Active-disturbance-rejection control method for processing position loop crossing
By designing differential tracker, state observer and nonlinear state error feedback control rate, sensor jump and system oscillation problems caused by position overturning in servo self-immune disturbance control algorithm are solved, and stable servo system control and variable overflow prevention are achieved.
Patent Information
- Application Number
- CN202510343651.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-22
- Publication Date
- 2025-07-04
AI Technical Summary
In the servo-automatic control algorithm, position overturning causes position sensor to jump, causing state observer oscillation, nonlinear state error feedback control rate to generate abnormal control amount, tracking differentials cannot arrange the shortest path, and there is a risk of program variable overflow.
A self-immune control method for handling position over-circle was designed, including determining the position sensor range, designing differential trackers, state observers and nonlinear state error feedback control rates, and avoiding variable overflow by optimizing differential trackers and state observers.
It realizes stable control of the servo system when the position is overturned, avoids system oscillation and variable overflow, and ensures the effectiveness of the self-immune control method.
Smart Images
Figure CN120255338A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of servo control, and particularly relates to an active disturbance rejection control method for processing position overrun. Background Art
[0002] The active disturbance rejection control algorithm can actively compensate for disturbances and is simply implemented and widely applied in servo control systems. However, during servo position control, the controlled object may rotate over a full circle, causing a jump in the position sensor. This jump in position will affect the normal operation of the active disturbance rejection control algorithm, resulting in system oscillation and even divergence. Summary of the Invention
[0003] (I) Technical Problems to be Solved
[0004] The technical problem to be solved by the present invention is: based on the servo active disturbance rejection control algorithm, how to improve the method for the position overrun problem. The main problems to be solved are:
[0005] 1) When the position jumps, the observed quantity of the state observer oscillates.
[0006] 2) When the position jumps, the nonlinear state error feedback control rate generates abnormal control quantities, causing the entire system to oscillate or diverge.
[0007] 3) The tracking differentiator cannot arrange the shortest path to reach the transition process according to the jumped position.
[0008] 4) Considering the embedded implementation of the program, a data processing method for preventing overflow is designed for internal variables.
[0009] (II) Technical Solutions
[0010] To solve the above technical problems, the present invention provides an active disturbance rejection control method for processing position overrun, and the method includes the following steps:
[0011] Step 1: Determine the range of the actual position θ of the position sensor;
[0012] Step 2: Determine the expression forms of the three links of the servo active disturbance rejection control algorithm;
[0013] Step 3: Design a tracking differentiator;
[0014] Step 4: Design a state observer;
[0015] Step 5: Design a nonlinear state error feedback control rate;
[0016] Step 6: Optimize the tracking differentiator and the state observer.
[0017] Among them, in step 1, for the position overrun system, when performing a full-circle continuous rotation, the range of the actual position θ of the position sensor is 0 ≤ θ < 2π (unit: radian); define the overrun jump position point of the position sensor as α. Then, when the overrun jump position point is α, the range of the actual position θ of the position sensor is adjusted to -α ≤ θ < 2π - α, where 0 ≤ α ≤ 2π.
[0018] Among them, in step 2, define: k as the sampling time, θ * (k) is the desired position of the position sensor at sampling time k, θ(k) is the actual position of the position sensor at sampling time k, h is the sampling period, u(k) is the control quantity calculated and output by the active disturbance rejection control algorithm at sampling time k, and b0 is the control parameter of the active disturbance rejection control algorithm;
[0019] Then the servo active disturbance rejection control algorithm consists of three parts: a differential tracker, a state observer, and a nonlinear state error feedback control law.
[0020] Among them, in step 2, the expression form of the differential tracker is:
[0021]
[0022] Among them, e TD (k) is the error of the differential tracker at sampling time k;
[0023] θ1(k) and θ2(k) are the output values planned by the differential tracker at sampling time k;
[0024] θ1(k + 1) and θ2(k + 1) are the output values planned by the differential tracker at sampling time k + 1;
[0025] f(θ2(k), e TD (k)) is the unified expression form of the fastest function of the differential tracker.
[0026] Among them, in step 2, the expression form of the state observer is:
[0027]
[0028] Among them, e is the state observer error;
[0029] z1(k), z2(k), and z3(k) are the three state variables of the state observer at sampling time k;
[0030] z1(k + 1), z2(k + 1), and z3(k + 1) are the three state variables of the state observer at sampling time k + 1;
[0031] β 01 、β02 、β 03 are the three control parameters of the state observer;
[0032] Among them, in the said step 2, the expression form of the non-linear state error feedback control law is:
[0033]
[0034] Among them, e1 and e2 are the two error quantities of the non-linear state error feedback control law, and β1 and β2 are the two control parameters of the non-linear state error feedback control law.
[0035] Among them, in the said step 3, considering that the position sensor will have a loop jump, and there is a situation where the position movement of the position sensor obtained by the differential tracker planning is not the shortest arrival path, so the differential tracker is designed as:
[0036]
[0037] Among them, in the said step 4, considering that the position sensor will have a loop jump and to avoid the oscillation of the observed quantity of the state observer, the state observer is designed as:
[0038]
[0039] Among them, in the said step 5, considering that the position sensor will have a loop jump and to avoid the generation of abnormal control quantities by the non-linear state error feedback control law, the non-linear state error feedback control law is designed as:
[0040]
[0041] Among them, in the said step 6, the active disturbance rejection control method for processing position over-loop can be realized through the above steps. However, considering that if the position command continuously rotates in one direction, in actual calculation, to avoid the risk of overflow of the stored variable value; θ1(k) of the differential tracker and z1(k) of the state observer are further designed as:
[0042] If θ1(k) is greater than 2π, subtract 2π, and loop like this until θ1(k) is less than 2π;
[0043] If θ1(k) is less than -2π, add 2π, and loop like this until θ1(k) is greater than -2π;
[0044] If z1(k) is greater than 2π, subtract 2π, and loop like this until θ1(k) is less than 2π;
[0045] If z1(k) is less than -2π, add 2π, and loop like this until θ1(k) is greater than -2π.
[0046] (III) Beneficial effects
[0047] Compared with the prior art, the protection points of the present invention include:
[0048] 1) When dealing with the situation of position overrun, the design method of the active disturbance rejection state observer.
[0049] 2) When dealing with the situation of position overrun, the design method of the active disturbance rejection nonlinear state error feedback control law.
[0050] 3) When dealing with the situation of position overrun, the design method of the active disturbance rejection differentiator.
[0051] 4) Considering the embedded implementation of the program, the data processing method for preventing overflow in the design of internal variables.
[0052] Through the present invention, it is possible to achieve that for a servo system capable of overrun operation, corresponding control can still be performed through the active disturbance rejection control method and the implementation is simple. Description of the Drawings
[0053] Figures 1 - 4 It is a schematic diagram of an embodiment of the present invention. Detailed Embodiment
[0054] To make the objectives, contents, and advantages of the present invention clearer, the following further describes in detail the specific embodiments of the present invention with reference to the drawings and embodiments.
[0055] To solve the above technical problems, the present invention provides an active disturbance rejection control method for dealing with position overrun, and the method includes the following steps:
[0056] Step 1: Determine the range of the actual position θ of the position sensor;
[0057] Step 2: Determine the expression forms of the three links of the servo active disturbance rejection control algorithm;
[0058] Step 3: Design a differentiator;
[0059] Step 4: Design a state observer;
[0060] Step 5: Design a nonlinear state error feedback control law;
[0061] Step 6: Optimize the differentiator and the state observer.
[0062] Among them, in the above Step 1, for the position overrun system, in the case of continuous rotation for a full circle, the range of the actual position θ of the position sensor is 0 ≤ θ < 2π (unit: radian); define the position sensor overrun jump position point as α, then in the case of the overrun jump position point being α, the range of the actual position θ of the position sensor is adjusted to -α ≤ θ < 2π - α, where 0 ≤ α ≤ 2π.
[0063] Among them, in the said step 2, it is defined that: k is the sampling time, θ * (k) is the desired position of the position sensor at the sampling time k, θ(k) is the actual position of the position sensor at the sampling time k, h is the sampling period, u(k) is the control quantity calculated and output by the active disturbance rejection control algorithm at the sampling time k, and b0 is the control parameter of the active disturbance rejection control algorithm;
[0064] Then the servo active disturbance rejection control algorithm has three links, namely: differential tracker, state observer, and nonlinear state error feedback control law.
[0065] Among them, in the said step 2, the expression form of the differential tracker is:
[0066]
[0067] Among them, e TD (k) is the error of the differential tracker at the sampling time k;
[0068] θ1(k), θ2(k) are the output values planned by the differential tracker at the sampling time k;
[0069] θ1(k + 1), θ2(k + 1) are the output values planned by the differential tracker at the sampling time k + 1;
[0070] f(θ2(k), e TD (k)) is the unified expression form of the fastest function of the differential tracker.
[0071] Among them, in the said step 2, the expression form of the state observer is:
[0072]
[0073] Among them, e is the state observer error;
[0074] z1(k), z2(k), z3(k) are the three state variables of the state observer at the sampling time k;
[0075] z1(k + 1), z2(k + 1), z3(k + 1) are the three state variables of the state observer at the sampling time k + 1;
[0076] β 01 、β 02 、β 03 are the three control parameters of the state observer;
[0077] Among them, in the said step 2, the expression form of the nonlinear state error feedback control law is:
[0078]
[0079] Among them, e1 and e2 are two error quantities of the nonlinear state error feedback control rate, and β1 and β2 are two control parameters of the nonlinear state error feedback control rate.
[0080] Among them, in step 3, considering that the position sensor may have an over - cycle jump, and there is a situation where the position movement of the position sensor obtained by the differential tracker planning is not the shortest arrival path, the differential tracker is designed as:
[0081]
[0082] Among them, in step 4, considering that the position sensor may have an over - cycle jump and to avoid the oscillation of the observed quantity of the state observer, the state observer is designed as:
[0083]
[0084] Among them, in step 5, considering that the position sensor may have an over - cycle jump and to avoid the generation of abnormal control quantities by the nonlinear state error feedback control rate, the nonlinear state error feedback control rate is designed as:
[0085]
[0086] Among them, in step 6, the active disturbance rejection control method for processing position over - cycle can be realized through the above steps. However, considering that if the position command continuously rotates in one direction, in actual calculations, to avoid the risk of overflow of the stored variable values; θ1(k) of the differential tracker and z1(k) of the state observer are further designed as:
[0087] If θ1(k) is greater than 2π, subtract 2π, and loop like this until θ1(k) is less than 2π;
[0088] If θ1(k) is less than - 2π, add 2π, and loop like this until θ1(k) is greater than - 2π;
[0089] If z1(k) is greater than 2π, subtract 2π, and loop like this until θ1(k) is less than 2π;
[0090] If z1(k) is less than - 2π, add 2π, and loop like this until θ1(k) is greater than - 2π.
[0091] Embodiment 1
[0092] In this embodiment, for a certain position over - cycle system, the continuous rotation position θ is 0 ≤ θ < 2π (unit: radian). The position point of the over - cycle jump of the position sensor is defined as π, then the position information of the sensor is - π ≤ θ < π.
[0093] According to the specific implementation steps 1-5 of the technical solution of the present invention, a differential tracker, a state observer, and a non-linear state error feedback control rate are designed, respectively:
[0094] Differential tracker:
[0095]
[0096] State observer:
[0097]
[0098] Non-linear state error feedback control rate:
[0099]
[0100] The input command is Figure 1 , and the control effect of the present invention is Figure 2 .
[0101] As can be seen from the figure, the servo system can move along the shortest arrival path and can handle the sensor jump caused by over-running of the position.
[0102] However, at this time, the variables θ1(k) of the differential tracker and z1(k) of the state observer are Figure 3 .
[0103] As the continuously rotating variable continues to increase / decrease, there is a risk of data overflow. In step 6, θ1(k) of the differential tracker and z1(k) of the state observer are designed as:
[0104]
[0105] and
[0106]
[0107] The control effect of the present invention remains unchanged, and the variables θ1(k) of the differential tracker and z1(k) of the state observer become Figure 4 .
[0108] As shown in the figure, the technical solution of the present invention avoids the risk of internal variable overflow.
[0109] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the technical principle of the present invention, several improvements and deformations can be made, and these improvements and deformations should also be regarded as the protection scope of the present invention.
Claims
1. An active disturbance rejection control method for processing position overrun, characterized in that The method includes the following steps: Step 1: Determine the range of the actual position θ of the position sensor; Step 2: Determine the expression forms of the three links of the servo active disturbance rejection control algorithm; Step 3: Design a differential tracker; Step 4: Design a state observer; Step 5: Design a non-linear state error feedback control law; Step 6: Optimize the differential tracker and the state observer.
2. The active disturbance rejection control method for processing position overrun according to claim 1, wherein In the above Step 1, for the position overrun system, in the case of continuous full-circle rotation, the range of the actual position θ of the position sensor is 0 ≤ θ < 2π; define the position sensor overrun jump position point as α, then in the case of the overrun jump position point being α, the range of the actual position θ of the position sensor is adjusted to -α ≤ θ < 2π - α, where 0 ≤ α ≤ 2π.
3. The active disturbance rejection control method for processing position overrun according to claim 2, characterized in that In the said step 2, it is defined that: k is the sampling time, and θ * (k) is the desired position of the position sensor at the sampling time k, θ(k) is the actual position of the position sensor at the sampling time k, h is the sampling period, u(k) is the control quantity calculated and output by the active disturbance rejection control algorithm at the sampling time k, and b0 is the control parameter of the active disturbance rejection control algorithm; Then the three links of the servo active disturbance rejection control algorithm are respectively: a differential tracker, a state observer, and a non-linear state error feedback control law.
4. The active disturbance rejection control method for processing position overrun according to claim 3, wherein In the above Step 2, the expression form of the differential tracker is: Among them, e TD (k) is the error of the differential tracker at sampling time k; θ1(k) and θ2(k) are the output values planned by the differential tracker at the sampling time k; θ1(k + 1) and θ2(k + 1) are the output values planned by the differential tracker at the sampling time k + 1; f(θ2(k),e TD (k)) is the unified expression form of the fastest function of the differential tracker.
5. The active disturbance rejection control method for processing position overrun according to claim 4, characterized in that In the above Step 2, the expression form of the state observer is: where e is the state observer error; z1(k), z2(k), and z3(k) are the three state variables of the state observer at the sampling time k; z1(k + 1), z2(k + 1), and z3(k + 1) are the three state variables of the state observer at the sampling time k + 1; β 01 , β 02 , β 03 are the three control parameters of the state observer.
6. The active disturbance rejection control method for processing position overrun according to claim 5, characterized in that, In the above Step 2, the expression form of the non-linear state error feedback control law is: where e1 and e2 are the two error quantities of the non-linear state error feedback control law, and β1 and β2 are the two control parameters of the non-linear state error feedback control law.
7. The active disturbance rejection control method for processing position overrun according to claim 6, characterized in that, In the above Step 3, considering that the position sensor will have an overrun jump, and there is a situation where the position movement process of the position sensor obtained by the differential tracker planning is not the shortest arrival path, therefore, the differential tracker is designed as:
8. The active disturbance rejection control method for processing position overrun according to claim 7, characterized in that, In the above Step 4, considering that the position sensor will have an overrun jump and to avoid the oscillation of the observed quantity of the state observer, the state observer is designed as:
9. The active disturbance rejection control method for processing position overrun according to claim 8, characterized in that, In the above Step 5, considering that the position sensor will have an overrun jump and to avoid the generation of abnormal control quantities by the non-linear state error feedback control law, the non-linear state error feedback control law is designed as:
10. The active disturbance rejection control method for processing position overrun according to claim 9, characterized in that, In the above Step 6, the active disturbance rejection control method for handling position overrun can be realized through the above steps. However, considering that if the position command continuously rotates in one direction, in actual calculations, to avoid the risk of overflow of the stored variable values; θ1(k) of the differential tracker and z1(k) of the state observer are further designed as: If θ1(k) is greater than 2π, subtract 2π, and loop like this until θ1(k) is less than 2π; If θ1(k) is less than -2π, add 2π, and loop like this until θ1(k) is greater than -2π; If z1(k) is greater than 2π, subtract 2π, and loop like this until θ1(k) is less than 2π; If z1(k) is less than -2π, add 2π, and loop like this until θ1(k) is greater than -2π.