A method for eliminating backlash and synchronization for multi-motor drive system

Abstract

The application provides a kind of for the method for eliminating clearance and synchronization of multi-motor drive system, belong to electromechanical control technical field, including the establishment of considering the dynamics model of gear clearance nonlinearity, load position is estimated using hysteresis model, and then improve dynamic clearance elimination method, introduce S-shaped transition curve, based on the characteristics of clearance elimination curve and its complementary curve, realize the coupling control of clearance elimination and speed synchronization, when running in one direction, speed compensation is carried out through differential negative feedback, clearance elimination control is carried out when starting commutation, system disturbance is observed and compensated using linear extended state observer, a predictive function speed controller based on virtual average motor model is established, through the discrete speed prediction model and the construction of cost function, system rolling optimization control is realized, and the performance of multi-motor drive system is improved.The application adopts the above-mentioned method for eliminating clearance and synchronization of multi-motor drive system, solves the problem of control precision decline caused by gear clearance phenomenon in multi-motor drive system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of electromechanical control, and particularly to a method for eliminating backlash and synchronization of a multi-motor driving system. BACKGROUND

[0002] In a multi-motor driving system, a gear transmission mechanism is often adopted, but this method inevitably introduces the phenomenon of backlash. The backlash phenomenon refers to the nonlinear position error caused by the gap between the gears during gear transmission. Specifically, when the system driving torque starts to act or changes direction, the phenomenon of empty return occurs, that is, the driving torque cannot be immediately and completely transmitted to the driven part, so that the driven part loses control for a short time, and then a deviation is generated between the input end and the output end of the backlash, which directly increases the output error of the system, and significantly negatively affects the control accuracy of the multi-motor driving system, especially in application scenarios that require accurate control of the load position.

[0003] In order to cope with the challenge of the backlash phenomenon to high-precision control tasks, researchers have been committed to improving the motor control scheme in order to eliminate or at least significantly reduce the influence of backlash on position control accuracy. The multi-motor synchronous backlash elimination mechanism emerged as the times required, and gradually gained wide application in the field of high-precision servo control. In order to completely eliminate the gap in the transmission mechanism, researchers have explored the method of applying a bias torque between the two motors. At present, the way to apply a bias torque mainly includes two kinds of constant bias torque and dynamic bias torque. The constant bias torque method is relatively simple and easy to implement. However, its significant disadvantage is that even after the system as a whole reaches a stable state, the bias torque still exists. This not only affects the synchronization performance of the motor, but also when the motor is reversing, the constant bias torque cannot effectively cope with the impact brought by the reversal, thereby causing the accuracy and stability of the system to decrease.

[0004] In order to overcome the limitations of the constant bias torque, researchers have proposed a dynamic bias torque method. This method timely eliminates the bias torque after the system passes through the backlash area, so that the driving system can restore to the common driving state of the multi-motor. Although the dynamic bias torque has made progress in eliminating backlash, as a piecewise linear method, it is easy to produce mutations at the region switching point, resulting in poor transition characteristics, which may cause system oscillation. SUMMARY

[0005] The purpose of the present application is to provide a method for eliminating backlash and synchronization of a multi-motor driving system, which solves the problem of control accuracy decrease caused by the backlash phenomenon in a multi-motor driving system, and provides an effective method for eliminating backlash and synchronization to improve the control performance of the system and the accuracy of the load position.

[0006] In order to achieve the above object, the application provides a method for eliminating backlash and synchronization of a multi-motor drive system, comprising the following steps:

[0007] S1, establishing a multi-motor drive system dynamics model based on a backlash dead zone model: considering the influence of gear backlash nonlinearity, a dynamics model containing motor electromagnetic torque, contact torque and load speed parameters is established;

[0008] S2, load position estimation: a hysteresis model is used to estimate the load position, and the load position estimation value is used in the control algorithm;

[0009] S3, improving the mathematical model of the dynamic backlash elimination method: on the basis of the existing dynamic backlash elimination method, an S-shaped function is introduced as a transition curve to obtain an improved dynamic backlash elimination method mathematical model;

[0010] S4, coupling control of multi-motor drive system backlash elimination and synchronization: differential negative feedback is used to realize multi-motor speed synchronization, and according to the backlash nonlinear curve and the complementary curve, speed compensation adjustment is carried out during one-way operation, and the control mode changes to the control mode in which the backlash elimination control plays a main role during starting and reversing;

[0011] S5, linear extended state observer anti-disturbance control: by rewriting the virtual average motor dynamic equation, the system is regarded as a whole containing various disturbances, the state equation containing the total disturbance of the system is established, and the linear extended state observer is constructed to observe and compensate the disturbance;

[0012] S6, establishing a predictive function speed controller based on a virtual average motor model: the virtual average motor dynamic equation is discretized using the forward Euler method to obtain a speed prediction model, based on the error sequence between the actual speed and the predicted speed, a cost function is constructed to realize system rolling optimization control.

[0013] Preferably, the multi-motor drive system dynamics model based on the backlash dead zone model in S1 is expressed as:

[0014]

[0015] Wherein, J m is the moment of inertia of the motor, J L is the moment of inertia of the load, ω1 is the speed of the first motor, ω2 is the speed of the second motor, ω L is the speed of the load, T e1 is the electromagnetic torque of the first motor, T e2 is the electromagnetic torque of the second motor, T L1 , T L2 are the contact torques between the pinion and the gear, T g is the gear torque, T L is the load torque, and Bm B is the motor damping coefficient L r is the load damping coefficient g R is the pinion radius g R is the gear radius

[0016] Preferably, the contact torque expression is:

[0017]

[0018]

[0019] wherein K g B is the gear stiffness coefficient g b is half of the gear backlash width, r g R is the pinion radius g R is the gear radius, θ1, θ2 and θ g are the positions of the No. 1 motor, No. 2 motor and load, respectively.

[0020] Preferably, the hysteresis model expression in S2 is:

[0021]

[0022] wherein N is the load position estimate s R is the gear ratio

[0023] Preferably, the improved dynamic backlash elimination method mathematical model expression in S3 is:

[0024]

[0025]

[0026]

[0027]

[0028] wherein i qref is the speed loop output reference current, i qref1 , i qref2 are the reference currents of the two motors after backlash elimination control, I0, I1 and I2 are control constraints, I0 is the reference current, I1 is the minimum current threshold, and I2 is the maximum current threshold. s is a nonlinear transition function, and t is a normalized parameter.

[0029] Preferably, the virtual average motor dynamic equation in S5 is:

[0030]

[0031] wherein ω is the virtual average motor speed, K T is the motor torque coefficient, i q is the q-axis actual current, T0 is the transmission torque between the large gear and the small gear, is the q-axis reference current, d(t) is the system disturbance to be observed.

[0032] Preferably, the state equation of the total system disturbance in S5 is:

[0033]

[0034]

[0035] wherein x1 is the virtual average motor speed; h is the change rate of the total system disturbance.

[0036] Preferably, the state observer expression in S5 is:

[0037]

[0038] wherein β1 is the gain value of observing and estimating the virtual average motor speed x1, β2 is the gain value of observing and estimating the total system disturbance x2, z1 is the estimated value of x1, and z2 is the estimated value of x2.

[0039] Preferably, the speed prediction model expression in S6 is:

[0040]

[0041] wherein K T is the motor torque coefficient, ω m (k) is the kth step speed value, T s is the speed loop sampling time.

[0042] Preferably, the cost function expression in S6 is:

[0043]

[0044] E(k) = [1...1] T e(k);

[0045] wherein r1 is the weight coefficient of the tracking error, r2 is the weight coefficient of the input increment, and E(k) is the error sequence of the actual speed and the predicted speed.

[0046] Therefore, the application adopts the above-mentioned method for eliminating backlash and synchronization in a multi-motor driving system, and the technical effects are as follows:

[0047] 1, Improved control strategy and model: an improved dynamic bias torque and speed synchronization coupling control strategy for multi-motor drive system is proposed, a system model based on gear gap dead zone model is established, and a prediction function speed controller is designed to eliminate the influence of transmission gear gap and improve the response speed and positioning accuracy.

[0048] 2, Dynamic bias torque gap elimination control: S-shaped function is introduced as a transition curve to avoid mechanical impact and vibration caused by sudden torque change.

[0049] 3, Speed synchronization and gap elimination coupling: speed compensation is performed during one-way operation, and gap elimination control is converted during start and reversal to ensure the combined requirements of gap elimination and synchronization.

[0050] 4, Prediction function control: prediction function control can balance speed and no overshoot, adapt to the application scenario of gear transmission, track curve start, stop slow, middle fast, reduce gear wear, and respond quickly.

[0051] 5, Extended state observer: the torque transmission characteristics between gear gaps are introduced, and the extended state observer is used to improve the anti-disturbance ability of the system, and solve the influence of other nonlinear factors on the tracking performance of the system after the elimination of gear gap.

[0052] 6, Virtual average motor model: the average value of the two motor speeds is used as the speed feedback value, so that the two motor speeds quickly approach and equal, compared with the traditional two speed controllers in parallel, the system calculation amount is greatly simplified. BRIEF DESCRIPTION OF DRAWINGS

[0053] Fig. 1 The mechanical structure diagram of the multi-motor drive system of the application;

[0054] Fig. 2 The system control block diagram of the application;

[0055] Fig. 3 The motor current curve under the improved dynamic bias torque of the application;

[0056] Fig. 4 The bias current curve of the application;

[0057] Fig. 5 The load position error curve comparison diagram under different control strategies before and after gap elimination of the application;

[0058] Fig. 6 The motor speed curve comparison diagram after gap elimination of the application. DETAILED DESCRIPTION

[0059] The technical solutions of the application are further described below through the drawings and examples.

[0060] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0061] Example 1

[0062] like Figs. 1-2 As shown, this invention provides a backlash elimination and synchronization method for multi-motor drive systems. Step one, establishing a dynamic model of the multi-motor drive system based on a backlash dead zone model, is as follows:

[0063]

[0064] Among them, J m J is the moment of inertia of the motor. L Let ω be the load's moment of inertia, ω1 be the rotational speed of motor 1, and ω2 be the rotational speed of motor 2. L T is the rotational speed of the load. e1 T represents the electromagnetic torque of motor number 1. e2 T represents the electromagnetic torque of motor number 2. L1 T L2 These are the contact torques, T, between the pinion and the gear. g For the torque of the large gear, T L For load torque, B m B is the motor damping coefficient. L r is the load damping coefficient. g R is the radius of the pinion. g For the large gear radius.

[0065] Considering the nonlinear effect of gear backlash, the expression for the contact torque between the large and small gears is a dead zone function, specifically:

[0066]

[0067]

[0068] Among them, K g B is the gear stiffness coefficient. g Here, b is the gear damping coefficient, and r is half the backlash width. g R is the radius of the pinion. g For the large gear radius, θ1, θ2 and θ g These are the positions of motor 1, motor 2, and the load, respectively.

[0069] Step 2: Estimate the load location using a hysteresis model, and then use the estimated load location in the control algorithm. The expression for the hysteresis model is:

[0070]

[0071] where, N is the load position estimate, N s is the size gear transmission ratio.

[0072] There are two motors in the system, so by the above formula, the estimate of the load position of the two motors can be obtained The two estimates are averaged as the estimate of the load position

[0073]

[0074] When the multi-motor system is added to the anti-backlash module, the effect of backlash on the system can be ignored, and the estimate of the load position is:

[0075]

[0076] In a multi-motor system, for cost-effectiveness considerations, the load end often does not install a position sensor. However, the control target of the system depends on accurately knowing the position and speed of the load. To solve this problem, the information of other parts of the system needs to be relied on to indirectly estimate the position of the load.

[0077] The present invention proposes to use a hysteresis model to estimate the load position, and integrate this estimate into the control algorithm. In a multi-motor system, due to factors such as friction and elastic deformation of mechanical components, the relationship between the load position and the motor position may exhibit hysteresis characteristics. By constructing and applying a hysteresis model, the present invention can more accurately estimate the load position, thereby improving the accuracy and performance of the control system. The model dynamically predicts the load position based on the values of the motor position sensor and other possible system state information, and this estimate is then used as the basis for the control algorithm to achieve accurate control of the load position and speed.

[0078] Step three, on the basis of the existing dynamic anti-backlash method, an S-shaped function is introduced as a transition curve to obtain the mathematical model of the improved dynamic anti-backlash method.

[0079] The basic principle of the existing dynamic anti-backlash method is to establish a bias current between the two motors, thereby forming an equivalent reverse bias torque, so that the large gear is subjected to tightening action from the bias torque, and the bias torque is eliminated after passing through the backlash, so that the drive system returns to the multi-motor common driving state. This piecewise linear method is prone to mutations at region switching points, has poor transition characteristics, and can cause system oscillation. The present invention improves on this basis by introducing an S-shaped function as a transition curve, avoiding the mutation phenomenon at the region switching point, and reducing the mechanical impact and vibration caused by torque mutation.

[0080] The mathematical model expression of the improved dynamic anti-backlash method is:

[0081]

[0082]

[0083]

[0084]

[0085] wherein, i qref is the reference current of the speed loop output, i qref1 , i qref2 are the reference currents of the two motors after the clearance elimination control, I0, I1, I2 are control constraints, I0 is the reference current, I1 is the minimum current threshold, and I2 is the maximum current threshold. s is a nonlinear transition function, and t is a normalized parameter.

[0086] The control constraints satisfy:

[0087] Step four, the working mode of differential negative feedback is adopted to realize the speed synchronization of the multiple motors, the speed difference is obtained by subtracting the speeds of the two motors, the compensation amount is calculated by the PI controller and added to the current command input end of the two motors to correct the speeds of the two motors at the same time.

[0088] If the adjustment effect of the coefficient on the output amplitude is not considered in the clearance elimination module, the clearance elimination nonlinear curve is equivalent to outputting 1 near the 0 value area and outputting 0 in other areas after a certain transition section. The complementary curve of the clearance elimination curve is calculated, that is, output 0 near the 0 value area and output 1 in other areas after the transition section. Multiplying the compensation adjustment value of the speed by the nonlinear output can realize the speed compensation adjustment during unidirectional operation, and change to the control mode in which the clearance elimination control plays a main role during starting and reversing.

[0089] Step five, by rewriting the virtual average motor dynamic equation, the system is regarded as a whole containing various disturbances, the state equation containing the total disturbance of the system is established, and the linear extended state observer is constructed to observe and compensate the disturbance.

[0090] The virtual average motor model is constructed, and the mathematical model is:

[0091]

[0092] The virtual average motor dynamic equation is:

[0093]

[0094] wherein, ω is the speed of the virtual average motor, K T is the motor torque coefficient, i qis the actual current of q-axis, T0is the transmission torque between the size gear, T e is the transmission torque of electromagnetic torque, is the reference current of q-axis, d(t) is the system disturbance to be observed.

[0095] The sum of each disturbance is observed and compensated as the total disturbance by using the linear state extended observer. The state equation containing the total disturbance of the system is:

[0096]

[0097]

[0098] wherein x1is the virtual average motor speed; h is the change rate of the total disturbance of the system.

[0099] The state observer expression constructed is:

[0100]

[0101] wherein β1is the gain value of observing and estimating the virtual average motor speed x1, β2is the gain value of observing and estimating the total disturbance x2of the system, z1is the estimated value of x1, and z2is the estimated value of x2.

[0102] Step six, the virtual average motor dynamic equation is discretized by using the forward Euler method to obtain the speed prediction model, a cost function is constructed based on the error sequence between the actual speed and the predicted speed, and the system rolling optimization control is realized.

[0103] According to the virtual average motor dynamic equation, the speed prediction model of the future P sampling periods at the kth time is obtained by using the forward Euler method:

[0104] W m (k)=[ω m (k+1)...ω m (k+P)] T ;

[0105] satisfies

[0106] The above formula is rewritten into vector form by sorting the entire prediction time domain:

[0107]

[0108] wherein K T is the motor torque coefficient, ω m (k) is the speed value at the kth step, T s is the speed loop sampling time.

[0109] The cost function is constructed:

[0110]

[0111] wherein, r1 is the weight coefficient of tracking error, r2 is the weight coefficient of input increment, E(k) = [1...1] T e(k) is the error sequence of actual speed and predicted speed.

[0112] The input of the optimization control is the virtual average motor speed, and the output is the optimal reference current of the multi-motor system. The optimization problem is solved for each period, and the rolling optimization control of the system is realized.

[0113] The optimal reference current sequence of future P steps is obtained by solving the optimization problem And the first component of is applied to the system at k+1 time.

[0114] At k+1 time, the future output of the system is predicted with the newly obtained motor speed value, and the optimization problem is solved. The first component of the optimal reference current sequence is applied to the system at k+2 time. This cycle is repeated, and in each control period, the optimal reference current value is found by solving the optimization problem, so as to realize rolling optimization control.

[0115] As can be seen from the current curve shown in Figs. 3-4 , when the system enters the forward starting process, from the 0 point, there is an equivalent reverse bias torque between the two motors. The gear connected with the No. 1 motor is in positive contact with the large gear, and the gear connected with the No. 2 motor is in reverse contact with the large gear. The large gear is under tightening action and remains stationary. Then the torque of the No. 1 motor begins to increase, the torque of the No. 2 motor decreases, and the combined torque between the two motors begins to increase in the positive direction. The large gear rotates in the positive direction until the current command is I1, and the torque of the No. 2 motor is 0. The large gear is driven by the No. 1 motor and begins to disengage from the gear of the No. 2 motor. The gear of the No. 2 motor can quickly pass through the gear gap and engage with the large gear in the positive direction. At this time, the two motors jointly drive the large gear to rotate. When the current command is I2, the bias torque disappears completely, and the two motors output equal positive torques to jointly drive the load to rotate in the positive direction. When the system enters the reversing process, from the current command of -I2, the two motors begin to appear bias torque, and the bias torque changes with the curve until the combined torque of the two motors is greater than 0. The large gear begins to accelerate in the positive direction, and the reversing is completed.

[0116] As shown in Fig. 5 ​​As shown in the figure, the load position error curve fluctuates greatly before the backlash elimination, which indicates that the nonlinear error caused by the backlash phenomenon is significant in the multi-motor driving system without the application of the backlash elimination control strategy, and the control accuracy of the load position is low. After the backlash elimination, the load position error curve becomes obviously smoother, and the fluctuation range is greatly reduced. After the application of the backlash elimination and synchronization method of the present application, the influence of the backlash on the system is effectively eliminated or reduced, and the control accuracy of the load position is significantly improved.

[0117] As shown in the figure, the speed curves of the two motors almost completely coincide after the backlash elimination, which indicates that the speed synchronization between them is well guaranteed, the speed curve is smooth and has small fluctuation, and the system runs more stably after the backlash elimination, reducing the phenomena of the backlash and speed mutation caused by the backlash. Fig. 6

[0118] Therefore, the present application adopts a backlash elimination and synchronization method for a multi-motor driving system, solves the problem of the decline in the control accuracy caused by the backlash phenomenon in the multi-motor driving system, and provides an effective backlash elimination and synchronization method to improve the control performance of the system and the accuracy of the load position.

[0119] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application but not to limit it, although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that: it can still modify or equivalently replace the technical solutions of the present application, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present application.​

Claims

1. A backlash elimination and synchronization method for a multi-motor drive system, characterized in that, The method comprises the following steps: S1, establishing a multi-motor drive system dynamics model based on a gear gap dead zone model: considering the influence of gear gap nonlinearity, a dynamics model containing motor electromagnetic torque, contact torque and load speed parameters is established; S2, load position estimation: a hysteresis model is used to estimate the load position, and the load position estimation value is used in the control algorithm; S3, improved dynamic gap elimination method mathematical model: the existing dynamic gap elimination method is improved, and an S-shaped function is introduced as a transition curve to obtain an improved dynamic gap elimination method mathematical model; S4, coupling control of multi-motor drive system gap elimination and synchronization: the differential negative feedback mode is used to realize the speed synchronization of the multi-motor, and according to the gap elimination nonlinear curve and the complementary curve, the speed compensation adjustment is carried out during the one-way operation, and the gap elimination control mode becomes the main control mode during the starting and reversing; S5, linear extended state observer anti-disturbance control: by rewriting the virtual average motor dynamic equation, the system is regarded as a whole containing various disturbances, the state equation containing the total disturbance of the system is established, and the linear extended state observer is constructed to observe and compensate the disturbance; S6, establishment of a predictive function speed controller based on a virtual average motor model: the virtual average motor dynamic equation is discretized using the forward Euler method to obtain a speed prediction model, a cost function is constructed based on the error sequence between the actual speed and the predicted speed, and rolling optimization control of the system is realized.

2. The method of claim 1, wherein, The expression of the multi-motor drive system dynamics model based on the gear gap dead zone model in S1 is: ； wherein, Jm is the moment of inertia of the motor, JL is the moment of inertia of the load, ωm is the rotational speed of the motor, ωL is the rotational speed of the load, ωL is the rotational speed of the load, Tm is the electromagnetic torque of the motor, Tm is the electromagnetic torque of the motor, , Tc is the contact torque between the pinion and the gear, Tg is the gear torque, TL is the load torque, Cm is the motor damping coefficient, CL is the load damping coefficient, Rpin is the pinion radius, Rg is the gear radius.

3. The method of claim 2, wherein, The expression of the contact torque is: ； ； wherein, is the gear stiffness coefficient, is the gear damping coefficient, is half of the gear backlash, is the pinion radius, is the gear radius, , and are the positions of the No. 1 motor, No. 2 motor, and load, respectively.

4. The method of claim 1, wherein, The expression of the hysteresis model in S2 is: ； wherein, is a load position estimate.

5. The method of claim 1, wherein, The expression of the improved dynamic gap elimination method mathematical model in S3 is: ； ； ； ； wherein, is the reference current output for the speed loop, , are the reference currents for the two motors after the back lash control, , , are the control constraints, is the reference current, is the minimum current threshold, is the maximum current threshold, s is the non-linear transition function, t is the normalization parameter.

6. The method of claim 1, wherein, The virtual average motor dynamic equation in S5 is: ； wherein, is the virtual average motor speed, is the motor torque coefficient, is is the shaft actual current, is the transmission torque between the pinion and the ring gear, is is the shaft reference current, is the system disturbance to be observed.

7. The method of claim 1, wherein, The state equation containing the total disturbance of the system in S5 is: ； ； wherein, is the rate of change of the total system disturbance.

8. The method of claim 1, wherein, The expression of the state observer in S5 is: ； wherein is a gain value for observing and estimating the virtual average motor speed is a gain value for observing and estimating the total disturbance of the system is a gain value for observing and estimating the total disturbance of the system is an estimate of is an estimate of is an estimate of is an estimate of is an estimate of 9. The method of claim 1, wherein, The expression of the speed prediction model in S6 is: ； wherein, is the motor torque coefficient, is the first step speed value, is the speed loop sampling time.

10. The method of claim 1, wherein, The expression of the cost function in S6 is: ； ； wherein, is a weight coefficient for the tracking error, is a weight coefficient for the input increment, is an error sequence of the actual rotational speed and the predicted rotational speed.

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