-standing tape winding machines according to the form. These forms are mainly classified according to the use scenarios and portability of the equipment. The handheld type is suitable for situations that require mobile operation, the desktop type is suitable for simple fixed winding work, and the floor-standing type is suitable for winding needs on large-scale production lines.

[0003] As one of the core components of automotive electrical appliances, the requirements for automotive wiring harnesses are increasing day by day. The demand for wiring harness tape winding is also increasing. It can provide protection and fixation for the circuit system of new energy vehicles to prevent the wiring harness from being damaged or loose during use. The wiring harness winding machine is driven by a brushless DC motor to wrap the wiring harnesses of various circuits inside the car to increase work efficiency.

[0004] Because the wiring harness inside the car is highly interconnected, the wiring harness has many branches, and the lengths and thicknesses of various lines vary.

[0005] This seriously affects the accuracy of tape winding, resulting in unqualified wire harness products. In order to solve this engineering application problem, improve the speed regulation accuracy of wire harness winding equipment and stabilize its operation, while reducing the impact of external load changes and improving the disturbance performance of the system, the present invention discloses a global sliding mode control method based on saving approaching modal response time. This method can speed up the convergence speed of the system, thereby improving the efficiency of control. The entire process from the start of the system movement to the equilibrium point is robust, and the system can reach a state of equilibrium faster, which has a wide range of application value. Summary of the invention

[0006] The object of the present invention is to provide an improved global sliding mode control method for a wire harness winding robot arm in view of the deficiencies in the prior art.

[0007] In order to achieve the above technical objectives, the present invention adopts the following technical solutions:

[0008] Step 1: By omitting the approaching mode, saving the response time of the approaching mode, accelerating the convergence speed of the system, and improving the control efficiency, a global sliding mode switching function is designed.

[0009] Step 2: In order to further improve the response speed of the system, an improved global sliding mode controller is proposed.

[0010] Step 3: Use the constant velocity reaching law to obtain the control law of the improved global sliding mode controller based on the constant velocity reaching law.

[0011] Step 4: Apply the controller designed in step 3 to the wire harness winding robot for numerical simulation analysis.

[0012] The beneficial effects of the present invention are as follows:

[0013] In terms of speed control applications for wire harness winding manipulators, compared with existing methods, the method described in the present invention is based on the improved global sliding mode controller proposed in step (2), which uses the adaptive principle to track and adjust system parameters, and adopts an improved special power approach rate strategy to enable the system to reach the sliding surface faster, thereby improving the performance and robustness of the controller. Based on the constant speed approach law adopted in step (3), a control law for improving the global sliding mode controller based on the constant speed approach law is proposed. The controller can better suppress the swing and jitter of the system, and improve the tracking accuracy and robustness of the system while ensuring the stability of the system. It is simple and easy to use, low cost, and can be widely used in control application fields such as wire harness winding manipulators. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is the control output diagram of the harness winding robot motor system under sinusoidal signal, which is based on the control law of the improved global sliding mode controller based on the constant velocity reaching law compared with the PID controller and ASMC.

[0015] Figure 2 This is a speed tracking comparison chart of the wire harness winding robot motor system under sinusoidal signals using an improved global sliding mode controller based on the constant speed reaching law compared to the PID controller and ASMC controller.

[0016] Figure 3 It is the control output diagram of the wire harness winding robot motor system under rectangular wave signal, which is based on the control law of the improved global sliding mode controller based on the constant velocity reaching law compared with the PID controller and ASMC.

[0017] Figure 4 This is a speed tracking comparison chart of the harness winding robot motor system under rectangular wave signal, which is based on the control law of the improved global sliding mode controller based on the constant speed reaching law compared with the PID controller and ASMC controller. DETAILED DESCRIPTION

[0018] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0019] like Figure 1-Figure 4 As shown, the present invention provides an improved global sliding mode control method for a wire harness winding robot. To achieve the above technical objectives, the present invention adopts the following technical solutions:

[0020] Step 1: By omitting the approaching mode, saving the response time of the approaching mode, accelerating the convergence speed of the system, and improving the control efficiency, a global sliding mode switching function is designed.

[0021] Step 2: In order to further improve the response speed of the system, an improved global sliding mode controller is proposed.

[0022] Step 3: Use the constant velocity reaching law to obtain the control law of the improved global sliding mode controller based on the constant velocity reaching law.

[0023] Step 4: Apply the controller designed in step 3 to the wire harness winding robot for numerical simulation analysis.

[0024] Furthermore, the specific implementation of step 1 includes the following sub-steps:

[0025] 1-1. Establish the mathematical model of the wire harness winding robot:

[0026]

[0027] Where: θ l is the load angle; ω l is the load speed; J = 2iJ m +2J l , i is the transmission ratio, J m is the moment of inertia, J l K is the moment of inertia of the transmission belt converted to the motor shaft; t is the motor torque constant; K e is the electromotive force constant; R is the equivalent resistance; C m , C l is the damping coefficient; u is the input voltage; T L is the external constant load torque; f tape Tape peel force; r is the bundle radius; d is the tape thickness; Δ is the external disturbance and unmodeled dynamics.

[0028] 1-2. In order to simplify the expression, we take the state variables as x1 and x2:

[0029]

[0030] 1-3. Rewrite the mathematical model of the harness winding robot as follows:

[0031]

[0032] In the formula, φ=-θ3x1-θ4, and |φ|≤D is satisfied within a finite number of events.

[0033] 1-4. Define tracking error as:

[0034]

[0035] In the formula, x d is the ideal angular displacement, The ideal speed.

[0036] 1-5. Design the global sliding mode switching function, the formula is as follows:

[0037]

[0038] Where c>0, satisfying the Hurwitz (Chinese Hurwitz theorem) condition, h(t) should satisfy the following three conditions:

[0039] (1)

[0040] (2) When t approaches infinity, h(t) approaches 0;

[0041] (3) h(t) has a first-order derivative.

[0042] In order to meet the above three conditions, both to meet the control requirements of the global sliding surface switching function and to give full play to the advantages of sliding mode control, thereby improving the control performance of the system, a function in exponential form and monotonically decreasing is designed. The formula is as follows:

[0043]

[0044] In the formula, α>0.

[0045] Substituting formula (6) into formula (5) we can obtain the switching surface function of global sliding mode control:

[0046]

[0047] Where c must satisfy the Hurwitz condition, that is, c>0. When t=0, the system state is on the sliding surface s=0, which means that the system satisfies the conditions of sliding mode control at the initial moment. As time goes by, the system moves toward the equilibrium point along the sliding surface without going through the process of approaching the mode. When time tends to infinity, the sliding surface switching function h(t) approaches 0, which means that the nonlinear term gradually decreases, and the global sliding mode switching surface function gradually degenerates into a linear sliding surface and passes through the origin. In this case, the control behavior of the system will tend to be linear, and the influence of nonlinearity will gradually disappear.

[0048] Derivative of both sides of equation (7) with respect to time t yields:

[0049]

[0050] Substituting formula (3) into (8), we can obtain:

[0051]

[0052] Using the constant velocity reaching law, the control law of the global sliding mode controller based on the constant velocity reaching law is obtained as follows:

[0053]

[0054] Furthermore, the step 2 is specifically implemented as follows:

[0055] In order to further improve the response speed of the system, h(t) is optimized and improved into the following form:

[0056]

[0057] In the formula, α1, α2, and α3 are adjustable parameters of the exponential decay function, and they are all greater than 0. z To improve the time when the global sliding mode switching surface becomes the linear switching surface of sliding mode control.

[0058] Therefore, the improved global sliding mode switching surface function is obtained as follows:

[0059]

[0060] Derivation of formula (9) yields:

[0061]

[0062] Among them, A c , B c , C c is a constant coefficient. The designed improved global sliding mode switching surface must still meet the three conditions for the establishment of the global sliding mode control surface. According to condition (1), the coefficient value of the exponential decay function should satisfy A c +B c +C c =1, and for the sake of convergence speed, let h(t z )=0, the above arrangement yields:

[0063]

[0064] Condition (3) needs to be met, h(t) at point t = t z The left derivative of must be equal to the right derivative, that is, h - '(t z )=h + '(t z )=0, we can get:

[0065]

[0066] In this way, the parameters in formula (13) should satisfy:

[0067]

[0068] Choose appropriate parameters α1, α2, α3 and C c Then, find t z In the design of sliding mode controller, the constant velocity reaching law is adopted as

[0069] In summary, the improved global sliding mode control law is designed as follows:

[0070]

[0071] Considering the actual working conditions of the brushless DC motor drive system, the sine signal and the rectangular wave signal are selected as the tracking target signal to examine the dynamic adjustment tracking effect of the controller. The present invention uses matlab software to simulate the winding manipulator. The system simulation parameters are determined according to the parameters on the motor nameplate, etc.

[0072] [θ1,θ2,θ3,θ4]

[0073] =[29.725,617.3,0.5,-338]. The simulation step is set to 2ms and the simulation duration is 15s. In order to simulate the external disturbance effect, the total disturbance is added in this simulation example as

[0074] Δ=5sin(2Πt)+100rand(1).

[0075] The sinusoidal tracking signal is set as:

[0076] ω d =200+25sin(0.4Πt) (18)

[0078] The rectangular wave tracking signal is set as:

[0079]

[0080] Where mod(t,4) means the remainder operation on t modulo 4.

[0081] In order to compare the performance of different controllers more intuitively, this paper adopts the maximum speed tracking error.

[0082] The performance of the above controllers is compared and analyzed using two indicators: maximum value (MAXE) and root mean square error (RMSE). These two indicators reflect the performance of the controller under instantaneous operation and over a period of time respectively.

[0083] The root mean square error (RMSE) is defined as:

[0084]

[0085] The maximum speed error (MAXE) is defined as:

[0086]

[0087] In this simulation system, three control methods, PID controller, global sliding mode controller (GSMC) and adaptive sliding mode controller (ASMC), are used to conduct speed tracking simulation experiments for sinusoidal signals and rectangular wave signals. These controllers are commonly used controller types with different advantages and limitations. In the simulation experiment, it is necessary to match the corresponding control algorithm for each controller and adjust the parameters.

[0088] Finally, through simulation, the speed tracking comparison chart is analyzed, and the RMSE and MAXE indicators are calculated to draw conclusions.

[0089] Experimental data:

[0090] Table 1 shows the root mean square error (RMSE) and maximum error (MAXE) performance indicators of the three controllers under different conditions obtained through simulation experiments.

[0091] Table 1 Control performance index results (t∈(0,15))

[0092]

[0093] Table 2 shows the performance indicators observed in a stable state and calculated 2 seconds later (i.e., after the initial step state).

[0094]

[0095] In summary, the present invention improves the tracking accuracy and robustness of the system while ensuring the stability of the system. It is simple and easy to use, has low cost, and can be widely used in control application fields such as wire harness winding robots.

Claims

1. An improved global sliding mode control method for a harness winding robot, characterized in that: The steps include: Step 1: Design a global sliding mode switching function to save the response time of the approaching mode and accelerate the convergence speed of the system by omitting the approaching mode; Step 2: Design an improved global sliding mode controller to improve the response speed of the system; Step 3: Using the constant velocity reaching law, obtain the control law of the improved global sliding mode controller based on the constant velocity reaching law; Step 4: Apply the controller designed in step 3 to the wire harness winding robot for numerical simulation analysis.

2. The improved global sliding mode control method for the harness winding robot according to claim 1, characterized in that: The specific implementation of step 1 includes the following sub-steps: 1-1. Establish the mathematical model of the wire harness winding robot: Where: θ l is the load angle; ω l is the load speed; J = 2iJ m +2J l , i is the transmission ratio, J m is the moment of inertia, J l K is the moment of inertia of the transmission belt converted to the motor shaft; t is the motor torque constant; K e is the electromotive force constant; R is the equivalent resistance; C m , C l is the damping coefficient; u is the input voltage; T L is the external constant load torque; f tape Tape peeling force; r is the bundle radius; d is the tape thickness; Δ is the external disturbance and unmodeled dynamics; 1-2. Simplify the expression, take the state variables as x1 and x2: 1-3. Rewrite the mathematical model of the harness winding robot as follows: In the formula, φ=-θ3x1-θ4, and |φ|≤D is satisfied in the finite event; 1-4. Define tracking error as: In the formula, x d is the ideal angular displacement, is the ideal speed; 1-5. Design the global sliding mode switching function, the formula is as follows: Where c>0, which satisfies the Chinese Hurwitz theorem conditions, and h(t) should satisfy the following three conditions: (1) (2) When t approaches infinity, h(t) approaches 0; (3) h(t) has a first-order derivative; In order to meet the above three conditions, a monotonically decreasing function in exponential form is designed. The formula is as follows: Where, α>0; Substituting formula (6) into formula (5) we can obtain the switching surface function of global sliding mode control: In the formula, c must satisfy the Hurwitz condition, that is, c>0; when t=0, the system state is on the sliding surface s=0, which means that the system satisfies the sliding mode control conditions at the initial moment; as time goes by, the system moves toward the equilibrium point along the sliding surface without going through the process of approaching the mode; when time tends to infinity, the sliding surface switching function h(t) approaches 0, which means that the nonlinear term gradually decreases, and the global sliding mode switching surface function gradually degenerates into a linear sliding surface and passes through the origin; in this case, the control behavior of the system will tend to be linear, and the influence of nonlinearity will gradually disappear; Derivative of both sides of equation (7) with respect to time t yields: Substituting formula (3) into (8), we can obtain: Using the constant velocity reaching law, the control law of the global sliding mode controller based on the constant velocity reaching law is obtained as follows:

3. The improved global sliding mode control method for the harness winding robot according to claim 2, characterized in that: The specific implementation of steps 2 and 3 includes the following steps: Optimize and improve h(t) into the following form: In the formula, α1, α2, and α3 are adjustable parameters of the exponential decay function, and they are all greater than 0. z To improve the time when the global sliding mode switching surface becomes the sliding mode control linear switching surface; Therefore, the improved global sliding mode switching surface function is obtained as follows: Derivation of formula (9) yields: Among them, A c , B c , C c is a constant coefficient; the designed improved global sliding mode switching surface must still meet the three conditions for the establishment of the global sliding mode control surface; according to condition (1), the coefficient value of the exponential decay function should satisfy A c +B c +C c =1, and for the sake of convergence speed, let h(t z )=0, the above arrangement yields: Condition (3) needs to be met, h(t) at point t = t z The left derivative of must be equal to the right derivative, that is, h - '(t z )=h + '(t z )=0, we can get: In this way, the parameters in formula (13) should satisfy: Choose appropriate parameters α1, α2, α3 and C c Then, find t z In the design of sliding mode controller, the constant velocity reaching law is adopted as In summary, the improved global sliding mode control law is designed as follows:

4. The improved global sliding mode control method for the harness winding robot according to claim 3 is characterized in that: The specific implementation of step 4 includes the following steps: Considering the actual working conditions of the brushless DC motor drive system, sinusoidal signals and rectangular wave signals are selected as tracking target signals to investigate the dynamic adjustment and tracking effect of the controller; Matlab software is used to simulate the winding manipulator; the system simulation parameters are determined according to the motor nameplate parameters, the simulation step is set to 2ms, and the simulation time is 15s. In order to simulate the external disturbance effect, the total disturbance description is added to the simulation example as follows: Δ=5sin(2Πt)+100rand(1); The sinusoidal tracking signal is set as: oh d =200+25sin(0.4Πt) (18) The rectangular wave tracking signal is set as: In the formula, mod(t,4) means the remainder operation of t modulo 4; Three control methods (PID controller, global sliding mode controller and adaptive sliding mode controller) were adopted to carry out speed tracking simulation experiments of sinusoidal signals and rectangular wave signals respectively; finally, through simulation, the speed tracking comparison chart was analyzed, and the RMSE and MAXE indicators were calculated to draw conclusions.

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