A servo control method based on active disturbance rejection control

Abstract

The present invention belongs to the field of servo control technology, and specifically relates to a servo control method based on anti-disturbance control. The method introduces a tracking differentiator at the input end to arrange a suitable transition process and obtain the differential of the input signal according to the tolerance of the system, the rationality of the change of the controlled quantity, and the control capability provided by the system. A tracking differentiator with a very low noise amplification effect is introduced at the feedback end to extract the differential of the feedback signal, and the controller generates a control quantity using the signal processed by the tracking differentiator. Compared with the traditional linear combination PID control method, the present invention can be applied to more scenarios by changing the linear combination mode; the introduction of the differential term instead of the integral term can suppress overshoot while ensuring the rapidity of the system.

Description

Technical Field

[0001] The present invention belongs to the technical field of servo control, and in particular relates to a servo control method based on active disturbance rejection control, which satisfies a servo system with different application requirements by changing the form of nonlinear combination. Background Art

[0002] The main advantage of the PID control method currently widely used in the servo control field is that the control strategy to eliminate the error is determined by the error between the target and the actual behavior, rather than by the input-output relationship of the object, that is, the control strategy is not determined by the input-output model of the object. As long as the PID gain is selected to stabilize the closed loop, the object can reach the static index. However, with the development of science and technology, the requirements for control accuracy, dynamic processes, and adaptability to environmental changes are getting higher and higher, and the classic PID is slowly beginning to fail to meet the requirements of the system. In order to obtain better control performance, a large number of advanced control methods have been proposed. Existing methods mainly focus on improving feedback controllers to improve control performance. However, there is an inherent hysteresis effect in feedback controllers, which limits the further improvement of control performance. Summary of the invention

[0003] 1. Technical issues to be resolved

[0004] The technical problem to be solved by the present invention is: in view of the problems existing in the prior art, the present invention provides a servo control method based on active disturbance rejection control.

[0005] (II) Technical solution

[0006] In order to solve the problems in the prior art, the present invention provides a servo control method based on active disturbance rejection control, the method comprising the following steps:

[0007] Step S1, obtaining a command signal to be tracked;

[0008] Step S2, obtaining a feedback signal;

[0009] Step S3, using a first tracking differentiator to filter the instruction, the input of the first tracking differentiator is the instruction signal, and the output of the first tracking differentiator is the filtered instruction signal and the differential of the instruction signal;

[0010] Step S4, using a second tracking differentiator to filter the feedback signal, the input of the second tracking differentiator is the feedback signal, and the output of the second tracking differentiator is the filtered feedback signal and the differential of the feedback signal;

[0011] Step S5, the calculation controller generates a control signal u; according to the filtered command signal output by the first tracking differentiator, the differential of the command signal, and the filtered feedback signal output by the second tracking differentiator, the differential of the feedback signal, the output of the controller is calculated to be the control quantity u.

[0012] The first tracking differentiator in step S3 has the following form:

[0013]

[0014] Among them, x 1 (k) is the command signal filtered by the tracking differentiator at the kth moment, k represents the sequence number of the moment, and the value range is k = 0, 1, 2, 3...; v 1 (k) is the differential of the command signal output by the tracking differentiator at the kth moment, x 1 (k+1) is the command signal filtered by the tracking differentiator at the k+1th moment, v 1 (k+1) is the differential of the command signal output by the tracking differentiator at the k+1th moment; s 1 (k) is the command signal at the kth moment, that is, the input of the first tracking differentiator; r 1 、h 1 is a positive constant, f 1 is an auxiliary variable, p 1 is a function whose input is x 1 (k)-s 1 (k), v 1 (k), r 1 、h 1 ;p 1 The specific expression is

[0015]

[0016] Among them, d 1 , d' 1 is a constant, y 1 , a 1 , a' 1 is an auxiliary variable,

[0017] sign(y 1 ) is expressed as

[0018]

[0019] sign(a 1 ) is expressed as

[0020]

[0021] The second tracking differentiator in step S4 has the following form:

[0022]

[0023] Among them, x 2 (k) is the feedback signal filtered by the tracking differentiator at the kth moment, k represents the sequence number of the moment, and the value range is k = 1, 2, 3...; v 2 (k) is the differential of the feedback signal output by the tracking differentiator at the kth moment, x 2 (k+1) is the feedback signal filtered by the tracking differentiator at the k+1th moment, v 2 (k+1) is the differential of the feedback signal output by the tracking differentiator at the k+1th moment; s 2 (k) is the feedback signal at the kth moment, which is the input of the second tracking differentiator; r 2 、h 2 is a positive constant, f 2 is an auxiliary variable, p 2 is a function whose input is x 2 (k)-s 2 (k), v 2 (k), r 2 、h 2 ;p 2 The expression is

[0024]

[0025] Among them, d 2 , d' 2 is a constant, y 2 , a 2 , a' 2 is an auxiliary variable,

[0026] sign(y 2 ) is expressed as

[0027]

[0028] sign(a 2 ) is expressed as

[0029]

[0030] The controller in step S5 has the following form:

[0031] u(k)=k p (x 1 (k)+k s v 1 (k)-x 2 (k))+kd (v 1 (k)-v 2 (k))

[0032] Among them, k p is the proportional term coefficient, k d is the differential term coefficient, k s is the coefficient of the speed compensation term.

[0033] (III) Beneficial effects

[0034] The servo control method in the present invention is based on the idea of ​​self-disturbance rejection control. On the basis of improving the feedback controller, the command and feedback are filtered by a tracking differentiator to make them smoother. At the same time, the differential signals of the command and feedback are extracted and introduced into the controller, thereby overcoming the inherent lag effect of the feedback controller and improving the control performance.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] (1) Compared with the traditional PID method, the method provided by the present invention performs smoothing on both the feedback signal and the command signal; instead of using the integral term, the differential term is introduced to suppress overshoot while ensuring the rapidity of the system.

[0037] (2) Using the first tracking differentiator to filter the instruction has a smoothing effect on the instruction, which is helpful to reduce the overshoot when tracking fast-changing instructions such as step instructions;

[0038] (3) The differential of the command signal is estimated using the first tracking differentiator and introduced into the controller, which is beneficial to enhancing the rapidity of servo system tracking.

[0039] (4) Using the second tracking differentiator to estimate the differential of the feedback signal is beneficial to enhancing the smoothness of the differential signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 The present invention is a principle block diagram of a servo control method based on active disturbance rejection control. DETAILED DESCRIPTION

[0041] In order to make the purpose, content, and advantages of the present invention more clear, the specific implementation methods of the present invention are further described in detail below in conjunction with the accompanying drawings and examples.

[0042] In order to solve the problems in the prior art, the present invention provides a servo control method based on anti-disturbance control. According to the tolerance of the system, the rationality of the change of the controlled quantity and the control capability provided by the system, a tracking differentiator is introduced at the input end to arrange a suitable transition process and obtain the differential of the input signal. A tracking differentiator with a very low noise amplification effect is introduced at the feedback end to extract the differential of the feedback signal. The error feedback law is formed in the form of nonlinear combination to generate the control quantity to realize closed-loop control of the controlled object. It includes:

[0043] 1. Filtering strategy for filtering instructions;

[0044] 2. Differentiation strategy for differentiating the feedback signal;

[0045] 3. A control strategy that generates a control signal using filtered instructions, feedback signals, and the differential of feedback signals.

[0046] The method comprises the following steps:

[0047] Step S1, obtaining a command signal to be tracked;

[0048] Step S2, obtaining a feedback signal;

[0049] Step S3, using a first tracking differentiator to filter the instruction, the input of the first tracking differentiator is the instruction signal, and the output of the first tracking differentiator is the filtered instruction signal and the differential of the instruction signal;

[0050] Step S4, using a second tracking differentiator to filter the feedback signal, the input of the second tracking differentiator is the feedback signal, and the output of the second tracking differentiator is the filtered feedback signal and the differential of the feedback signal;

[0051] Step S5, the calculation controller generates a control signal u; according to the filtered command signal output by the first tracking differentiator, the differential of the command signal, and the filtered feedback signal output by the second tracking differentiator, the differential of the feedback signal, the output of the controller is calculated to be the control quantity u.

[0052] The first tracking differentiator in step S3 has the following form:

[0053]

[0054] Among them, x 1 (k) is the command signal filtered by the tracking differentiator at the kth moment, k represents the sequence number of the moment, and the value range is k = 0, 1, 2, 3...; v 1 9k) is the differential of the command signal output by the tracking differentiator at the kth moment, x 1(k+1) is the command signal filtered by the tracking differentiator at the k+1th moment, v 1 (k+1) is the differential of the command signal output by the tracking differentiator at the k+1th moment; s 1 (k) is the command signal at the kth moment, that is, the input of the first tracking differentiator; r 1 、h 1 is a positive constant, f 1 is an auxiliary variable, p 1 is a function whose input is x 1 (k)-s 1 (k), v 1 (k), r 1 、h 1 ;p 1 The specific expression is

[0055]

[0056] Among them, d 1 , d' 1 is a constant, y 1 , a 1 , a' 1 is an auxiliary variable,

[0057] sign(y 1 ) is expressed as

[0058]

[0059] sign(a 1 ) is expressed as

[0060]

[0061] The second tracking differentiator in step S4 has the following form:

[0062]

[0063] Among them, x 2 (k) is the feedback signal filtered by the tracking differentiator at the kth moment, k represents the sequence number of the moment, and the value range is k = 1, 2, 3...; v 2 (k) is the differential of the feedback signal output by the tracking differentiator at the kth moment, x 2 (k+1) is the feedback signal filtered by the tracking differentiator at the k+1th moment, v 2 (k+1) is the differential of the feedback signal output by the tracking differentiator at the k+1th moment; s 2 (k) is the feedback signal at the kth moment, which is the input of the second tracking differentiator; r 2 、h2 is a positive constant, f 2 is an auxiliary variable, p 2 is a function whose input is x 2 (k)-s 2 (k), v 2 (k), r 2 、h 2 ;p 2 The expression is

[0064]

[0065] Among them, d 2 , d' 2 is a constant, y 2 , a 2 , a' 2 is an auxiliary variable,

[0066] sign(y 2 ) is expressed as

[0067]

[0068] sign(a 2 ) is expressed as

[0069]

[0070] The controller in step S5 has the following form:

[0071] u(k)=k p (x 1 (k)+k s v 1 (k)-x 2 (k))+k d (v 1 (k)-v 2 (k))

[0072] Among them, k p is the proportional term coefficient, k d is the differential term coefficient, k s is the coefficient of the speed compensation term.

[0073] Example 1

[0074] The servo control method based on the active disturbance rejection control provided in this embodiment has a control structure as follows: Figure 1As shown in the figure, it can be seen that after the command signal is filtered by the first tracking differentiator, two signals are generated, namely the filtered command signal and the differential of the command signal. After the feedback signal is filtered by the second tracking differentiator, two signals are generated, namely the filtered feedback signal and the differential of the feedback signal. These four signals are used as the input of the controller, so that the controller generates the control quantity, thereby controlling the movement of the servo system.

[0075] The specific implementation steps are as follows:

[0076] A servo control method based on active disturbance rejection control comprises the following steps

[0077] Step 1: Obtain a command signal, which may be a step signal, a ramp signal, or other more complex curve signals.

[0078] Step 2: Get feedback signal. The feedback signal is generally measured by a sensor.

[0079] Step 3: Based on the acquired command signal, calculate the two outputs of the first tracking differentiator according to the following formula.

[0080]

[0081] Among them, x 1 (k) is the command signal filtered by the tracking differentiator at the kth moment, k represents the sequence number of the moment, and the value range is k = 0, 1, 2, 3... 1 (k) is the differential of the command signal output by the tracking differentiator at the kth moment, x 1 (k+1) is the command signal filtered by the tracking differentiator at the k+1th moment, v 1 (k+1) is the differential of the command signal output by the tracking differentiator at the k+1th moment. 1 (k) is the command signal at the kth moment, which is the input of the first tracking differentiator. 1 、h 1 is a positive constant, f 1 is an auxiliary variable, p 1 is a function whose input is x 1 (k)-s 1 (k), v 1 (k), r 1 、h 1 . p 1 The specific expression is

[0082]

[0083] Among them, d 1 , d' 1 is a constant, y 1 , a1 , a' 1 is an auxiliary variable,

[0084] sign(y 1 ) is expressed as

[0085]

[0086] sign(a 1 ) is expressed as

[0087]

[0088] Step 4: Based on the obtained feedback signal, calculate the two outputs of the second tracking differentiator as follows:

[0089]

[0090] Among them, x 2 (k) is the feedback signal filtered by the tracking differentiator at the kth moment, k represents the sequence number of the moment, and the value range is k = 1, 2, 3... 2 (k) is the differential of the feedback signal output by the tracking differentiator at the kth moment, x 2 (k+1) is the feedback signal filtered by the tracking differentiator at the k+1th moment, v 2 (k+1) is the differential of the feedback signal output by the tracking differentiator at the k+1th moment. 2 (k) is the feedback signal at the kth moment, which is also the input of the second tracking differentiator. 2 、h 2 is a positive constant, f 2 is an auxiliary variable, p 2 is a function whose input is x 2 (k)-s 2 (k), v 2 (k), r 2 、h 2 . p 2 The expression is

[0091]

[0092] Among them, d 2 , d' 2 is a constant, y 2 , a 2 , a' 2 is an auxiliary variable,

[0093] sign(y 2 ) is expressed as

[0094]

[0095] sign(a 2 ) is expressed as

[0096]

[0097] Step 5: Calculate the output of the controller according to the following formula based on the outputs of the first tracking differentiator and the second tracking differentiator.

[0098] u(k)=k p (x 1 (k)+k s v 1 (k)-x 2 (k))+k d (v 1 (k)-v 2 (k))

[0099] Among them, k p is the proportional term coefficient, k d is the differential term coefficient, k s is the speed compensation coefficient.

[0100] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A servo control method based on active disturbance rejection control, characterized in that: The method comprises the following steps: Step S1, obtaining a command signal to be tracked; Step S2, obtaining a feedback signal; Step S3, using a first tracking differentiator to filter the instruction, the input of the first tracking differentiator is the instruction signal, and the output of the first tracking differentiator is the filtered instruction signal and the differential of the instruction signal; Step S4, using a second tracking differentiator to filter the feedback signal, the input of the second tracking differentiator is the feedback signal, and the output of the second tracking differentiator is the filtered feedback signal and the differential of the feedback signal; Step S5, the calculation controller generates a control signal u; according to the filtered command signal output by the first tracking differentiator, the differential of the command signal, and the filtered feedback signal output by the second tracking differentiator, the differential of the feedback signal, the output of the controller is calculated to be the control quantity u.

2. The servo control method based on active disturbance rejection control according to claim 1, characterized in that: The first tracking differentiator in step S3 has the following form: Among them, x1(k) is the command signal filtered by the tracking differentiator at the kth moment, k represents the sequence number of the moment, and the value range is k=0,1,2,3...; v1(k) is the differential of the command signal output by the tracking differentiator at the kth moment, x1(k+1) is the command signal filtered by the tracking differentiator at the k+1th moment, and v1(k+1) is the differential of the command signal output by the tracking differentiator at the k+1th moment; s1(k) is the command signal at the kth moment, that is, the input of the first tracking differentiator; r1 and h1 are positive constants, f1 is an auxiliary variable, and p1 is a function whose input is x1(k)-s1(k), v1(k), r1, h1; the specific expression of p1 is Among them, d1, d'1 are constants, y1, a1, a'1 are auxiliary variables, The expression of sign(y1) is The expression of sign(a1) is 3. The servo control method based on active disturbance rejection control as claimed in claim 2, characterized in that: The second tracking differentiator in step S4 has the following form: Among them, x2(k) is the feedback signal filtered by the tracking differentiator at the kth moment, k represents the sequence number of the moment, and the value range is k=1,2,3...; v2(k) is the differential of the feedback signal output by the tracking differentiator at the kth moment, x2(k+1) is the feedback signal filtered by the tracking differentiator at the k+1th moment, v2(k+1) is the differential of the feedback signal output by the tracking differentiator at the k+1th moment; s2(k) is the feedback signal at the kth moment, that is, the input of the second tracking differentiator; r2 and h2 are positive constants, f2 is an auxiliary variable, p2 is a function, and its input is x2(k)-s2(k), v2(k), r2, h2; the expression of p2 is Among them, d2, d'2 are constants, y2, a2, a'2 are auxiliary variables, The expression of sign(y2) is The expression of sign(a2) is 4. The servo control method based on active disturbance rejection control as claimed in claim 3, characterized in that: The controller in step S5 has the following form: u(k)=k p (x1(k)+k s v1(k)-x2(k))+k d (v1(k)-v2(k)) Among them, k p is the proportional term coefficient, k d is the differential term coefficient, k s is the coefficient of the speed compensation term.

5. The servo control method based on active disturbance rejection control according to claim 4, characterized in that: The servo control method is based on the idea of ​​self-disturbance rejection control. On the basis of improving the feedback controller, the command and feedback are filtered by a tracking differentiator to make them smoother. At the same time, the differential signals of the command and feedback are extracted and introduced into the controller, thereby overcoming the inherent lag effect of the feedback controller and improving the control performance.

6. The servo control method based on active disturbance rejection control according to claim 4, characterized in that: Compared with the traditional PID method, the servo control method performs smoothing on both the feedback signal and the command signal.

7. The servo control method based on active disturbance rejection control as claimed in claim 4, characterized in that: The servo control method does not use an integral term but introduces a differential term, which can suppress overshoot while ensuring the rapidity of the system.

8. The servo control method based on active disturbance rejection control as claimed in claim 4, characterized in that: The servo control method uses the first tracking differentiator to filter the instruction, which has a smoothing effect on the instruction, and is beneficial to reducing the overshoot when tracking fast-changing instructions such as step instructions.

9. The servo control method based on active disturbance rejection control as claimed in claim 4, characterized in that: The servo control method estimates the differential of the command signal using the first tracking differentiator and introduces it into the controller, which is beneficial to enhancing the rapidity of servo system tracking.

10. The servo control method based on active disturbance rejection control according to claim 4, characterized in that: The servo control method uses the second tracking differentiator to estimate the differential of the feedback signal, which is beneficial to enhancing the smoothness of the differential signal.

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