Anti-backlash and synchronization method for multi-motor driving system

Abstract

The invention provides an anti-backlash and synchronization method for a multi-motor driving system, which belongs to the technical field of electromechanical control, and comprises the following steps of: establishing a dynamic model considering backlash nonlinearity, estimating a load position by adopting a hysteresis model, further improving a dynamic anti-backlash method, introducing an S-shaped transition curve, and determining the backlash based on the characteristics of an anti-backlash curve and a complementary curve of the anti-backlash curve. The method comprises the following steps: realizing coupling control of anti-backlash and rotating speed synchronization, performing rotating speed compensation through differential negative feedback during one-way operation, performing anti-backlash control during starting reversing, observing and compensating system disturbance by using a linear expansion state observer, and establishing a prediction function speed controller based on a virtual average motor model; through discretization of a rotating speed prediction model and construction of a cost function, rolling optimization control of the system is realized, and the performance of the multi-motor driving system is improved. By adopting the anti-backlash and synchronization method for the multi-motor driving system, the problem that the control precision is reduced due to a backlash phenomenon in the multi-motor driving system is solved.

Description

Technical Field

[0001] The invention relates to the field of electromechanical control technology, and in particular to a backlash elimination and synchronization method for a multi-motor drive system. Background Art

[0002] In multi-motor drive systems, gear transmission mechanisms are often used, but this method inevitably introduces backlash. Backlash refers to the nonlinear position error caused by the gap between gears during gear transmission. Specifically, when the system driving torque begins to act or changes direction, backlash occurs, that is, the driving torque cannot be immediately and completely transmitted to the driven part, causing the driven part to lose control in a short period of time, and then a deviation is generated between the input and output ends of the backlash. This deviation directly increases the output error of the system and has a significant negative impact on the control accuracy of the multi-motor drive system, especially in application scenarios that require precise control of the load position.

[0003] In order to cope with the challenges of backlash phenomenon to high-precision control tasks, researchers are committed to improving motor control schemes in order to eliminate or at least significantly reduce the impact of backlash on position control accuracy. Multi-motor synchronous backlash elimination mechanisms came into being in this context and have gradually been widely used in the field of high-precision servo control. In order to completely eliminate the gap in the transmission mechanism, researchers have explored in depth the method of applying a bias torque between the two motors. At present, the methods of applying bias torque are mainly divided into fixed bias torque and dynamic bias torque. The fixed bias torque method is relatively simple and easy to implement. However, its significant disadvantage is that the bias torque continues to exist even after the system as a whole reaches a stable state. This not only affects the synchronization performance of the motor, but also when the motor is commutating, the fixed bias torque cannot effectively cope with the impact caused by commutation, resulting in a decrease in the accuracy and stability of the system.

[0004] In order to overcome the limitations of the fixed bias torque, researchers proposed a dynamic bias torque method. This method eliminates the bias torque in a timely manner after the system passes through the backlash area, so that the drive system can be restored to the common drive state of multiple motors. Although the dynamic bias torque has made progress in eliminating backlash, as a piecewise linear method, it is easy to produce mutations at the regional switching point, resulting in poor transition characteristics, which may cause system oscillation. Summary of the invention

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

[0006] To achieve the above object, the present invention provides a backlash elimination and synchronization method for a multi-motor drive system, comprising the following steps:

[0007] S1. Establish a dynamic model of a multi-motor drive system based on a backlash dead zone model: Considering the influence of gear backlash nonlinearity, establish a dynamic model including parameters such as motor electromagnetic torque, contact torque and load speed;

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

[0009] S3. Improved mathematical model of dynamic gap elimination method: Based on the existing dynamic gap elimination method, an S-type function is introduced as a transition curve to obtain an improved mathematical model of dynamic gap elimination method;

[0010] S4, coupling control of backlash elimination and synchronization of multi-motor drive system: adopt differential negative feedback working mode to realize multi-motor speed synchronization, and perform speed compensation adjustment in unidirectional operation according to backlash elimination nonlinear curve and complementary curve, and become the control mode in which backlash elimination control plays the main role in 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 multiple 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 for the disturbance;

[0012] S6. Establish a prediction function speed controller based on the virtual average motor model: discretize the virtual average motor dynamic equation using the forward Euler method to obtain a speed prediction model, and construct a cost function based on the error sequence between the actual speed and the predicted speed to achieve system rolling optimization control.

[0013] Preferably, the dynamic model expression of the multi-motor drive system based on the backlash dead zone model in S1 is:

[0014]

[0015] Among them, J m is the moment of inertia of the motor, J L is the load moment of inertia, ω 1 is the speed of motor No. 1, ω 2 is the speed of motor 2, ω L is the speed of the load, T e1 is the electromagnetic torque of motor No. 1, T e2 is the electromagnetic torque of motor No. 2, T L1 , T L2 are the contact torque between the small gear and the large gear, T gis the large gear torque, T L is the load torque, B m is the motor damping coefficient, B L is the load damping coefficient, r g is the radius of the pinion, R g is the radius of the large gear.

[0016] Preferably, the contact torque expression is:

[0017]

[0018]

[0019] Among them, K g is the gear stiffness coefficient, B g is the gear damping coefficient, b is half of the tooth gap width, r g is the radius of the pinion, R g is the radius of the large gear, θ 1 ,θ 2 and θ g They are the positions of motor No. 1, motor No. 2 and load respectively.

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

[0021]

[0022] in, is the estimated value of load position, N s is the gear ratio.

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

[0024]

[0025]

[0026]

[0027]

[0028] Among them, i qref is the reference current output by the speed loop, i qref1 、i qref2 are the reference currents of the two motors after backlash elimination control, I 0 ,I 1 ,I 2 To control the constraints, I 0 is the reference current, I 1 is the minimum current threshold, I 2is the maximum current threshold, s is the nonlinear transition function, and t is the normalization parameter.

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

[0030]

[0031] Among them, ω is the virtual average motor speed, K T is the motor torque coefficient, i q is the actual current of q axis, T 0 is the transmission torque between the large and small gears, is the q-axis reference current, and d(t) is the system disturbance to be observed.

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

[0033]

[0034]

[0035] Among them, x 1 is the virtual average motor speed; h is the rate of change of the total disturbance of the system.

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

[0037]

[0038] Among them, β 1 To observe and estimate the virtual average motor speed x 1 The gain value, β 2 is the total disturbance x of the observed and estimated system 2 The gain value, z 1 For x 1 The estimated value of z 2 For x 2 The estimated value of .

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

[0040]

[0041] Among them, K T is the motor torque coefficient, ω m (k) is the speed value of the kth step, T s It 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] Among them, r 1 is the weight coefficient of tracking error, r 2 is the weight coefficient of the input increment, and E(k) is the error sequence between the actual speed and the predicted speed.

[0046] Therefore, the present invention adopts the above-mentioned backlash elimination and synchronization method for a multi-motor drive system, and the technical effects are as follows:

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

[0048] 2. Dynamic bias torque anti-backlash control: Introducing the S-type function as the transition curve avoids mechanical shock and vibration caused by sudden changes in torque.

[0049] 3. Speed ​​synchronization and backlash elimination coupling: speed compensation is performed during unidirectional operation, and it is switched to backlash elimination control during starting and reversing to ensure the combined requirements of backlash elimination and synchronization.

[0050] 4. Predictive function control: Predictive function control can take into account both rapidity and no overshoot, adapt to the application scenarios of gear transmission, track the curve with slow start and stop, fast in the middle, reduce gear wear, and respond quickly.

[0051] 5. Extended state observer: Introduce the torque transfer characteristics between tooth gaps, use the extended state observer to improve the system's anti-disturbance ability, and solve the impact of other nonlinear factors on the system tracking performance after the tooth gap is eliminated.

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

[0053] Figure 1 The mechanical structure diagram of the multi-motor drive system of the present invention;

[0054] Figure 2 This is a control block diagram of the system of the present invention;

[0055] Figure 3 The motor current curve diagram under the improved dynamic bias torque of the present invention;

[0056] Figure 4 is a bias current curve diagram of the present invention;

[0057] Figure 5 A comparison diagram of load position error curves under different control strategies before and after backlash elimination of the present invention;

[0058] Figure 6 This is a comparison diagram of the motor speed curve after backlash elimination according to the present invention. DETAILED DESCRIPTION

[0059] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0060] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0061] Embodiment 1

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

[0063]

[0064] Among them, J m is the moment of inertia of the motor, J L is the load moment of inertia, ω 1 is the speed of motor No. 1, ω 2 is the speed of motor 2, ω L is the speed of the load, T e1 is the electromagnetic torque of motor No. 1, T e2 is the electromagnetic torque of motor No. 2, T L1 , T L2 are the contact torque between the small gear and the large gear, T g is the large gear torque, T L is the load torque, B m is the motor damping coefficient, B L is the load damping coefficient, r g is the radius of the pinion, R g is the radius of the large gear.

[0065] Considering the influence of gear clearance nonlinearity, the contact torque expression between the large and small gears is a dead zone function, and the specific expression is:

[0066]

[0067]

[0068] Among them, K g is the gear stiffness coefficient, B gis the gear damping coefficient, b is half of the tooth gap width, r g is the radius of the pinion, R g is the radius of the large gear, θ 1 ,θ 2 and θ g They are the positions of motor No. 1, motor No. 2 and load respectively.

[0069] Step 2: Use the hysteresis model to estimate the load position, and use the load position estimate in the control algorithm. The hysteresis model expression is:

[0070]

[0071] in, is the estimated value of load position, N s is the gear ratio.

[0072] There are two motors in the system, so the above formula can be used to obtain estimates of the two load positions: The two estimates are averaged as the estimate of the load position.

[0073]

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

[0075]

[0076] In multi-motor systems, position sensors are often not installed at the load end for cost-effectiveness reasons. However, the control objectives of the system rely on knowing the position and speed of the load accurately. To solve this problem, it is necessary to rely on information from other parts of the system 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, the relationship between the load position and the motor position may exhibit hysteresis characteristics due to factors such as friction and elastic deformation of mechanical components. 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 value of the motor position end position sensor and other possible system state information. This estimate is then used as the basis of the control algorithm to achieve precise control of the load position and speed.

[0078] Step 3: Improve the existing dynamic backlash elimination method by introducing an S-type function as a transition curve to obtain a mathematical model of the improved dynamic backlash elimination method.

[0079] The basic principle of the existing dynamic backlash elimination method is to establish a bias current between the two motors, thereby forming an equal and opposite bias torque, so that the large gear is subjected to the tightening effect from the bias torque, and the bias torque is eliminated after passing through the tooth gap, so that the drive system is restored to the common drive state of multiple motors. This piecewise linear method is prone to mutations at the regional switching point, and the transition characteristics are poor, which will cause system oscillation. The present invention makes improvements on this basis, introduces an S-type function as a transition curve, avoids the mutation phenomenon of the regional switching point, and reduces the mechanical shock and vibration caused by the torque mutation.

[0080] The mathematical model expression of the improved dynamic gap elimination method is:

[0081]

[0082]

[0083]

[0084]

[0085] Among them, i qref is the reference current output by the speed loop, i qref1 、i qref2 are the reference currents of the two motors after backlash elimination control, I 0 ,I 1 ,I 2 To control the constraints, I 0 is the reference current, I 1 is the minimum current threshold, I 2 is the maximum current threshold, s is the nonlinear transition function, and t is the normalization parameter.

[0086] The control constraints are satisfied:

[0087] Step 4: Use the differential negative feedback working mode to achieve multi-motor speed synchronization. Subtract the speeds of the two motors to get the speed difference. The compensation amount is calculated by the PI controller and added to the current command input of the two motors to correct the speeds of the two motors at the same time.

[0088] In the anti-backlash module, if the effect of the coefficient on the output amplitude is not considered, the anti-backlash 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 anti-backlash curve is calculated, that is, outputting 0 near the 0 value area and outputting 1 in other areas after the transition section. The speed compensation adjustment value is multiplied by the nonlinear output, so that the speed compensation adjustment can be realized during unidirectional operation, and the control mode in which the anti-backlash control plays a major role during starting and reversing can be realized.

[0089] Step 5: By rewriting the virtual average motor dynamic equation, the system is regarded as a whole containing multiple disturbances, a state equation containing the total disturbance of the system is established, and a linear extended state observer is constructed to observe and compensate for the disturbance.

[0090] Construct a virtual average motor model, whose mathematical model is:

[0091]

[0092] The virtual average motor dynamic equation is:

[0093]

[0094] Among them, ω is the virtual average motor speed, K T is the motor torque coefficient, i q is the actual current of q axis, T 0 is the transmission torque between the large and small gears, T e is the transmission torque of electromagnetic torque, is the q-axis reference current, and d(t) is the system disturbance to be observed.

[0095] The linear state extended observer is used to observe and compensate the sum of various disturbances as the total disturbance. The state equation containing the total disturbance of the system is:

[0096]

[0097]

[0098] Among them, x 1 is the virtual average motor speed; h is the rate of change of the total disturbance of the system.

[0099] The constructed state observer expression is:

[0100]

[0101] Among them, β 1 To observe and estimate the virtual average motor speed x 1 The gain value, β 2 is the total disturbance x of the observed and estimated system 2 The gain value, z 1 For x 1 The estimated value of z 2 For x 2 The estimated value of .

[0102] Step 6: Discretize the virtual average motor dynamic equation using the forward Euler method to obtain a speed prediction model. Based on the error sequence between the actual speed and the predicted speed, construct a cost function to achieve system rolling optimization control.

[0103] According to the virtual average motor dynamic equation, the forward Euler method is used to discretize the speed prediction model of the future P sampling periods at the kth moment:

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

[0105] satisfy

[0106] Sort the entire prediction time domain and rewrite the above formula into vector form:

[0107]

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

[0109] Construct the cost function:

[0110]

[0111] Among them, r 1 is the weight coefficient of tracking error, r 2 is the weight coefficient of the input increment, E(k)=[1...1] T e(k) is the error sequence between the actual speed and the 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 cycle and the rolling optimization control of the system can be realized.

[0113] By solving the optimization problem, the optimal reference current sequence for the next P steps is obtained. And at time k+1 The first component Act on the system.

[0114] At the k+1th moment, the new motor speed value is used to re-predict the future output of the system and solve the optimization problem, and then the optimal reference current sequence is The first component The system is acted on at time k+2, and this cycle is repeated. In each control cycle, the optimal set of reference current values ​​is found by solving the optimization problem, thereby realizing rolling optimization control.

[0115] Depend on Figure 3-Figure 4 It can be seen from the current curve shown that when the system enters the forward starting process, starting from point 0, there is an equal and reverse bias torque between the two motors, the gear connected to motor No. 1 is in positive contact with the large gear, and the gear connected to motor No. 2 is in reverse contact with the large gear, and the large gear is tightened and remains stationary; then the torque of motor No. 1 begins to increase, the torque of motor No. 2 decreases, the combined torque between the two motors begins to increase positively, and the large gear rotates positively until the current command is I 1 When the torque of motor 2 is 0, the large gear is driven by motor 1 and begins to disengage from the gear of motor 2. The gear of motor 2 is able to quickly mesh with the large gear in the positive direction through the tooth gap. At this time, the two motors jointly drive the large gear to rotate. When the current command is I 2 When the bias torque disappears completely, both motors output equal torque in the positive direction, driving the load to rotate in the positive direction. 2 At the beginning, the two motors begin to have bias torque, and the bias torque changes along the curve until the combined torque of the two motors is greater than 0, and the large gear begins to accelerate in the positive direction to complete the commutation.

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

[0117] like Figure 6 As shown in the figure, the speed curves of the two motors almost completely overlap after the backlash is eliminated, which shows that the speed synchronization between them is well guaranteed. The speed curve is smooth with small fluctuation, which means that the system runs more stably after the backlash is eliminated, reducing the backlash and speed mutation caused by the tooth gap.

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

[0119] 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 they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A backlash elimination and synchronization method for a multi-motor drive system, characterized in that: The following steps are involved: S1. Establish a dynamic model of a multi-motor drive system based on a backlash dead zone model: Considering the influence of gear backlash nonlinearity, establish a dynamic model including parameters such as motor electromagnetic torque, contact torque and load speed; S2, load position estimation: use the hysteresis model to estimate the load position, and use the load position estimation value in the control algorithm; S3. Improved mathematical model of dynamic gap elimination method: Based on the existing dynamic gap elimination method, an S-type function is introduced as a transition curve to obtain an improved mathematical model of dynamic gap elimination method; S4, coupling control of backlash elimination and synchronization of multi-motor drive system: adopt differential negative feedback working mode to realize multi-motor speed synchronization, and perform speed compensation adjustment in unidirectional operation according to backlash elimination nonlinear curve and complementary curve, and become the control mode in which backlash elimination control plays the main role in 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 multiple 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 for the disturbance; S6. Establish a prediction function speed controller based on the virtual average motor model: discretize the virtual average motor dynamic equation using the forward Euler method to obtain a speed prediction model, and construct a cost function based on the error sequence between the actual speed and the predicted speed to achieve system rolling optimization control.

2. A backlash elimination and synchronization method for a multi-motor drive system according to claim 1, characterized in that: The dynamic model expression of the multi-motor drive system based on the backlash dead zone model in S1 is: Among them, J m is the moment of inertia of the motor, J L is the load moment of inertia, ω1 is the speed of motor No. 1, ω2 is the speed of motor No. 2, ω L is the speed of the load, T e1 is the electromagnetic torque of motor No. 1, T e2 is the electromagnetic torque of motor No. 2, T L1 , T L2 are the contact torque between the small gear and the large gear, T g is the large gear torque, T L is the load torque, B m is the motor damping coefficient, B L is the load damping coefficient, r g is the radius of the pinion, R g is the radius of the large gear.

3. A backlash elimination and synchronization method for a multi-motor drive system according to claim 2, characterized in that: The contact torque expression is: Among them, K g is the gear stiffness coefficient, B g is the gear damping coefficient, b is half of the tooth gap width, r g is the radius of the pinion, R g is the radius of the large gear, θ1, θ2 and θ g They are the positions of motor No. 1, motor No. 2 and load respectively.

4. The backlash elimination and synchronization method for a multi-motor drive system according to claim 1, characterized in that: The hysteresis model expression in S2 is: in, is the estimated value of load position, N s is the gear ratio.

5. The backlash elimination and synchronization method for a multi-motor drive system according to claim 1, characterized in that: The mathematical model expression of the improved dynamic backlash elimination method in S3 is: Among them, i qref is the reference current output by the speed loop, 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 the nonlinear transition function, and t is the normalization parameter.

6. The backlash elimination and synchronization method for a multi-motor drive system according to claim 1, characterized in that: The virtual average motor dynamic equation in S5 is: Among them, ω is the virtual average motor speed, K T is the motor torque coefficient, i q is the actual current of the q axis, T0 is the transmission torque between the large and small gears, is the q-axis reference current, and d(t) is the system disturbance to be observed.

7. The backlash elimination and synchronization method for a multi-motor drive system according to claim 1, characterized in that: The state equation containing the total disturbance of the system in S5 is: Among them, x1 is the virtual average motor speed; h is the rate of change of the total disturbance of the system.

8. The backlash elimination and synchronization method for a multi-motor drive system according to claim 1, characterized in that: The state observer expression in S5 is: Among them, 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 disturbance x2 of the system, z1 is the estimated value of x1, and z2 is the estimated value of x2.

9. The backlash elimination and synchronization method for a multi-motor drive system according to claim 1, characterized in that: The speed prediction model expression in S6 is: Among them, K T is the motor torque coefficient, ω m (k) is the speed value of the kth step, T s It is the speed loop sampling time.

10. The backlash elimination and synchronization method for a multi-motor drive system according to claim 1, characterized in that: The cost function expression in S6 is: E(k)=[1...1] T e(k); Among them, r1 is the weight coefficient of tracking error, r2 is the weight coefficient of input increment, and E(k) is the error sequence between actual speed and predicted speed.

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