Nonlinear extended state observer, control method and servo system

Abstract

The application provides a nonlinear extended state observer, a control method and a servo system, and relates to the technical field of photoelectric devices.The nonlinear extended state observer comprises: an input unit, which is used for acquiring input signals of voltages or currents of a motor in a closed-loop control process, and simultaneously receiving and processing speed or position measurement signals of a load; a disturbance observation unit, which is used for observing and tracking total disturbances based on the signals acquired by the input unit; and an output unit, which is used for outputting total disturbance observation values observed by the disturbance observation unit, and constructing a control signal for offsetting disturbances according to the total disturbance observation values.The nonlinear extended state observer can effectively observe and track total disturbances according to input signals, and can construct offsetting signals, so that disturbances can be accurately compensated, the nonlinear extended state observer is suitable for low-resolution sensors and transmission mechanisms with large gear gaps, and low-frequency oscillation after position switching is eliminated.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of photoelectric equipment, in particular to a nonlinear extended state observer, a control method and a servo system. BACKGROUND

[0002] The purpose of the servo system is to control the position or speed of the load. In engineering, for the convenience of parameter setting, the speed is generally controlled in a closed loop. On the basis of the speed closed loop control, whether to perform position closed loop control is determined according to the requirement.

[0003] In the case that a displacement sensor with low resolution or a large gear gap is used at the load end, the control gain or amplification factor between the control signal and the output signal tends to 0 when the gear is in a non-engaged state, and tends to a constant state after engagement. The extended state observer produces a jitter phenomenon in actual application, which causes the parameters of the extended state observer to mismatch and the disturbance observation to fail. At the same time, due to the limitation of the use scene, it is impossible to use a harmonic gear or other measures to perform gap elimination.

[0004] Therefore, how to improve the existing extended state observer to solve the low-frequency jitter caused by a large gear gap or a displacement sensor with low resolution has become a technical problem to be solved at present. SUMMARY

[0005] Therefore, the present application aims to solve the problem of low-frequency jitter caused by a large gear gap or a displacement sensor with low resolution.

[0006] Specifically, the present application is realized by the following technical solutions:

[0007] According to a first aspect of the present application, a nonlinear extended state observer for coping with gear backlash is provided for a servo system, the servo system comprising a motor, a load, a load end sensor and a gear transmission structure. The nonlinear extended state observer comprises: an input unit for obtaining an input signal of the voltage or current of the motor in a closed loop control process, and receiving and processing a speed or position measurement signal of the load; a disturbance observation unit for observing and tracking the total disturbance based on the signal obtained by the input unit; and an output unit for outputting the total disturbance observation value observed by the disturbance observation unit, and constructing a control signal for offsetting the disturbance according to the total disturbance observation value.

[0008] Optionally, in some technical solutions, the nonlinear extended state observer for coping with gear backlash further comprises: a nonlinear adjustment unit for adjusting the nonlinear parameter according to the transmission characteristics of the gear transmission structure; and a limiting processing unit for limiting the result generated by the nonlinear adjustment unit.

[0009] Optionally, in some embodiments, the formula for observing and tracking the total disturbance includes:

[0010]

[0011] wherein y(k) represents the output signal at the current sampling time, z1(k-1) represents the observation value of the output signal at the previous sampling time, and d represents the first intermediate variable;

[0012] d1 represents the second intermediate variable, sat(d, s1) represents the saturation function for limiting the range of the input signal, s1 represents the first nonlinear parameter to be adjusted, γ1 represents the third nonlinear parameter to be adjusted, and sign(d) represents the sign function, which takes the value of 1 when the value of d is positive and takes the value of -1 when the value of d is negative;

[0013] z1(k) represents the observation value of the output signal at the current sampling time, T s represents the discrete period, which is generally within 10 ms, b represents the constant, u represents the input signal, and τ represents the equivalent delay, represents the down rounding of β1 and β2 represent the parameters to be adjusted during use, fal(d1, α1, δ1) represents the ternary function, d1, α1, and δ1 are input parameters of the ternary function, and z2(k-1) represents the observation value of the total disturbance at the previous sampling time;

[0014] d2 represents the third intermediate variable, sat(d, s2) represents the saturation function, s2 represents the second nonlinear parameter to be adjusted, and γ2 represents the fourth nonlinear parameter to be adjusted for limiting the range of the input signal;

[0015] z2(k) represents the observation value of the total disturbance at the current sampling time, and fal(d2, α2, δ2) represents the ternary function, d2, α2, and δ2 are input parameters of the ternary function.

[0016] Optionally, in some embodiments, the value of the first nonlinear parameter to be adjusted s1 is greater than 0, the value of the second nonlinear parameter to be adjusted s2 is greater than 0, the value of the third nonlinear parameter to be adjusted γ1 is greater than 0 and less than or equal to 1, and the value of the fourth nonlinear parameter to be adjusted γ2 is greater than 0 and less than or equal to 1.

[0017] Optionally, in some embodiments, the third nonlinear parameter to be adjusted γ1 and the fourth nonlinear parameter to be adjusted γ2 both take the value of 1, and the saturation limit value of the saturation function is infinite.

[0018] Optionally, in some embodiments, the initial angular frequency ω o represents the parameters to be adjusted β1 and β2, β1 = 2·ω o,

[0019] According to a second aspect of the present application, a control method of a nonlinear extended state observer for gear backlash is provided, and the control method is used for a servo system, the servo system comprising a motor, a load, a load end sensor and a gear transmission structure, the control method comprising: obtaining an input signal of voltage or current of the motor in a closed loop control process; receiving and processing a speed or position measurement signal of the load; observing and tracking a total disturbance based on the signal obtained by the input unit; observing and tracking the total disturbance based on the input signal and the output signal; determining a total disturbance observation value observed by a disturbance observation unit, and constructing a control signal for counteracting the disturbance according to the total disturbance observation value.

[0020] Optionally, in some technical solutions, the control method of the nonlinear extended state observer for gear backlash further comprises: obtaining a transmission characteristic of the gear transmission structure; and adjusting a nonlinear parameter according to the transmission characteristic of the gear transmission structure.

[0021] According to a third aspect of the present application, a servo system with a gear transmission structure is provided, and the servo system comprises the nonlinear extended state observer according to the first aspect of the present application or any possible implementation manner of the first aspect.

[0022] Optionally, in some technical solutions, the servo system with the gear transmission structure further comprises: a feedback controller for generating an input signal; a motor connected to a driving circuit and receiving the input signal after power conversion by the driving circuit; a gear transmission structure connected to an output end of the motor at one end; a load connected to the other end of the gear transmission structure; a load end sensor connected to the load for detecting an output signal of the load; and a filter connected to the load end sensor for filtering the output signal; wherein the nonlinear extended state observer is configured to receive the input signal and the output signal, and send a control signal for counteracting the disturbance to the feedback controller, and the feedback controller adjusts the input signal according to the control signal and a desired signal.

[0023] The technical solutions provided by the present application at least bring the following beneficial effects:

[0024] The nonlinear extended state observer provided by the present application can effectively solve the low-frequency oscillation after the traditional extended state observer is adjusted to the position in the scene with a large gear backlash or a low-resolution position sensor, thereby overcoming the oscillation problem after the adjustment to the position, improving the control precision and stability of the servo system, and being particularly suitable for the servo system with gear backlash and a low-resolution sensor. BRIEF DESCRIPTION OF DRAWINGS

[0025] The accompanying drawings, which are incorporated herein and constitute part of the specification, illustrate embodiments consistent with the present application and, together with the description, further serve to explain the principles of the application.

[0026] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the accompanying drawings needed to be used in the embodiments or the related description will be briefly introduced. Obviously, for those skilled in the art, based on the drawings, other drawings can be obtained without creative labor.

[0027] Figure 1 A block diagram of a nonlinear extended state observer provided for the embodiments of the present application;

[0028] Figure 2 A block diagram of another nonlinear extended state observer provided for the embodiments of the present application;

[0029] Figure 3 A flowchart of a control method of a nonlinear extended state observer provided for the embodiments of the present application;

[0030] Figure 4 A flowchart of another control method of a nonlinear extended state observer provided for the embodiments of the present application;

[0031] Figure 5 A flowchart of a servo system provided for the embodiments of the present application;

[0032] Figure 6 A flowchart of another servo system provided for the embodiments of the present application;

[0033] Figure 7 A line graph of an application of an extended state observer provided for the embodiments of the present application in a servo system;

[0034] Figure 8 A line graph of an application of a nonlinear extended state observer provided for the embodiments of the present application in a servo system;

[0035] Figure 9 A flowchart of a process of eliminating jitter by a nonlinear extended state observer provided for the embodiments of the present application.

[0036] Figure 1 , Figure 2 , Figure 5 and Figure 6 The correspondence between the reference signs and the component names in the drawings is as follows:

[0037] 1. Servo system, 2. Feedback controller, 3. Motor, 4. Gear transmission structure, 5. Load, 6. Load-end sensor, 7. Filter, 8. Driving circuit, 10. Nonlinear extended state observer, 11. Input unit, 12. Disturbance observation unit, 13. Output unit, 14. Nonlinear adjustment unit, 15. Limiting processing unit. DETAILED DESCRIPTION

[0038] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0039] like Figure 1 As shown, according to an embodiment of the first aspect of the present invention, a nonlinear extended state observer 10 for dealing with gear backlash is provided, which is used for a servo system 1. The servo system 1 includes a motor 3, a load 5, a load-end sensor 6 and a gear transmission structure 4. The nonlinear extended state observer 10 includes: an input unit 11, which is used to obtain an input signal of the voltage or current of the motor 3 during a closed-loop control process, and simultaneously receives and processes a speed or position measurement signal of the load 5; a disturbance observation unit 12, which observes and tracks the total disturbance based on the signal obtained by the input unit; and an output unit 13, which outputs a total disturbance observation value observed by the disturbance observation unit 12, and constructs a control signal for offsetting the disturbance based on the total disturbance observation value.

[0040] The nonlinear extended state observer 10 provided by the present invention is used in a servo system 1, which includes a motor 3, a load 5, a load-end sensor 6, and a gear transmission structure 4. The nonlinear extended state observer 10 includes an input unit 11, a disturbance observation unit 12, and an output unit 13. The input unit 11 is used to receive the voltage or current input signal of the motor 3 and output the speed or position measurement signal of the load 5; the disturbance observation unit 12 observes and tracks the total disturbance based on the signal obtained by the input unit; the output unit 13 outputs the observed total disturbance signal and constructs a control signal to cancel the disturbance based on the signal. As can be seen, the nonlinear extended state observer 10 of the present invention can effectively observe and track the total disturbance based on the input signal and construct a cancellation signal. In a gear transmission servo mechanism, when disturbances such as tooth system clearance or external vibration occur, it can accurately compensate for the disturbance. It is also suitable for low-resolution sensors and transmission mechanisms with large gear clearance, eliminating low-frequency oscillations after position adjustment. At the same time, the control accuracy and response speed are improved, ensuring accurate control of the position and speed of the load 5 and enhancing the system's robustness and anti-interference ability.

[0041] Optionally, in some embodiments, as shown in FIG. 1, the nonlinear extended state observer 10 further comprises a nonlinear adjustment unit 14 for adjusting the nonlinear parameters according to the transmission characteristics of the gear transmission structure 4, and a limiting processing unit 15 for limiting the results generated by the nonlinear adjustment unit 14. Figure 2

[0042] In this embodiment, the nonlinear extended state observer 10 further comprises a nonlinear adjustment unit 14 for adjusting the nonlinear parameters according to the transmission characteristics of the gear transmission structure 4, and a limiting processing unit 15 for limiting the results generated by the nonlinear adjustment unit 14. That is, the nonlinear adjustment unit 14 adjusts the parameters according to the gear transmission characteristics, which can accurately adapt to the transmission gap and sensor characteristics in servo mechanisms with large gear gaps or low-resolution sensors, maintain stable operation of the system, and reduce oscillation and errors. At the same time, the limiting processing unit 15 limits the nonlinear adjustment results to prevent system instability caused by signal distortion. In high disturbance, strong noise or extreme working conditions, the control signal is prevented from losing control due to abnormal fluctuations in the observation value.

[0043] Optionally, in some embodiments, the formula for observing and tracking the total disturbance comprises:

[0044]

[0045] wherein y(k) represents the output signal at the current sampling time, z1(k-1) represents the observation value of the output signal at the previous sampling time, and d represents the first intermediate variable;

[0046] d1 represents the second intermediate variable, sat(d, s1) represents the saturation function for limiting the range of the input signal, s1 represents the first nonlinear parameter to be adjusted, γ1 represents the third nonlinear parameter to be adjusted, and sign(d) represents the sign function, which takes the value of 1 when the value of d is positive, and takes the value of -1 when the value of d is negative;

[0047] z1(k) represents the observation value of the output signal at the current sampling time, T s represents the discrete period, which is generally within 10 ms, b represents the constant, u represents the input signal, τ represents the equivalent delay, represents the downward rounding of , β1 and β2 represent the parameters to be adjusted during use, and fal(d1, α1, δ1) represents a ternary function, wherein d1, α1, and δ1 are input parameters of the ternary function, and z2(k-1) represents the observation value of the total disturbance at the previous sampling time.

[0048] ​d2 represents a third intermediate variable, sat(d, s2) represents a saturation function, s2 represents a second to-be-adjusted nonlinear parameter, and γ2 represents a fourth to-be-adjusted nonlinear parameter, which is used to limit the range of an input signal;

[0049] z2(k) represents an observation value of the total disturbance at a current sampling moment, fal(d2, α2, δ2) represents a ternary function, d2, α2, and δ2 are input parameters of the ternary function.

[0050] In this embodiment, in a servo mechanism with a large gear gap and a low-resolution position sensor at the load end, the problem of low-frequency oscillation of the device after reaching the position caused by the traditional extended state observer is effectively overcome. Meanwhile, the above formula is highly compatible with the traditional extended state observer, and when a specific nonlinear parameter takes a specific value, it degenerates into the traditional form, thereby improving the application range of the nonlinear extended state observer.

[0051] Optionally, in some embodiments, the first to-be-adjusted nonlinear parameter s1 has a value greater than 0, the second to-be-adjusted nonlinear parameter s2 has a value greater than 0, the third to-be-adjusted nonlinear parameter γ1 has a value greater than 0 and less than or equal to 1, and the fourth to-be-adjusted nonlinear parameter γ2 has a value greater than 0 and less than or equal to 1.

[0052] In this embodiment, the first to-be-adjusted nonlinear parameter s1, the second to-be-adjusted nonlinear parameter s2, the third to-be-adjusted nonlinear parameter γ1, and the third to-be-adjusted nonlinear parameter γ2 have a wide range of values, so that the nonlinear extended state observer has high flexibility and precise control capability. In different gear transmission ratios, load characteristics, and disturbance intensity scenarios, the disturbance can be accurately tracked by parameter adjustment, thereby improving the control accuracy.

[0053] Optionally, in some embodiments, the third to-be-adjusted nonlinear parameter γ1 and the fourth to-be-adjusted nonlinear parameter γ2 both take the value 1, and the saturation limit value of the saturation function takes infinity.

[0054] In this embodiment, when the third to-be-adjusted nonlinear parameter γ1 and the fourth to-be-adjusted nonlinear parameter γ2 both take the value 1, and the saturation limit value of the saturation function takes infinity (a very large floating point number in engineering use), the nonlinear extended state observer tends to be the nonlinear extended state observer proposed by Han Jingqing in his book. At this time, the nonlinear extended state observer can effectively control the nonlinear system and the uncertain system through the total disturbance. That is, the nonlinear extended state observer of the present application has good compatibility, and the nonlinear extended state observer is a special extended state observer. Under different requirements, the third to-be-adjusted nonlinear parameter and the fourth to-be-adjusted nonlinear parameter can be changed to meet the different requirements of users.

[0055] Optionally, in some embodiments, the initial angular frequency ω o denote the parameters to be adjusted β1 and β2, β1 = 2·ω o ,

[0056] In this embodiment, the initial angular frequency ω o denote the parameters to be adjusted β1 and β2, β1 = 2·ω o , That is, the two parameters are unified to the initial angular frequency, greatly simplifying the adjustment complexity, and further simplifying the formula, improving the efficiency of observing and tracking the total disturbance, and accelerating the response speed of the nonlinear extended state observer.

[0057] Based on the same inventive concept, according to the embodiments of the second aspect of the present application, a control method of a nonlinear extended state observer is provided, which is used in a servo system including a motor, a load, a load end sensor and a gear transmission structure, as shown in Figure 3 The control method of the nonlinear extended state observer includes:

[0058] S101: obtaining an input signal of voltage or current of the motor in a closed-loop control process;

[0059] S102: receiving and processing a speed or position measurement signal of the load;

[0060] S103: observing and tracking the total disturbance based on the signal obtained by the input unit;

[0061] S104: determining the total disturbance observation value observed by the disturbance observation unit, and constructing a control signal for offsetting the disturbance according to the total disturbance observation value.

[0062] According to the control method of the nonlinear extended state observer provided by the present application, which is used in a servo system including a motor, a load, a load end sensor and a gear transmission structure. First, an input signal of voltage or current of the motor is received, then a speed or position measurement signal of the load is received and processed, and the speed or position measurement signal of the load is taken as an output signal, then the total disturbance is observed and tracked based on the input signal and the output signal, and finally, a control signal for offsetting the disturbance is constructed based on the total disturbance observation value output by the disturbance observation unit. As can be seen, the nonlinear extended state observer of the present application can effectively observe and track the total disturbance according to the input signal and the output signal, and construct an offsetting signal. In the gear transmission servo mechanism, when the disturbance is caused by gear clearance or external vibration, the disturbance can be accurately compensated, and it is suitable for low-resolution sensors and transmission mechanisms with large gear clearance, eliminating low-frequency oscillation after position switching. At the same time, the control precision and response speed are improved, ensuring accurate control of the load position and speed, and enhancing the system robustness and anti-interference ability.

[0063] Optionally, in some embodiments, as Figure 4 The control method of the nonlinear extended state observer further comprises:

[0064] S201: obtaining an input signal of voltage or current of the motor in the closed-loop control process;

[0065] S202: receiving and processing a speed or position measurement signal of the load;

[0066] S203: obtaining a transmission characteristic of the gear transmission structure;

[0067] S204: adjusting the nonlinear parameter according to the transmission characteristic of the gear transmission structure;

[0068] S205: observing and tracking the total disturbance based on the signal obtained by the input unit;

[0069] S206: determining the total disturbance observation value observed by the disturbance observation unit, and constructing a control signal for offsetting the disturbance according to the total disturbance observation value.

[0070] In this embodiment, the nonlinear extended state observer can also adjust the nonlinear parameter according to the transmission characteristic of the gear transmission structure, and for a servo mechanism with a large gear gap or a low-resolution sensor, the transmission gap and the sensor characteristic can be accurately adapted, the system can be stably operated, and oscillation and error can be reduced.

[0071] Based on the same inventive concept, according to the embodiment of the third aspect of the present application, a servo system with a gear transmission structure is provided, which comprises the nonlinear extended state observer according to the first aspect of the present application or any possible implementation manner of the first aspect.

[0072] According to the servo system with a gear transmission structure provided by the present application, the servo system comprises the nonlinear extended state observer according to the first aspect of the present application or any possible implementation manner of the first aspect, and therefore has all the beneficial effects of the nonlinear extended state observer according to the first aspect of the present application or any possible implementation manner of the first aspect.

[0073] Optionally, in some embodiments, as Figure 5As shown, the servo system with gear transmission structure further comprises: a feedback controller 2 for generating an input signal; a motor 3 connected to a driving circuit 8 and receiving the input signal amplified in power through the driving circuit 8; a gear transmission structure 4 having one end connected to an output end of the motor 3; a load 5 connected to the other end of the gear transmission structure 4; a load end sensor 6 connected to the load 5 for detecting an output signal of the load 5; and a filter 7 connected to the load end sensor 6 for filtering the output signal; wherein the nonlinear extended state observer 10 is configured to receive the input signal and the output signal and send a control signal for counteracting disturbance to the feedback controller 2, and the feedback controller 2 adjusts the input signal according to the control signal and a desired signal.

[0074] In this embodiment, the servo system with gear transmission structure further comprises a feedback controller 2, a motor 3, a gear transmission structure 4, a load 5, a load end sensor 6 and a filter 7, the feedback controller 2 is configured to generate an input signal, the motor 3 is connected to a driving circuit 8 and receives the input signal amplified in power through the driving circuit 8. The gear transmission structure 4 has one end connected to an output end of the motor 3, the load 5 is connected to the other end of the gear transmission structure 4, the load end sensor 6 is connected to the load 5 for detecting an output signal of the load 5. The filter 7 is connected to the load end sensor 6 for filtering the output signal. The nonlinear extended state observer 10 is configured to receive the input signal and the output signal and send a control signal for counteracting disturbance to the feedback controller 2, and the feedback controller 2 adjusts the input signal according to the control signal and a desired signal, and each component is closely coordinated to build a high-efficiency and stable control loop. It can be seen that the nonlinear extended state observer 10 of the present application can accurately capture the total disturbance of the system, construct a counteracting signal feedback to the controller, and effectively cope with the complex disturbances such as gear transmission gap, friction, vibration and load 5 variation.

[0075] In one specific application, the extended state observer in the related art is described for a system with a relative order of 1, and is aimed at a controlled object of the following relative order of 1 type,

[0076]

[0077] In formula (10),

[0078] y represents an output signal, which is generally obtained by filtering a sensor measurement signal. In the present application, it refers to a signal obtained by filtering the speed measured by the load end sensor of the gear transmission servo mechanism. When the load rotates, the rotational speed at the load end can be calculated by differentiating the angle measurement signal, or can be directly measured by a tachometer or a gyroscope. When the load moves linearly, the rotational speed at the load end is generally calculated by differentiating the displacement measured by a displacement sensor. The filter is generally a second-order critical damping low-pass filter with a frequency of 5Hz-500Hz; y(t) represents an output signal at time t, represents the derivative of the output signal at time t with respect to time t; t represents time, the unit is second, generally the time when the servo control system starts to perform closed-loop control is taken as the zero time; b represents a constant, which is related to the control gain or amplification factor, generally obtained by theoretical modeling or system identification; u represents the input signal, generally refers to the value of the voltage of the motor or the current. In the present application, it refers to the voltage loaded on the two ends of the DC motor or the current loaded on the AC motor. u(t) represents the input signal at time t, u(t-τ) represents the input signal at time t-τ; τ represents the equivalent time delay; f represents the equivalent total disturbance, the variables that affect the system output signal are regarded as the total disturbance, such as external disturbances caused by vibration, friction and temperature, which will affect the output signal, i.e. external disturbance. The sum of internal disturbance and external disturbance is equivalent to the total disturbance, and f(t) represents the total disturbance at time t.

[0079] For the system in formula (10), the following extended state observer is used to observe and track the disturbance f(t).

[0080]

[0081] In formula (2):

[0082] The meanings and values of t, τ, b and u are the same as those in formula (10), which will not be described here.

[0083] z1 and z2 represent the state quantities of the extended state observer, z1 represents the observed state of the output signal y in formula (10), and z2 represents the observed state of the total disturbance f(t) in formula (10), z1(t) represents the z1 state value at time t, and z2(t) represents the z2 state value at time t, represents the derivative of the z1 state value at time t with respect to time t, represents the derivative of the z2 state value at time t with respect to time t.

[0084] β1 and β2 are parameters to be adjusted during use, and β1=2·ω o , In this way, the two parameters to be adjusted β1 and β2 can be reduced to one parameter to be adjusted ω o .

[0085] sign() represents the sign function, which takes the value 1 when the value in the parentheses is positive, and takes the value -1 when the value in the parentheses is negative.

[0086] Since formula (2) is described in the continuous time domain, the actual algorithm implementation process is in the computer or microprocessor, so it needs to be discretized, and the chattering situation after discretization is considered, and formula (3) is obtained by discretization:

[0087]

[0088] Among them, T s represents the discrete period, i.e., the control sampling period, which is generally within 10 ms in practical engineering. The meanings and values ​​of τ, b, and u are the same as those in formula (10) and will not be described here.

[0089] The meanings and values ​​of z1, z2, β1, and β2 are the same as those in formula (2) and will not be described here. k represents the discrete sampling time, z1(k) represents the value of z1(t) at t = k·T s The value at the moment, z2(k) means z2(t) at t = k·T s The value at the time, y(k) represents y(t) at t = k·T s The value at the moment, z1(k-1) means z1(t) at t = (k-1)·T s The value at the moment, z2(k-1) means z2(t) at t = (k-1)·T s The value of the moment; Express Round down, u(k-1- ) indicates that u(t) is α1, δ1, α2, and δ2 represent the nonlinear parameters of the extended state observer to be tuned, and their value ranges are 0<α1≤1, 0<α2≤1, 0<δ1, and 0<δ2.

[0090] For example: the values ​​are α1=1, α2=0.5, and δ1 and δ2 are adjusted and set according to actual conditions.

[0091] fal(,,) represents a ternary function, and the corresponding expression is shown in the following formula (4).

[0092]

[0093] In formula (4), e, α, and δ are the three input parameters of the fal function, which are used to describe the relationship between the fal function value and the function input parameters.

[0094] The flow chart of the servo mechanism control signal with gear transmission is as follows Figure 6As shown, the input signal obtained by the control algorithm is converted into a driving voltage by the driving circuit 8, so as to control the motor 3 to generate a force or torque, and the corresponding force or torque drives the gear transmission structure 4 to operate, so as to transmit the corresponding force or torque to the load 5. The load end sensor 6 fixedly connected to the load 5 detects the speed and position of the load 5 after movement, and the speed is converted into an output signal of the control system after passing through the filter 7, and the position is converted into a displacement signal after passing through the filter 7. The corresponding control signal is constructed by the control algorithm, and finally the output signal meets the target requirement.

[0095] The jitter of the gear transmission servo mechanism in the related art when the nonlinear extended state observer is added is as shown in Figure 7 As shown, when the turning angle is required to be -50°, a constant amplitude oscillation with a period of about 1 second is generated after the turning angle reaches the position due to the effect of the nonlinear extended state observer. The reason may be that the gear backlash is large and the angle resolution is low, so that the control gain or amplification factor between the control signal and the output signal when the gear is in the non-engaged state tends to 0, and the control gain or amplification factor is in a constant constant state after the gear is engaged, so that the parameters of the nonlinear extended state observer are mismatched, and the disturbance observation fails.

[0096] Therefore, the application provides a nonlinear extended state observer for a gear transmission servo mechanism, which is described in the form of the following formula (5) by taking a second-order extended state observer as an example:

[0097]

[0098] In formula (5):

[0099] T s , tau, b, u, z1, z2, beta1, beta2, k, The meanings of the symbols alpha1, delta1, alpha2, delta2, fal(,,) and the like are the same as those in formula (3), and will not be described here again. d, d1 and d2 represent intermediate variables; s1, s2, gamma1 and gamma2 represent nonlinear parameters to be adjusted, which are used to cope with the influence of the gear transmission characteristics on the extended state observer, and the value ranges are 0

[0100] sat(,) represents a limiting function, and its expression is shown in the following formula (6):

[0101]

[0102] In formula (6), m and n are two input parameters of sat(,) function, which are used to describe the relationship between the value of sat(,) function and the input parameters of the function.

[0103] By adjusting the parameters, the nonlinear extended state observer of the application can overcome the oscillation problem after the turning to the position in the scene of large backlash and low resolution sensor. Figure 8 As shown in the servo mechanism of some devices, by changing the traditional extended state observer to the nonlinear extended state observer of the application (parameter values: s1=s2=2, γ1=γ2=0.9) without changing other control parameters, the low-frequency oscillation phenomenon after the turning to the position can be eliminated.

[0104] Meanwhile, the application is compatible with the extended state observer in related technologies in engineering, and can be used as the extended state observer in related technologies by parameter configuration, without worrying about the compatibility problem in use.

[0105] As shown in the servo mechanism of some devices, by changing the traditional extended state observer to the nonlinear extended state observer of the application (parameter values: s1=s2=2, γ1=γ2=0.9) without changing other control parameters, the low-frequency oscillation phenomenon after the turning to the position can be eliminated. Figure 9 As shown in the servo mechanism of some devices, by changing the traditional extended state observer to the nonlinear extended state observer of the application (parameter values: s1=s2=2, γ1=γ2=0.9) without changing other control parameters, the low-frequency oscillation phenomenon after the turning to the position can be eliminated.

[0106] S301: using the nonlinear extended state observer in the speed control loop;

[0107] S302: encoding the nonlinear extended state observer according to formula (5);

[0108] S303: setting s1 and s2 in formula (5) to positive numbers beyond the actual use range and setting γ1 and γ2 to 1 according to the situation;

[0109] S304: parameter setting according to the conventional extended state observer in formula (3);

[0110] S305: when low-frequency oscillation and jitter problems occur, adjusting parameters s1, s2, γ1 and γ2 to eliminate the jitter problem.

[0111] It has to be noted that, in the present document, relational terms are intended only to convey a possible relationship between elements or

[0112] The above description is merely that of the specific embodiments of the application and alterations and further modifications in the illustrated embodiments can be effected without departing from the spirit or scope of the application. Additionally, although the application has been described above with reference to particular means, materials and embodiments, the application is not intended to be limited to the particulars disclosed; rather, changes can be made in the specific details, as well as in the order of the steps, without departing from the spirit or scope of the application as defined by the appended claims. Thus, the scope of the application should be determined by the appended claims and their legal equivalents, rather than by the specific embodiments which have been discussed.

Claims

1. A nonlinear extended state observer (10) for backlash compensation of a gear, characterized by, A nonlinear extended state observer (10) for a servo system (1) comprising a motor (3), a load (5), a load end sensor (6) and a gear transmission structure (4), the nonlinear extended state observer (10) comprising: an input unit (11) for obtaining input signals of voltage or current of the motor (3) in a closed loop control process, and receiving and processing speed or position measurement signals of the load (5); a disturbance observation unit (12) for observing and tracking total disturbance based on signals obtained by the input unit; an output unit (13) for outputting total disturbance observation values observed by the disturbance observation unit (12), and constructing a control signal for counteracting disturbance according to the total disturbance observation values; the formula for observing and tracking total disturbance comprises: ； wherein denotes the output signal at the current sampling instant, denotes the observation of the output signal at the previous sampling instant, denotes the first intermediate variable; denotes a second intermediate variable, denotes a saturation function for limiting the range of the input signal, denotes a first nonlinear parameter to be adjusted, denotes a third nonlinear parameter to be adjusted, denotes a sign function which takes the value 1 when the value of d is positive and -1 when the value of d is negative; denotes the observation of the output signal at the current sampling instant, denotes the discrete period, denotes a constant, denotes the input signal, denotes the equivalent delay, denotes the floor operation on denotes the floor operation on and denotes the parameter to be adjusted during the use, denotes a ternary function, are the input parameters of the ternary function, respectively, denotes the observation of the total disturbance at the previous sampling instant; denotes a third intermediate variable, denotes a saturation function, denotes a second nonlinear parameter to be adjusted, denotes a fourth nonlinear parameter to be adjusted for limiting the range of the input signal; represents the observation of the total disturbance at the current sampling instant, represents a ternary function, are input parameters of the ternary function, respectively.

2. The nonlinear extended state observer (10) to cope with gear backlash according to claim 1, characterized in that further comprising: a nonlinear adjustment unit (15) for adjusting nonlinear parameters according to transmission characteristics of the gear transmission structure (4); an amplitude limiting processing unit (16) for performing amplitude limiting processing on results generated by the nonlinear adjustment unit (15).

3. The nonlinear extended state observer (10) to cope with gear backlash according to claim 1, characterized in that the first to-be-adjusted nonlinear parameter has a value greater than 0, the second to-be-adjusted nonlinear parameter has a value greater than 0, the third to-be-adjusted nonlinear parameter has a value greater than 0 and less than or equal to 1, and the fourth to-be-adjusted nonlinear parameter has a value greater than 0 and less than or equal to 1.

4. The nonlinear extended state observer (10) to cope with gear backlash of claim 3, wherein, the third to-be-adjusted nonlinear parameter and the fourth to-be-adjusted nonlinear parameter are all valued as 1, and the saturation limit value of the saturation function is infinite.

5. The nonlinear extended state observer (10) to cope with gear backlash of claim 4, wherein, With initial angular frequency representing said parameter to be regulated and , , .

6. A control method of a nonlinear extended state observer for backlash of a gear, characterized by, A control method for a servo system comprising a motor, a load, a load end sensor and a gear transmission structure, the control method comprising: obtaining input signals of voltage or current of the motor in a closed loop control process; receiving and processing speed or position measurement signals of the load; observing and tracking total disturbance based on signals obtained by the input unit; observing and tracking total disturbance based on the input signals and output signals; the formula for observing and tracking total disturbance comprises: ； wherein denotes the output signal at the current sampling instant, denotes the observation of the output signal at the previous sampling instant, denotes a first intermediate variable; denotes a second intermediate variable, denotes a saturation function for limiting the range of the input signal, denotes a first nonlinear parameter to be adjusted, denotes a third nonlinear parameter to be adjusted, denotes a sign function which takes the value 1 when the value of d is positive and -1 when the value of d is negative; denotes the observation of the output signal at the current sampling instant, denotes the discrete period, denotes a constant, denotes the input signal, denotes the equivalent delay, denotes the rounding down of and denotes the parameter to be adjusted during use, denotes a ternary function, are respectively the input parameters of the ternary function, denotes the observation of the total disturbance at the previous sampling instant;​ denotes a third intermediate variable, denotes a saturation function, denotes a second nonlinear parameter to be adjusted, denotes a fourth nonlinear parameter to be adjusted for limiting the range of the input signal; represents an observation of the total disturbance at the current sampling instant, represents a ternary function, are, respectively, input parameters of the ternary function; determining total disturbance observation values observed by the disturbance observation unit, and constructing a control signal for counteracting disturbance according to the total disturbance observation values.

7. The control method of the nonlinear extended state observer for backlash of gears according to claim 6, wherein further comprising: obtaining transmission characteristics of the gear transmission structure; adjusting nonlinear parameters according to transmission characteristics of the gear transmission structure.

8. A servo system (1) with a gear transmission, characterized in that comprising the nonlinear extended state observer (10) according to any one of claims 1 to 5.

9. Servo system (1) with gear transmission according to claim 8, characterized in that further comprising: a feedback controller (2) for generating input signals; a motor (3) connected to a driving circuit (8) and receiving the input signals after power conversion by the driving circuit (8); a gear transmission structure (4) connected to an output end of the motor (3) at one end; a load (5) connected to the other end of the gear transmission structure (4); a load end sensor (6) connected to the load (5) for detecting output signals of the load (5); a filter (7) connected to the load end sensor (6) for filtering the output signals; wherein the nonlinear extended state observer (10) is used for receiving the input signals and the output signals, and sending the constructed control signal for counteracting disturbance to the feedback controller (2), and the feedback controller (2) adjusts the input signals according to the control signal and a desired signal.

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