High-precision multi-motor variable bias anti-backlash driving control system

Abstract

The application discloses a high-precision multi-motor variable-bias anti-backlash driving control system and belongs to the technical field of servo control systems. The application comprises a position controller, a position loop correction module, a speed loop correction module, a plurality of servo drivers, speed feedback, electric anti-backlash control, current loop correction, current feedback, an azimuth large gear, an azimuth synchronous gear system and the like. The azimuth rotary transformer and the azimuth synchronous gear system are real-time sensitive to azimuth angle information, and the azimuth angle digital value is calculated. The position controller receives the azimuth angle digital value, calculates the speed given instruction and sends the speed given instruction to the servo driver 1. The rotational speed of each motor is averaged, and the error value of the given motor speed is calculated to control the current. Each electric anti-backlash control calculates the bias current between the motors in each group, and each current loop correction controls the PWM power amplifier in real time to complete the motor current closed-loop control and realize the azimuth angle position closed-loop control. The application can avoid the simultaneous entry or exit of the anti-backlash motors into or out of the anti-backlash state.

Description

Technical Field

[0001] This invention belongs to the field of servo control system technology, specifically relating to a high-precision multi-motor variable bias backlash elimination drive control system. Background Technology

[0002] Large, heavy-duty turntables require high-power servo drive systems. Conventional dual-motor drives cannot meet the demands, necessitating a multi-motor synchronous drive scheme with four or more motors. The antenna mount drivetrain exhibits nonlinear factors such as backlash and bearing clearance during design and assembly, affecting high-precision servo tracking performance. Therefore, a well-designed backlash elimination control scheme is required. Directly transplanting the bias current setting method of conventional dual-motor backlash elimination strategies to multi-motor backlash elimination can lead to frequent switching between backlash elimination and de-backlash elimination modes when the bias current is too small, causing frequent impacts and oscillations. Conversely, excessively large bias currents result in high system power consumption, and the transition from backlash elimination to de-backlash elimination mode causes significant impact damage to the drivetrain. Therefore, a well-designed multi-motor backlash elimination control strategy with four or more motors is necessary to reduce system power consumption while minimizing impacts and damage to the drivetrain. Summary of the Invention

[0003] The purpose of this invention is to address the aforementioned problems of large, heavy-duty turntables by providing a high-precision multi-motor variable offset backlash elimination drive control system. This system can prevent all backlash elimination motors from simultaneously entering or exiting the backlash elimination state, effectively reducing the impact and oscillation during the switching between backlash elimination and backlash exit states, and lowering the system's operating power consumption.

[0004] Specifically, this invention provides a high-precision multi-motor variable bias backlash elimination drive control system, including a position controller, a position loop correction module, servo drivers 1, 2, 3, 4, ..., n, a speed loop correction module, speed feedback 1, 2, 3, 4, ..., n, electrical backlash elimination control 1, 2, ..., n / 2, current loop correction 1, current feedback 1, PWM power amplifier 1, motor 1, reducer 1, and current loop correction 2. The system consists of: current feedback 2, PWM power amplifier 2, motor 2, reducer 2, current loop correction 3, current feedback 3, PWM power amplifier 3, motor 3, reducer 3, current loop correction 4, current feedback 4, PWM power amplifier 4, motor 4, reducer 4, ..., current loop correction n, current feedback n, PWM power amplifier n, motor n, reducer n, azimuth gear, azimuth synchronous gear train, azimuth rotary transformer, and shaft angle conversion module, where n≥4 and n / 2 is an integer; motors 1 and 2 form the first group of dual motors, motors 3 and 4 form the second group of dual motors, and so on;

[0005] The azimuth rotary transformer and the azimuth synchronous gear train are coaxially mounted. The azimuth synchronous gear train and the azimuth large gear mesh with each other. The azimuth rotary transformer and the azimuth synchronous gear train are sensitive to the azimuth angle information in real time and input into the shaft angle transformation module to calculate the azimuth angle digital value in real time. The position controller receives the azimuth angle feedback value and calculates the difference with the azimuth given signal. The error value is input into the position loop correction module to calculate the speed given command and send it to the servo driver 1.

[0006] The servo driver 1 acts as the main speed controller. The speed feedback 1 to n collects the rotational speeds of the motors 1 to n and transmits them to the servo driver 1. The average rotational speed is then calculated and subtracted from the given motor speed. The error value is input to the speed loop correction module to calculate the control current I. c The backlash elimination control 1 to n / 2 respectively calculates the bias current I between motors 1 and 2, ..., and between motors n-1 and n based on the current feedback 1 to n. p1 ~I pn / 2 The current given for multiple motors is: I p1 +I c I c -I p1 ... I pn / 2 +I c I c -I pn / 2 ;

[0007] The current loop correction 1 to n inside each of the servo drivers controls the PWM power amplifier 1 to n in real time based on the error between the current setpoint and the current feedback 1 to n. The PWM power amplifier 1 to n outputs the drive signal to the motor 1 to n to ensure that the motor current changes in real time with the change of the current setpoint, thus completing the closed-loop control of the motor current. Then, the motor speed control is realized by the servo control of the current.

[0008] Motors 1 to n are coaxially mounted with reducers 1 to n. The ends of reducers 1 to n are respectively meshed with the azimuth gear. The rotation of motors 1 to n drives the azimuth gear to rotate, thus completing the closed-loop control of the azimuth angle position.

[0009] Furthermore, the speed and current information between drivers 1 and 2, ..., and between drivers n-1 and n is transmitted via SPI bus, and the speed and current information between drivers 1, 3, ..., n-1 is transmitted via 422 bus.

[0010] Furthermore, the bias current and inflection point current parameters between each group of dual motors are set using the following smoothing strategy:

[0011] 1) First, adjust the bias current and inflection point current parameters between motors 1 and 2 separately to ensure that the system impact and bandwidth meet the usage requirements.

[0012] Based on the preset relationship curve between the current setpoint and the feedback current, the backlash elimination control 1 obtains the current setpoint values ​​for drivers 1 and 2 according to the set bias current and inflection point current between motors 1 and 2, as well as the feedback currents 1 and 2; the initial value of the bias current between motors 1 and 2 is I′. p1 Set to 5% to 15% of the motor's rated current, the inflection point current I g1 It is 2 to 3 times the initial value of the bias current;

[0013] 2) Transfer the backlash elimination parameters of motors 1 and 2 to the backlash elimination control modules of other dual-motor groups, and simultaneously change the initial value I′ of the bias current between the dual motors of other groups. p2 ~I′ pn / 2 and inflection point current I gn / 2 Compared to dual motors 1 and 2, the reduction is (20%~40%)×i / (n / 2-1), where i=1,…,(n / 2-1);

[0014] Based on the preset relationship curve between current setpoint and feedback current, the gap elimination control 2~n / 2 calculates the current setpoint values ​​of motors 3~n in real time according to the bias current and inflection point current between each group of motors, as well as the feedback currents 3~n.

[0015] Furthermore, the relationship curve between the preset current input and the feedback current is specifically as follows:

[0016] The default motor reference curve without setting the bias current is curve y = x;

[0017] When the motor feedback current is 0, the intersection of the curve and the vertical axis is the initial value of the bias current I′. p1 ~I′ pn / 2 Point A is the inflection point of motor n-1 and n, and the x-coordinate of the inflection point is the inflection point current I. gn / 2 Point B is the inflection point of motors 1 and 2. The x-coordinate of the inflection point is the inflection point current I. g1 When the feedback currents of motor n-1 and n are less than the inflection point current at point A, the bias current remains at its initial value, i.e., I. pn / 2 =I′ pn / 2 Point C is the intersection of the given currents of motors n-1 and n with the curve y = x. When the feedback currents of motors n-1 and n are greater than the current at point C, the given currents and feedback currents of motors n-1 and n are exactly equal, and the bias current is I. pn / 2 =0; When the motor n-1 and n feedback currents are between the currents at points A and C, the bias current I pn / 2 As the current changes linearly to 0, the given currents for motors n-1 and n also change linearly accordingly.

[0018] When the feedback currents of motors 1 and 2 are less than the inflection point current at point B, the bias current remains at its initial value, i.e., I.p1 =I′ p1 Point D is the intersection of the given currents of motors 1 and 2 and the curve y = x. When the feedback current of motors 1 and 2 is greater than the current at point D, the given current and feedback current of motors 1 and 2 are exactly equal, and the bias current is I. p1 =0;

[0019] When the feedback currents of motors 1 and 2 are between points B and D, the bias current I p1 Linear change to 0;

[0020] Points A′, B′, C′, and D′ are symmetrical about the vertical axis with respect to points A, B, C, and D, respectively. When the motor feedback current is negative, the absolute value of the control current is equal to that when it is positive, but the sign is opposite.

[0021] The beneficial effects of the high-precision multi-motor variable bias backlash-eliminating drive control system of the present invention are as follows:

[0022] To address the challenge that conventional dual-motor backlash-eliminating architectures cannot meet the power and torque requirements of large, heavy-duty servo drive mechanisms, a scalable multi-motor backlash-eliminating architecture is adopted. The motors employ a pairwise backlash-eliminating mode, and different pairs of motors and drivers are configured based on the required drive power. Appropriate power ratings for motors and drivers are selected, and a formula is established to determine the relationship between the multi-motor setpoint current and the feedback current. This allows the system's power and torque requirements to be met without significantly increasing the complexity of motor design. Furthermore, the multi-motor backlash-eliminating architecture can be expanded and extended using 422 and SPI buses.

[0023] To reduce the impact of the multi-motor backlash elimination control architecture, a variable bias current smoothing strategy is adopted. Depending on the number of motors, the reduction values ​​of the bias current and inflection point current between each pair of motors relative to backlash elimination motor pairs 1 and 2 are adjusted in different proportions. This avoids all backlash elimination motor pairs entering / exiting the backlash elimination state at the same time, effectively reducing the impact and oscillation during the switching between backlash elimination and backlash elimination states, and reducing the system's operating power consumption. Attached Figure Description

[0024] Figure 1 This is a system schematic diagram according to an embodiment of the present invention.

[0025] Figure 2 This is a schematic diagram of the relationship between the current input and the feedback current in an embodiment of the present invention. Detailed Implementation

[0026] The present invention will now be described in further detail with reference to the embodiments and the accompanying drawings.

[0027] Example 1:

[0028] One embodiment of the present invention is a high-precision multi-motor variable bias backlash elimination drive control system, such as... Figure 1 As shown, it includes: a position controller, a position loop correction module, servo driver 1, servo driver 2, servo driver 3, servo driver 4, ..., servo driver n, a speed loop correction module, speed feedback 1, speed feedback 2, speed feedback 3, speed feedback 4, ..., speed feedback n, electrical backlash elimination control 1, electrical backlash elimination control 2, ..., electrical backlash elimination control n / 2, current loop correction 1, current feedback 1, PWM power amplifier 1, motor 1, reducer 1, current loop correction 2, current feedback 2, PWM power amplifier 2, motor 2, reducer 2, current loop correction 3, current feedback 3, PWM power amplifier 3, motor 3, reducer 3, current loop correction 4, current feedback 4, PWM power amplifier 4, motor 4, reducer 4, ..., current loop correction n, current feedback n, PWM power amplifier n, motor n, reducer n, azimuth gear, azimuth synchronous gear train, azimuth rotary transformer, and shaft angle conversion module. Where n ≥ 4, and n / 2 is an integer.

[0029] The azimuth rotary transformer and the azimuth synchronous gear train are coaxially mounted. The azimuth synchronous gear train and the azimuth large gear mesh with each other. The change in azimuth angle can be reflected by the sine and cosine analog voltage signals of the azimuth rotary transformer. The azimuth rotary transformer and the azimuth synchronous gear train are sensitive to the azimuth angle information in real time. This signal is input to the shaft angle transformation module, which calculates the digital value of the azimuth angle in real time. The position controller receives the azimuth angle feedback value and calculates the difference with the azimuth given signal. The error value is input to the position loop correction module, which calculates the speed given command and sends it to the servo driver 1.

[0030] Servo driver 1 acts as the main speed controller. Speed ​​feedback 1~n collects the rotational speeds of motors 1~n and transmits them to servo driver 1 via SPI and 422 buses. After taking the average speed, the difference between this average speed and the given motor speed is calculated. The error value is input to the speed loop correction module to calculate the control current I. c The backlash elimination control 1 to n / 2 respectively relies on current feedback 1 to n to calculate the bias current I between motors 1 and 2, ..., between motors n-1 and n. p1 ~I pn / 2 Then the current given for multiple motors is: I p1 +I c I c -I p1 ... I pn / 2 +I c I c -I pn / 2The internal current loop correction of multiple servo drivers 1-n, based on the error between the current setpoint and the current feedback 1-n, controls the PWM power amplifiers 1-n in real time. The PWM power amplifiers 1-n output drive signals to motors 1-n, ensuring that the motor current changes in real time following the current setpoint, thus completing the closed-loop control of the motor current. Motor speed control is then achieved through servo control of the current. Motors 1-n are coaxially mounted with reducers 1-n. The ends of reducers 1-n mesh with azimuth gears. The rotation of motors 1-n drives the azimuth gears to rotate, achieving azimuth angle changes, thereby completing the closed-loop control of the azimuth angle position. Speed ​​and current information are transmitted between drivers 1, 2, ..., and between drivers n-1, n via SPI bus communication. Speed ​​and current information are transmitted between drivers 1, 3, ..., n-1 via 422 bus communication.

[0031] For conventional dual-motor backlash elimination control systems, if the bias current is too small, the transmission system tends to repeatedly switch between backlash elimination and de-backlash elimination states, causing system instability and frequent abnormal noises. If the bias current is too large, the transmission system may remain in backlash elimination mode, resulting in significant torque and power losses. Furthermore, the switching between backlash elimination and de-backlash elimination states causes significant system impacts, potentially damaging the transmission chain. Compared to conventional dual-motor backlash elimination systems, multi-motor backlash elimination systems, due to the increased number of motors, are more prone to oscillations and impacts if the backlash elimination settings are not properly configured.

[0032] Therefore, the high-precision multi-motor bias backlash-free drive control system of this invention employs a variable bias current smoothing strategy to reduce impact. The relationship curves between the given current of motors 1 to n and the motor feedback current are shown below. Figure 2 As shown, the preset curve y = x is the motor reference curve without bias current, where the reference current and the motor feedback current are equal everywhere on this curve. In backlash elimination control mode, the intersection of the motor reference curve and the vertical axis when the motor feedback current is 0 is the initial value of the bias current I′. p1 ~I′ pn / 2 Point A is the inflection point of motor n-1 and n, and the x-coordinate of the inflection point is the inflection point current I. gn / 2 Point B is the inflection point of motors 1 and 2. The x-coordinate of the inflection point is the inflection point current I. g1 When the feedback currents of motor n-1 and n are less than the inflection point current at point A, the bias current remains at its initial value, i.e., I. pn / 2 =I′ pn / 2 Point C is the intersection of the given currents of motors n-1 and n with the curve y = x. When the feedback currents of motors n-1 and n are greater than the current at point C, the given currents and feedback currents of motors n-1 and n are exactly equal, and the bias current is I. pn / 2 =0; When the motor n-1 and n feedback currents are between the currents at points A and C, the bias current I pn / 2As the current changes linearly to 0, the given currents for motors n-1 and n also change linearly.

[0033] Similarly, when the feedback currents of motors 1 and 2 are less than the inflection point current at point B, the bias current remains at its initial value, i.e., I. p1 =I′ p1 Point D is the intersection of the given currents of motors 1 and 2 and the curve y = x. When the feedback current of motors 1 and 2 is greater than the current at point D, the given current and feedback current of motors 1 and 2 are exactly equal, and the bias current is I. p1 =0; When the feedback current of motors 1 and 2 is between point B and point D, the bias current I p1 The linear change is reduced to 0. Points A′, B′, C′, and D′ are symmetrical about the vertical axis with respect to points A, B, C, and D, respectively. When the motor feedback current is negative, the absolute value of the control current is equal to that in the positive direction, but with the opposite sign. The calculation formula is similar to the process described above and will not be repeated. Therefore, the electrical backlash elimination control 1 to n / 2 is based on the set bias current I. p1 ~I pn / 2 Inflection point current value I g1 ~I gn / 2 With feedback currents 1 to n, the current setpoint values ​​for motors 1 to n can be calculated in real time. By reasonably setting the bias current and inflection point current parameters between each dual motor, the impact is reduced. The specific smoothing strategy is as follows:

[0034] 1) First, adjust the bias current and inflection point current parameters between motors 1 and 2 individually until the system impulse and bandwidth meet the usage requirements. Based on... Figure 2 The curve showing the relationship between the current setpoint and the feedback current illustrates how the backlash elimination control 1, based on the initial bias current and inflection point current between the first set of dual motors (i.e., motors 1 and 2), and the feedback currents 1 and 2, can obtain the current setpoint values ​​for drivers 1 and 2. The initial bias current value I′ between motors 1 and 2 is... p1 It is generally set at 5% to 15% of the motor's rated current, with the inflection point current I... g1 It is 2 to 3 times the initial value of the bias current between motors 1 and 2;

[0035] 2) The backlash elimination parameters of motors 1 and 2 are transferred to other dual-motor backlash elimination control modules (e.g., motors 3 and 4, motors n-1 and n). Meanwhile, to reduce the significant impact caused by multiple motors simultaneously entering and exiting backlash elimination, the initial value of the bias current I′ between other dual motors is adjusted. p2 ~I′ pn / 2 and inflection point current I g2 ~I gn / 2 Compared to dual motors 1 and 2, the cost is reduced by (20%–40%) × i / (n / 2–1), where i = 1, …, (n / 2–1), avoiding multiple motors simultaneously entering and exiting the backlash elimination mode. Based on… Figure 2The relationship curve between the current setpoint and the feedback current is shown in the figure. The current setpoint values ​​of motor 3 to n can be calculated in real time based on the set bias current and inflection point current, as well as the feedback current 3 to n, in the electric gap elimination control 2 to n / 2.

[0036] To address the challenge that conventional dual-motor backlash elimination architectures cannot meet the power and torque requirements of large, heavy-duty servo drive mechanisms, this invention presents a high-precision multi-motor variable bias backlash elimination drive control system. This system employs a scalable multi-motor backlash elimination architecture, using a pairwise backlash elimination mode for the motors. Different numbers of motors and drivers are configured based on the required drive power, and the power ratings of the motors and drivers are rationally selected. A formula for the relationship between the given current of the multiple motors and the feedback current is established, thereby meeting the system's power and torque requirements without significantly increasing the complexity of motor design. Furthermore, the multi-motor backlash elimination architecture can be expanded and extended through 422 bus and SPI bus.

[0037] To reduce the impact of multi-motor backlash elimination control architecture, the high-precision multi-motor variable bias backlash elimination drive control system of the present invention adopts a variable bias current smoothing strategy. Depending on the number of motors, the bias current and inflection point current between each pair of motors are adjusted in different proportions relative to backlash elimination motor pairs 1 and 2. This avoids all backlash elimination motor pairs from entering / exiting the backlash elimination state at the same time, effectively reducing the impact and oscillation during the switching between backlash elimination and de-backlash elimination states, and reducing the system's operating power consumption.

[0038] While the present invention has been disclosed above with reference to preferred embodiments, these embodiments are not intended to limit the invention. Any equivalent changes or modifications made without departing from the spirit and scope of the invention are also within the scope of protection of the invention. Therefore, the scope of protection of the present invention should be determined by the claims of this application.

Claims

1. A high-precision multi-motor variable bias backlash elimination drive control system, characterized in that, The system includes a position controller, a position loop correction module, servo drivers 1, 2, 3, 4, ..., n, a speed loop correction module, speed feedback 1, 2, 3, 4, ..., n, electrical backlash elimination control 1, 2, ..., n / 2, current loop correction 1, current feedback 1, PWM power amplifier 1, motor 1, reducer 1, current loop correction 2, current feedback 2, PWM power amplifier 2, motor 2, reducer 2, current loop correction 3, current feedback 3, PWM power amplifier 3, motor 3, reducer 3, current loop correction 4, current feedback 4, PWM power amplifier 4, motor 4, reducer 4, ..., current loop correction n, current feedback n, PWM power amplifier n, motor n, reducer n, azimuth gear, azimuth synchronous gear train, azimuth rotary transformer, and shaft angle conversion module, where n≥4 and n / 2 is an integer; motors 1 and 2 form the first group of dual motors, motors 3 and 4 form the second group of dual motors, and so on; The azimuth rotary transformer and the azimuth synchronous gear train are coaxially mounted. The azimuth synchronous gear train and the azimuth large gear mesh with each other. The azimuth rotary transformer and the azimuth synchronous gear train are sensitive to the azimuth angle information in real time and input into the shaft angle transformation module to calculate the azimuth angle digital value in real time. The position controller receives the azimuth angle feedback value and calculates the difference with the azimuth given signal. The error value is input into the position loop correction module to calculate the speed given command and send it to the servo driver 1. The servo driver 1 acts as the main speed controller. The speed feedback 1 to n collects the rotational speeds of the motors 1 to n and transmits them to the servo driver 1. The average rotational speed is then calculated and subtracted from the given motor speed. The error value is input to the speed loop correction module to calculate the control current I. c ; The electrical gap elimination control 1 to n / 2 respectively calculates the bias current I between motors 1 and 2, ..., and between motors n-1 and n based on the current feedback 1 to n. p1 ~I pn / 2 The current given for multiple motors is: I p1 +I c I c -I p1 ... I pn / 2 +I c I c -I pn / 2 ; The current loop correction 1 to n inside each of the servo drivers controls the PWM power amplifier 1 to n in real time based on the error between the current setpoint and the current feedback 1 to n. The PWM power amplifier 1 to n outputs the drive signal to the motor 1 to n to ensure that the motor current changes in real time with the change of the current setpoint, thus completing the closed-loop control of the motor current. Then, the motor speed control is realized by the servo control of the current. Motors 1 to n are coaxially mounted with reducers 1 to n. The ends of reducers 1 to n are respectively meshed with the azimuth gear. The rotation of motors 1 to n drives the azimuth gear to rotate, thus completing the closed-loop control of the azimuth angle position.

2. The high-precision multi-motor variable bias backlash elimination drive control system according to claim 1, characterized in that, Speed ​​and current information is transmitted between drivers 1 and 2, ..., and between drivers n-1 and n via SPI bus, and speed and current information is transmitted between drivers 1, 3, ..., n-1 via 422 bus.

3. The high-precision multi-motor variable bias backlash elimination drive control system according to claim 1, characterized in that, The bias current and inflection point current parameters between each group of dual motors are set using the following smoothing strategy: 1) First, adjust the bias current and inflection point current parameters between motors 1 and 2 separately to ensure that the system impact and bandwidth meet the usage requirements. Based on the preset relationship curve between the current setpoint and the feedback current, the backlash elimination control 1 obtains the current setpoint values ​​for drivers 1 and 2 according to the set bias current and inflection point current between motors 1 and 2, as well as the feedback currents 1 and 2; the initial value of the bias current between motors 1 and 2 is I′. p1 Set to 5% to 15% of the motor's rated current, the inflection point current I g1 It is 2 to 3 times the initial value of the bias current; 2) Transfer the backlash elimination parameters of motors 1 and 2 to the backlash elimination control modules of other dual-motor groups, and simultaneously change the initial value I′ of the bias current between the dual motors of other groups. p2 ~I′ pn / 2 and inflection point current I gn / 2 Compared to dual motors 1 and 2, the reduction is (20%~40%)×i / (n / 2-1), where i=1,…,(n / 2-1); Based on the preset relationship curve between current setpoint and feedback current, the gap elimination control 2~n / 2 calculates the current setpoint values ​​of motors 3~n in real time according to the bias current and inflection point current between each group of motors, as well as the feedback currents 3~n.

4. The high-precision multi-motor variable bias backlash elimination drive control system according to claim 3, characterized in that, The preset relationship curve between the current setpoint and the feedback current is specifically as follows: The default motor reference curve without setting the bias current is curve y = x; When the motor feedback current is 0, the intersection of the curve and the vertical axis is the initial value of the bias current I′. p1 ~I′ pn / 2 Point A is the inflection point of motor n-1 and n, and the x-coordinate of the inflection point is the inflection point current I. gn / 2 Point B is the inflection point of motors 1 and 2. The x-coordinate of the inflection point is the inflection point current I. g1 When the feedback currents of motor n-1 and n are less than the inflection point current at point A, the bias current remains at its initial value, i.e., I. pn / 2 =I′ pn / 2 Point C is the intersection of the given currents of motors n-1 and n with the curve y = x. When the feedback currents of motors n-1 and n are greater than the current at point C, the given currents and feedback currents of motors n-1 and n are exactly equal, and the bias current is I. pn / 2 =0; When the motor n-1 and n feedback currents are between the currents at points A and C, the bias current I pn / 2 As the current changes linearly to 0, the given currents for motors n-1 and n also change linearly accordingly. When the feedback currents of motors 1 and 2 are less than the inflection point current at point B, the bias current remains at its initial value, i.e., I. p1 =I′ p1 Point D is the intersection of the given currents of motors 1 and 2 and the curve y = x. When the feedback current of motors 1 and 2 is greater than the current at point D, the given current and feedback current of motors 1 and 2 are exactly equal, and the bias current is I. p1 =0; When the feedback currents of motors 1 and 2 are between points B and D, the bias current I p1 Linear change to 0; Points A′, B′, C′, and D′ are symmetrical about the vertical axis with respect to points A, B, C, and D, respectively. When the motor feedback current is negative, the absolute value of the control current is equal to that when it is positive, but the sign is opposite.

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