Track control method based on time-varying fuzzy sliding mode

Abstract

The invention relates to a trajectory control method based on a time-varying fuzzy sliding mode, and the method comprises the steps: building a system dynamic model, designing a high-order observer, estimating the position, speed, acceleration and lumped disturbance in real time, and avoiding the conservative property of a fixed gain through adaptive gain adjustment; constructing a fuzzy sliding mode control law, combining an equivalent control item and a switching control item, and dynamically adjusting an error weight by using a fuzzy logic system; and designing a dynamic amplitude limiter and a delay compensation mechanism, smoothly limiting the control instruction to the physical limit of the actuator, and feeding back the correction control instruction based on the observer to offset the delay influence. According to the invention, through time-varying fuzzy sliding mode control, adaptive observer gain and anti-saturation compensation, trajectory tracking precision and system robustness are effectively improved.

Description

Technical Field

[0001] The invention belongs to the field of motion control, and in particular relates to a trajectory control method based on a time-varying fuzzy synovial film. Background Art

[0002] Traditional synovial control methods have high-frequency jitter problems in robot trajectory tracking, and fixed gain observers need to rely on the upper limit of interference, which can easily lead to conservative or insufficient gain. In addition, actuator saturation and response delay will reduce control accuracy and even cause system instability. In the prior art, although the fuzzy logic system can partially suppress jitter, it is not combined with the adaptive observer gain and cannot dynamically respond to time-varying disturbances; anti-saturation compensation mostly uses hard limiting, which makes the control law boundary non-differentiable and exacerbates jitter. Summary of the invention

[0003] The present invention provides a trajectory control method based on a time-varying fuzzy sliding film, which comprises the following steps: Step 1, conduct system dynamics modeling of the robot, and its dynamic equation includes inertia matrix, Coriolis force matrix, gravity term and lumped disturbance term; Step 2: Design a high-order observer to estimate position, velocity, acceleration, and disturbance in real time by extending the state vector, and dynamically adjust the state estimate by nonlinear compensation terms and adaptive gains; Step 3, construct a time-varying fuzzy synovial control law, combine the equivalent control term and the switching control term, use the fuzzy logic system to dynamically adjust the tracking error weight, and use the nonlinear switching term to compensate for unknown interference; Step 4: Design a dynamic limiter to smoothly limit the control command to the physical limit of the actuator, obtain the anti-saturation control command, and correct the model through observer feedback.

[0004] Furthermore, the sliding surface is defined as a nonlinear combination of the second-order derivative of the tracking error and the output of the fuzzy logic system.

[0005] Furthermore, the observer gain satisfies: , where η i is the adaptive rate parameter, k i,max is the safety upper limit of the gain.

[0006] Furthermore, the observer gain satisfies: , where sat(⋅) is the saturation function, Δ is the dead zone threshold, η i is the adaptive rate parameter.

[0007] Furthermore, the input variables of the fuzzy logic system are configured as Gaussian membership functions, the rule base is dynamically constructed based on the error, and the gradient descent method is used to adjust the consequent parameters online.

[0008] Furthermore, the switching control items of the synovial control are: , where K 3 ,K 4 is the adaptive gain matrix, ε is the smoothing factor, B is the input transformation matrix, B + is the pseudo-inverse of matrix B, -B + Represented by the pseudo-inverse matrix B + The control input is reverse mapped, M is the inertia matrix, d is the lumped disturbance, β is the smoothness parameter, and σ is the sliding membrane surface.

[0009] Furthermore, the synovial surface of the synovial control includes a time-varying scaling term.

[0010] Furthermore, the dynamic limiter gradually saturates the control command via a smoothing function.

[0011] The present invention also provides a trajectory control system based on a time-varying fuzzy sliding film, which is used to execute the above method.

[0012] Beneficial technical effects: The adaptive gain observer adjusts the gain in real time, combines the fuzzy logic system to optimize the error weight, and designs a dynamic limiter and delay compensation mechanism to smooth the transition instructions. At the same time, the observer feedback correction model is used to improve the state estimation accuracy. This method can significantly reduce jitter, enhance anti-interference ability and suppress actuator saturation. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Attached Figure 1 The figure is a schematic diagram of trajectory control based on time-varying fuzzy sliding film according to the present invention.

[0014] Attached Figure 2 : is a tracking diagram of the robot joint angle error according to the present invention. DETAILED DESCRIPTION

[0015] like Figure 1 As shown, this embodiment provides a trajectory control method based on a time-varying fuzzy sliding film, which includes the following steps: Step 1: Model the system dynamics of the robot, and its dynamic equations include inertia matrix, Coriolis force matrix, gravity term and lumped disturbance term.

[0016] Step 2, high-order observer design: The definition includes the robot end position x 1 , speed x 2 , acceleration x 3 The extended state vector x is used to construct a high-order observer:

[0017] Among them, α 1 ,α 2,α 3 is the homogeneity parameter, Γ 1 , Γ 2 is nonlinear compensation, which is used to offset the model error. The nonlinear compensation term Γ 1 , Γ 2 By correcting the inertia matrix, Coriolis force and delay compensation torque, the state estimation accuracy is improved. u is the generalized control input, k 1 ,k 2 ,k 3 is the observer gain, which is used to determine the estimated speed. The observer gain is an adaptive gain, which can be adjusted in real time according to the observation error. For example, when the gain does not reach the safety upper limit, the gain is dynamically increased according to the power function of the error, or the saturation function is used to constrain the gain adjustment range. Specifically, it can be: , where η i is the adaptive rate parameter, which is used to control the gain adjustment speed, for example, it can be 0.5, k i,max is the safety upper limit of the gain to prevent excessive gain due to noise; alternatively, the observer gain k i It can be adjusted by the saturation function, that is, , where sat(⋅) is the saturation function, Δ is the dead zone threshold, which can be taken as 5% of the tracking error. i Beyond Δ, gain k i At rate η i Linear growth.

[0018] in the formula is a nonlinear function used to accelerate convergence, where sign is the sign function.

[0019] Furthermore, a time-varying scaling term can be introduced in the observer design, specifically:

[0020] Among them, θ is the scaling parameter, which controls the decay rate of the time-varying scaling factor. The larger θ is, the faster the scaling factor decays over time, and the faster the observer dynamic component is suppressed. κ is the power decay parameter, which controls the exponential decay rate of the nonlinear gain term. The larger κ is, the faster the gain term converges. In the initial stage, high gain quickly tracks the error, and low gain suppresses noise in the steady state stage. The homogeneity parameter α i , determines the convergence characteristics of the nonlinear term. When the error is large, the gain is high, and when the error is small, the gain is low.

[0021] By introducing the time-varying scaling term, in the initial stage, that is, when t is small, the observer dynamic equation retains the original fast response characteristics, the nonlinear gain is high, and the error convergence is accelerated, thereby ensuring that the observer quickly tracks the real state and improving the initial tracking accuracy. In the steady-state stage, that is, when t is large, the high-frequency dynamic components of the observer (such as oscillations caused by noise) are suppressed, the nonlinear gain is reduced, and the jitter caused by excessive gain is avoided, ensuring that the observer output tends to be smooth, and working together with the dynamic limiter to further reduce the risk of actuator saturation.

[0022] By adaptively adjusting the gain, there is no need to predetermine the upper limit of the interference to determine the fixed gain, and the present invention can dynamically adjust the gain according to the real-time error to avoid being overly conservative or insufficient.

[0023] Step 3, fuzzy synovial control: The sliding surface is designed as a nonlinear combination of the second-order derivative of the tracking error and the output of the fuzzy logic system, specifically: , where e is the tracking error, i.e. the difference between the actual position and the target position, γ 1 ,γ 2 is a nonlinear index used to control the convergence speed, K 1 ,K 2 Is a diagonal matrix used to determine the weight of the error term. FLS (ξ) is the output of the fuzzy logic system, ξ is the input variable, and the specific calculation steps of the output are: (1) Define the input variables including tracking error, error derivative and integral; (2) Membership function configuration: Three Gaussian membership functions are defined for each input variable; (3) Construct a fuzzy rule base, which is dynamically constructed based on the error; (4) Defuzzification: Use the centroid method to calculate the output Φ FLS (ξ), where the activation weight of a single rule can be taken as the minimum product of the input membership, and the initial value of the consequent parameter is set empirically and adjusted online using the gradient descent method.

[0024] The control law is: τ=τ eq +τ sw , τ eq is the equivalent control term, τ sw is a switching control term used to compensate for unknown disturbances and unmodeled states. , where B, M, and d parameters are set as shown in the dynamic model, B is the input transformation matrix, and B + is the pseudo-inverse of matrix B, -B + Represented by the pseudo-inverse matrix B + Reverse mapping of the control input, M is the inertia matrix, d is the lumped disturbance, K3 ,K 4 is the adaptive gain matrix, β is the smoothness parameter, β∈(0,1), which is used to control the smoothness of the switching term, and ε is the smoothing factor, which is used to determine the transition interval of the tanh function.

[0025] Alternatively, on the basis of retaining the output of the fuzzy logic system, a fractional step sliding surface and multi-scale gain can be constructed in the sliding film control. The sliding film surface can be specifically:

[0026] Where D t ζ is a fractional differential, used to smooth historical errors and suppress high-frequency noise, ζ is the order, ζ∈(0,1), Λ k is a multi-scale gain matrix, which assigns weights to errors at different levels, such as position error, velocity error, and integral error. The multi-scale gain Λ k e |k / m| The output of the fuzzy logic system can be combined to dynamically adjust the weights of each level to adapt to different working conditions, such as sudden load or friction changes, and enhance adaptability to different dynamics.

[0027] By introducing time-varying scaling terms and fractional step sliding surfaces, combined with the flexibility of fuzzy logic systems, the control scheme significantly improves the anti-disturbance capability, vibration suppression effect and parameter robustness while retaining the advantages of time-varying fuzzy sliding films. The observer and sliding surface are adaptively adjusted in different control stages to balance fast response and steady-state smoothness. Multi-scale gains and fractional order differentials achieve refined error processing to adapt to complex interference scenarios.

[0028] In order to match the dynamic characteristics of the fractional-order sliding surface and avoid gain conflict, the switching control term τ sw The corresponding adjustments are:

[0029] The parameter definitions are the same as above.

[0030] The synovial control of the present invention can significantly reduce high-frequency chattering, and can also enhance anti-interference capability through feed-forward compensation.

[0031] Step 4: Anti-saturation delay compensation, design a dynamic limiter, generate anti-saturation control instructions, and perform delay compensation: Limit the control command within the physical limit of the actuator to avoid saturation or damage of the actuator due to excessive command. The observer may make wrong estimates due to unrealistic commands. Therefore, a dynamic limiter can be designed to generate anti-saturation control commands. The dynamic limiter gradually saturates the control command through a smoothing function to avoid the boundary non-differentiable problem caused by hard limiting. The anti-saturation control command can be: , Alternatively, the anti-saturation control instruction may be: , where τ max is the maximum value of the actuator torque, τ is the original control command, δ is the saturation factor, which is used to adjust the curvature of the limiting transition zone and its value can be 1.

[0032] After dynamic limiting is implemented, when τ is much smaller than τ max When the limit output τ cmd Approximately equal to τ, retaining the linear characteristics of the original instruction; when τ is much larger than τ max When the limit output τ cmd Approximately equal to τ max , achieving progressive saturation; thus avoiding the control law chattering caused by traditional hard limiting at the boundary.

[0033] Delay compensation compares the original command with the limit command in real time, estimates the delay torque and feeds it back to the observer to correct the model error. Delay compensation can be designed as:

[0034] Among them, τ max is the maximum value of the actuator torque, T m is the motor time constant, reflecting the actuator response speed, k d is the convergence coefficient, k d >0, which determines the convergence speed of the delay estimation. By converting the original control command τ from the sliding mode controller into the limited command τ cmd , and sent to the actuator, by comparing τ cmd The torque after delay compensation is estimated in real time with τ, and this value is fed back to the controller so that it can adjust the command in advance to offset the delay effect. At the same time, the torque after delay compensation is introduced into the observer, thereby further improving the state estimation accuracy of the observer, specifically: , where M, C, G, F are the inertia matrix, Coriolis force matrix, gravity term, and friction term respectively, and B is the input transformation matrix. By modifying the model, the accuracy of state estimation is improved.

[0035] The gain is adjusted in real time through an adaptive gain observer, the error weight is optimized by combining a fuzzy logic system, and a dynamic limiter and delay compensation mechanism are designed to smooth the transition instructions. At the same time, the model is corrected through observer feedback to improve the state estimation accuracy. This method can significantly reduce jitter, enhance anti-interference ability and suppress actuator saturation. Figure 2 As shown, as the control proceeds, the tracking error of the joint angle decreases rapidly.

[0036] In the several embodiments provided by the present invention, it should be understood that the disclosed methods can be implemented in other ways. For example, the above-described embodiments of the invention are merely schematic. For example, the division of method modules and steps is only a logical function division, and there may be other division methods in actual implementation. The modules and steps described as separate components or separate steps may or may not be physically separated, and the components displayed as modules may or may not be physical modules, which may be located in one place or distributed on multiple network modules. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment.

[0037] In addition, each functional module and step in each embodiment of the present invention may be integrated into a processing module or method, or each module or step may exist physically separately, or two or more modules or steps may be integrated into one module or method. The above-mentioned integrated module may be implemented in the form of hardware or in the form of hardware plus software functional modules.

[0038] It is obvious to a person skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the essential characteristics of the present invention.

[0039] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the spirit and scope of the technical solution of the present invention.

Claims

1. A trajectory control method based on time-varying fuzzy sliding film, characterized in that: The following steps are involved: Step 1, conduct system dynamics modeling of the robot, and its dynamic equation includes inertia matrix, Coriolis force matrix, gravity term and lumped disturbance term; Step 2: Design a high-order observer to estimate position, velocity, acceleration, and disturbance in real time by extending the state vector, and dynamically adjust the state estimate by nonlinear compensation terms and adaptive gains; Step 3, construct a time-varying fuzzy synovial control law, combine the equivalent control term and the switching control term, use the fuzzy logic system to dynamically adjust the tracking error weight, and use the nonlinear switching term to compensate for unknown interference; Step 4: Design a dynamic limiter to smoothly limit the control command to the physical limit of the actuator, obtain the anti-saturation control command, and correct the model through observer feedback.

2. The method according to claim 1, characterized in that The sliding surface is defined as the nonlinear combination of the second-order derivative of the tracking error and the output of the fuzzy logic system.

3. The method according to claim 1, characterized in that: The observer gain satisfies: , where η i is the adaptive rate parameter, k i,max is the safety upper limit of the gain.

4. The method according to claim 1, characterized in that The observer gain satisfies: , where sat(⋅) is the saturation function, Δ is the dead zone threshold, η i is the adaptive rate parameter.

5. The method according to claim 1, characterized in that The input variables of the fuzzy logic system are configured as Gaussian membership functions, the rule base is dynamically constructed based on the error, and the gradient descent method is used to adjust the consequent parameters online.

6. The method according to claim 1, characterized in that The switching control items of the synovial control are: , where K3, K4 are adaptive gain matrices, ε is the smoothing factor, B is the input transformation matrix, B + is the pseudo-inverse of matrix B, -B + Represented by the pseudo-inverse matrix B + The control input is reverse mapped, M is the inertia matrix, d is the lumped disturbance, β is the smoothness parameter, and σ is the sliding membrane surface.

7. The method according to claim 1, characterized in that The synovial surface of the synovial control contains a time-varying scaling term.

8. The method according to claim 1, characterized in that The dynamic limiter gradually saturates the control command via a smoothing function.

9. A trajectory control system based on time-varying fuzzy synovial film, characterized in that: Used to execute the method according to any one of claims 1 to 8.

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