A backlash oscillation suppression control method based on transmission torque estimation and compensation

Abstract

The present invention discloses a backlash oscillation suppression control method based on transmission torque estimation and compensation, which belongs to the field of gear transmission control, including: establishing a two-inertia model of an electromechanical servo system; designing a third-order nonlinear extended state observer to estimate the transmission torque: defining the third-order state variables of the third-order nonlinear extended state observer, rewriting the two-inertia model and determining the specific form of the third-order nonlinear extended state observer according to the boundedness of the transmission torque; designing a current value for compensating the backlash nonlinear disturbance according to the estimated value of the transmission torque; adding the current value for compensating the backlash nonlinear disturbance to the reference current to obtain the current loop input of the compensated servo system. The present invention can solve the limit cycle oscillation problem caused by backlash in the gear transmission system.

Description

Technical Field

[0001] The invention belongs to the field of gear transmission control, and in particular to a backlash oscillation suppression control method based on transmission torque estimation and compensation. Background Art

[0002] The clearance of gear transmission (hereinafter referred to as: backlash) is widely present in electromechanical servo systems, which can lead to limit cycle oscillation, mechanical wear and inaccurate positioning. If not resolved in time, the limit cycle may destroy the stability of the control system, and the resulting vibration will aggravate the internal mechanical wear of the system, thereby further expanding the backlash and forming a vicious circle.

[0003] Many researchers have proposed their own methods for the backlash problem. Some methods use online or offline identification methods to obtain an estimate of the backlash width, and then process it manually or in other ways, which is complicated to operate. Other researchers have provided an inverse feedforward compensation algorithm for the backlash problem, which effectively improves the tracking performance. However, this method is only applicable to the backlash hysteresis model based on the input end, and this model cannot accurately represent the oscillation phenomenon caused by the backlash in the mechanical structure. Some other research works have established a multi-model switching system to control each meshing and disengagement process in the gear transmission separately. The structure is similar to a switching control method based on the meshing state, but the multi-model switching system has discontinuities. Another group of researchers proposed state feedback compensation based on the pole configuration method or used a continuous differentiable function to approximate the backlash model, and then compensated according to the approximate model. This method has high requirements on the accuracy of the actual parameters of the system and is not very practical. In addition, treating the backlash as a disturbance and then using the disturbance compensation method is also a common method to suppress backlash oscillation. At present, the commonly used disturbance estimation methods for electromechanical servo systems include disturbance observer (DOB), extended state observer (ESO), sliding mode disturbance observer (SMDOB), equivalent input disturbance observer (EIDOB), etc. ESO uses an additional state variable in the augmented system to estimate external disturbances. Many researchers use ESO tools to solve the backlash problem. Some researchers set a coarse value based on the backlash in the feedforward compensation system of the observer to eliminate the error between the real value and the coarse value, and obtain the relevant parameters that affect the estimation accuracy. However, they study the hysteresis backlash model, which is not good in motion control. Other researchers use differential equations to model the gap to capture the main characteristics and approximate errors of the backlash, and then use ESO to process the approximate error. However, although the adaptive robust controller used has good performance, high tracking accuracy requires high feedback gain, which is not conducive to implementation. Some researchers have introduced new nonlinear functions in ESO to improve the estimation accuracy, but the impact of tooth clearance is only addressed by compensating for disturbances, and the effect is not particularly good. Summary of the invention

[0004] The purpose of the present invention is to provide a backlash oscillation suppression control method based on transmission torque estimation and compensation, aiming to solve the limit cycle oscillation problem caused by backlash in a gear transmission system.

[0005] The technical solution to achieve the purpose of the present invention is:

[0006] A backlash oscillation suppression control method based on transmission torque estimation and compensation, comprising:

[0007] Establish a two-inertia model of the electromechanical servo system;

[0008] Design a third-order nonlinear extended state observer to estimate the transfer torque: define the third-order state variables of the third-order nonlinear extended state observer, rewrite the two-inertia model and determine the specific form of the third-order nonlinear extended state observer based on the boundedness of the transfer torque;

[0009] According to the estimated value of the transmitted torque, the current value for compensating the nonlinear disturbance of the gap is designed;

[0010] The current value of the compensation gap nonlinear disturbance is added to the reference current to obtain the current loop input of the servo system after compensation.

[0011] Compared with the prior art, the present invention has the following significant advantages:

[0012] (1) The backlash disturbance compensation algorithm proposed in the present invention is easy to implement due to its simple structure and principle, requires fewer parameters, and has a wide range of applications.

[0013] (2) The real-time transmission torque required by the backlash compensation algorithm in the present invention is estimated by a third-order nonlinear extended state observer (ESO). Compared with the traditional ESO, the third-order nonlinear extended state observer (TNESO) has the advantage of high estimation accuracy. At the same time, the use of observer technology can also avoid the use of high-cost measurement methods such as torque sensors. The value of the transmission torque is calculated only through the state quantities that are easily measured by the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 A block diagram of a backlash oscillation suppression control method based on transmission torque estimation and compensation provided in an example of the present invention.

[0015] Figure 2 (ad) are the displacement and velocity curves during the backlash oscillation suppression process under the trapezoidal desired trajectory condition.

[0016] Figure 3 (ad) are the displacement and velocity curves during the backlash oscillation suppression process under the sinusoidal desired trajectory condition.

[0017] Figure 4 (ad) are the displacement and velocity curves during the backlash oscillation suppression process under the step desired trajectory condition.

[0018] Figure 5 (ac) are the estimated curves of the transmitted torque using two different estimation methods, TNESO and traditional ESO, under the same working condition. DETAILED DESCRIPTION

[0019] The present invention is further described below with reference to the accompanying drawings and specific embodiments. Represented as a variable The first derivative of Represented as a variable The second-order derivative of Represented as a variable The estimated value of Represented as a variable of error.

[0020] Combination Figure 1 The present invention provides a backlash oscillation suppression control method based on transmission torque estimation and compensation, which specifically includes the following steps:

[0021] Step 1: Establish a two-inertia model of the electromechanical servo system

[0022] The two-inertia model of the electromechanical servo system is expressed as:

[0023] (1)

[0024] In the formula, is the motor rotor angular displacement, is the motor rotor moment of inertia, is the equivalent viscous friction coefficient of the motor rotor, is the motor electromagnetic torque, is the motor electromagnetic torque coefficient, is the motor q-axis current, is the transmitted torque acting on the load side, is the equivalent stiffness of the transmission shaft from the motor to the load, is the transmission ratio from motor to load, is the load angular displacement, is the load moment of inertia, is the load equivalent viscous friction coefficient. Definition is the motor rotor angular velocity, is the motor rotor angular acceleration.

[0025] Step 2: Design a third-order nonlinear extended state observer (TNESO) to estimate the transferred torque

[0026] Define the third-order state variables of the third-order nonlinear extended state observer They are , , , then the two-inertia model in equation (1) can be written as:

[0027] (2)

[0028] Due to the constraints of the physical system, it can be understood that the transmitted torque is bounded, that is, ,in is a small positive constant. The TNESO design of system (2) is as follows:

[0029] (3)

[0030] in, is the design parameter of TNESO, is a nonlinear function of the design. The estimated errors are , , ,in , , Respectively , , The estimated value of , , Respectively , , The first derivative of the estimate.

[0031] Step 3: Design the nonlinear function of TNESO

[0032] (4)

[0033] in: , , is the design parameter of TNESO, is the estimation error, is a sign function.

[0034] Step 4: Design a backlash compensation algorithm based on the estimated value of the transmitted torque

[0035] After obtaining the estimated value of the transmitted torque in step 2, the current value that compensates for the nonlinear disturbance of the gap is designed:

[0036] (5)

[0037] in: is the transmitted torque estimated by the nonlinear extended state observer.

[0038] Step 5: Add the backlash compensation signal to the reference current

[0039] The current loop input of the compensated servo system is:

[0040] (6)

[0041] in, is the current reference value output by the speed loop, is the compensated current loop input, It is the reference current value for backlash disturbance compensation.

[0042] In this experiment, TNESO and nonlinear function (3) (4) contain three gain coefficients greater than 0: , , and the four nonlinear function design parameters are , , , , the sampling period is set to 0.0001 seconds. Since the trajectory required to be tracked during the operation of the electromechanical servo system is in various forms, the present invention selects three expected trajectories, namely trapezoidal, sine, and step, to verify the ability of the present invention to suppress oscillation caused by tooth backlash under different working conditions. Figure 2 (ad) is the backlash oscillation suppression process under the trapezoidal desired trajectory condition; Figure 3 (ad) is the backlash oscillation suppression process under the sinusoidal desired trajectory condition; Figure 4 (ad) is the backlash oscillation suppression process under the step desired trajectory condition; Figure 5 (ac) show the accuracy advantage of the TNESO used compared with the traditional ESO estimation method. Figure 1-4 It can be found that no matter what the expected trajectory is, the backlash oscillation suppression method proposed in the present invention can be well reflected. Figure 2 It shows a commonly used relatively smooth expected trajectory, which is widely used in industrial applications. The oscillation suppression effect under this trajectory is good. Figure 3 It shows that under relatively smooth sine and cosine curve conditions, the oscillation caused by the gap during tracking is very small, and after compensation, the speed curve can also become smoother. Figure 4 It is composed of a staircase-like step signal, and each change of the input value is a fast approximation process. It can be seen that the compensation algorithm can still work well on this trajectory. Figure 5 After giving the system a reference expected trajectory, the actual value of the transmitted torque is recorded and compared with the estimated results of the two observers, and the estimation errors of the two are plotted. The 0-0.15 second zoomed-in image of the motion can clearly compare the estimation accuracy of the traditional ESO and TNESO, and the estimation error of the latter is reduced by about 1 / 3.

[0043] The embodiments of the present invention are described in detail above, but the contents described are only preferred embodiments of the present invention and are not intended to limit the present invention.

Claims

1. A backlash oscillation suppression control method based on transmission torque estimation and compensation, characterized in that: include: Establish a two-inertia model of the electromechanical servo system: In the formula, θ m is the motor rotor angular displacement, J m is the motor rotor inertia, B m is the equivalent viscous friction coefficient of the motor rotor, T e =K t ·i q is the electromagnetic torque of the motor, K t is the motor electromagnetic torque coefficient, i q is the motor q-axis current, τ s is the transmitted torque acting on the load side, K s is the equivalent stiffness of the transmission shaft from the motor to the load, g r is the transmission ratio from motor to load, θ l is the load angular displacement, J l is the load moment of inertia, B l is the load equivalent viscous friction coefficient; definition is the motor rotor angular velocity, is the motor rotor angular acceleration; Design a third-order nonlinear extended state observer to estimate the transfer torque: define the third-order state variables of the third-order nonlinear extended state observer, rewrite the two-inertia model and determine the specific form of the third-order nonlinear extended state observer based on the boundedness of the transfer torque; According to the estimated value of the transmitted torque, the current value that compensates for the nonlinear disturbance of the gap is designed: is the reference current value for backlash disturbance compensation, is the transmission torque estimated by the nonlinear extended state observer; The current value of the compensation gap nonlinear disturbance is added to the reference current to obtain the current loop input of the servo system after compensation.

2. The backlash oscillation suppression control method based on transmission torque estimation and compensation according to claim 1 is characterized in that: The third-order nonlinear extended state observer is in the form of: where k tne1 ,k tne2 ,k tne3 >0 is the design parameter of the third-order nonlinear extended state observer, is a nonlinear function of the design, They represent the estimated values ​​of the third-order state variables x1, x2, and x3 of the third-order nonlinear extended state observer, Represent the first-order derivatives of the estimated values ​​of x1, x2, and x3, respectively. is the transmission torque estimated by the nonlinear extended state observer, x1 = θ m , x3=-τ s (g r J m ) -1 =-K s (θ m / g r -θ l )(g r J m ) -1 , is a nonlinear function of the design.

3. The backlash oscillation suppression control method based on transmission torque estimation and compensation according to claim 2 is characterized in that: Nonlinear functions for: Among them: ρ1, ρ2>0, 0<μ1<1, μ2>1 are the design parameters of the third-order nonlinear extended state observer, is the estimation error and sgn(·) is the sign function.

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