Double-speed loop position tracking control method of servo system based on active disturbance rejection control

Abstract

The invention discloses a double-speed loop position tracking control method of a servo system based on active disturbance rejection control. The method comprises the following steps: designing a double-speed loop controller; designing a double-speed-ring position controller based on the double-speed-ring controller; and performing closed-loop feedback control on the input angle position theta R based on a double-speed-loop position controller, and outputting a compensated angle position theta L. According to the method provided by the invention, the advantage that the active disturbance rejection control (ADRC) does not depend on an accurate system model is fully exerted; meanwhile, in order to improve the dynamic performance of a speed ring, a double-speed ring disturbance suppression servo system position control scheme based on active-disturbance-rejection control is designed, the capacity of a double-speed ring structure for disturbance block suppression and the advantages of rapid convergence and strong disturbance rejection capacity of active-disturbance-rejection control are fully utilized, and the control precision is improved. The adverse effects of uncertainty of rotational inertia, friction interference, measurement noise and various external disturbances are effectively suppressed, and stable, rapid and high-precision target tracking of the servo system is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of position tracking control of a servo system, and in particular relates to a dual-speed loop position tracking control method of a servo system based on auto-disturbance rejection control. Background Art

[0002] In recent years, as a key component of modern military defense, inertial navigation systems have developed rapidly and attracted much attention. Among them, high-precision servo indexing control is the key link for the three-autonomous inertial navigation to achieve self-calibration, self-alignment and rotation modulation functions. Its control accuracy is an important indicator affecting system performance.

[0003] From the control perspective, the servo motor control system is a single-input, single-output, single-variable control system. Therefore, both classical control theory and modern control theory are applicable. With the widespread application of servo control systems, the performance requirements are getting higher and higher. The servo control system studied in this paper is a nonlinear coupling system, and there are also various internal and external disturbances such as external interference, parameter uncertainty, friction interference, and measurement noise, which increase the difficulty of control. It is urgent to find a control solution that can achieve high-precision tracking and has strong anti-interference ability.

[0004] For stable control, the commonly used method is to improve the accuracy and reliability of the speed measuring element to achieve effective isolation of disturbances, which increases the working pressure of the speed measuring element and the dependence on the performance of the speed measuring element. For position tracking control, among the traditional control methods, the classic PID control algorithm is the most commonly used, with a simple structure and easy parameters to adjust. However, due to the complex working environment of the system and the existence of many unknown disturbances, PI / PID control is difficult to meet the standards of high-precision and high-speed positioning applications. In order to solve this limitation, researchers have proposed many improved methods, such as DMC-PID series control strategy, sliding mode variable structure control (SMC), adaptive robust control (ARC), H∞ control, etc., but these methods have problems such as complex control or the requirement to assume that uncertain nonlinear dynamics can be linearly parameterized. Summary of the invention

[0005] The technology of the present invention solves the problem: overcomes the shortcomings of the prior art, provides a dual-speed loop position tracking control method for a servo system based on ADRC, and gives full play to the advantage of ADRC (Advanced Disturbance Rejection Control) that it does not rely on an accurate system model; at the same time, in order to improve the dynamic performance of the speed loop, a dual-speed loop disturbance suppression servo system position control scheme based on ADRC is designed, which fully utilizes the ability of the dual-speed loop structure to suppress disturbance blocks, and the advantages of the rapid convergence and strong anti-disturbance ability of the ADRC, effectively suppresses the adverse effects of moment of inertia uncertainty, friction interference, measurement noise and various external disturbances, and achieves the stable, rapid and high-precision tracking target of the servo system.

[0006] In order to solve the above technical problems, the present invention discloses a dual-speed loop position tracking control method of a servo system based on active disturbance rejection control, comprising:

[0007] Design dual speed loop controller;

[0008] Based on the dual-speed loop controller, a dual-speed loop position controller is designed;

[0009] Based on the dual speed loop position controller, the input angular position θ R Perform closed-loop feedback control and output the compensated angular position θ L .

[0010] In the dual-speed loop position tracking control method of the servo system based on the above-mentioned active disturbance rejection control, for the dual-speed loop controller, there are:

[0011]

[0012] Among them, u d represents the internal disturbance of the system, ω d represents the external disturbance of the system, G c (s) represents the transfer function of the inner loop speed measuring element, G f (s) represents the transfer function of the outer loop speed measuring element, G1(s) represents the transfer function of the outer loop speed regulator, G2(s) represents the transfer function of the inner loop speed regulator, k PWM Indicates the power driver magnification, G m (s) represents the transfer function of the DC torque motor, ω R and ω L denote the input and output angular velocities respectively.

[0013] In the dual-speed loop position tracking control method of the servo system based on the above-mentioned anti-disturbance control, the speed outer loop regulator and the speed inner loop regulator are designed so that G1(s) and G2(s) satisfy:

[0014]

[0015] Then, formula (1) is simplified to:

[0016]

[0017] In the dual-speed loop position tracking control method of the servo system based on the anti-disturbance control, based on the dual-speed loop position controller, the input angular position θ R The closed-loop feedback control is expressed as follows:

[0018]

[0019] Where G3(s) represents the position regulator transfer function, G n (s) represents the dual speed loop transfer function, G θ (s) represents the transfer function of the position outer loop angle measuring element, and s represents a complex variable.

[0020] In the dual-speed loop position tracking control method of the servo system based on ADRC, the input angular position θ R The angular position difference Δθ from the angular position output by the angle measuring element is obtained after G3(s) R ,ω R After the dual speed loop controller, we get ω L .

[0021] In the dual-speed loop position tracking control method of the servo system based on the above-mentioned anti-disturbance control, the speed outer loop regulator, the speed inner loop regulator and the position regulator are designed as follows:

[0022] Define z1, z2 and z3 as the output of the linear extended state observer, the observation error is e1 = z1-x1, and design the following linear extended state observer:

[0023]

[0024] Among them, β i >0(i=1,2,3), represents observer gain; x1=y, represents system output; u represents error compensation control law, b represents control gain;

[0025] The designed state error feedback control law u0 is as follows:

[0026] u0=k1(r-z1)-k2z2…(6)

[0027] The designed error compensation control law u is as follows:

[0028]

[0029] Among them, k1 and k2 represent the parameters to be adjusted. represents the estimated value of the control gain, and r represents the reference input signal.

[0030] The present invention has the following advantages:

[0031] (1) The present invention discloses a dual-speed loop position tracking control method for a servo system based on anti-disturbance control. Taking into account uncertainties such as moment of inertia uncertainty, friction interference, measurement noise and external interference, the dual-speed loop structure is analyzed and designed to achieve block suppression of disturbances. The pressure of a single speed loop suppressing both internal and external disturbances and the system's dependence on the performance of the speed measurement element are resolved, thereby improving the control stability of the system.

[0032] (2) The present invention discloses a dual-speed loop position tracking control method for a servo system based on ADRC, and proposes a novel dual-speed loop plus position tracking loop ADRC strategy, which fully utilizes the control advantages of ADRC for multi-disturbance systems, and improves the stability accuracy, tracking accuracy and anti-disturbance capability of the servo system by estimating and compensating for the uncertainty dynamics of the servo system in real time. In addition, this paper adopts a linear ADRC controller structure, which avoids the assumption of variables in nonlinear functions and reduces the number of controller parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 is a flowchart of the steps of a dual-speed loop position tracking control method of a servo system based on active disturbance rejection control in an embodiment of the present invention;

[0034] Figure 2 is a control structure diagram of a dual speed loop controller in an embodiment of the present invention;

[0035] Figure 3 is a control structure diagram of a dual-speed loop position controller in an embodiment of the present invention;

[0036] Figure 4 is a schematic diagram of an angular position tracking response in an embodiment of the present invention;

[0037] Figure 5 is a schematic diagram of a speed tracking response in an embodiment of the present invention;

[0038] Figure 6 is a schematic diagram of an angular position tracking response when a disturbance is added in an embodiment of the present invention;

[0039] Figure 7 is a schematic diagram of angular velocity tracking response when disturbance is added in an embodiment of the present invention;

[0040] Figure 8 is a schematic diagram of an angular position tracking response when white noise disturbance is added in an embodiment of the present invention;

[0041] Fig. 9 It is a schematic diagram of angular velocity tracking response when white noise disturbance is added in an embodiment of the present invention. DETAILED DESCRIPTION

[0042] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments disclosed in the present invention will be further described in detail below with reference to the accompanying drawings.

[0043] Reference Figure 1 In this embodiment, the dual-speed loop position tracking control method of the servo system based on active disturbance rejection control includes:

[0044] Step 1: Design a dual speed loop controller.

[0045] In this embodiment, the control structure of the dual speed loop controller is as follows: Figure 2 As shown, for the dual speed loop controller, there are:

[0046]

[0047] Among them, u d represents the internal disturbance of the system, ω d represents the external disturbance of the system, G c (s) represents the transfer function of the inner loop speed measuring element, G f (s) represents the transfer function of the outer loop speed measuring element, G1(s) represents the transfer function of the outer loop speed regulator, G2(s) represents the transfer function of the inner loop speed regulator, k PWM Indicates the power driver magnification, G m (s) represents the transfer function of the DC torque motor, ω R and ω L denote the input and output angular velocities respectively.

[0048] Design the speed outer loop regulator and the speed inner loop regulator so that G1(s) and G2(s) satisfy:

[0049]

[0050] Then, formula (1) can be simplified as:

[0051]

[0052] From formula (3), we can see that the internal disturbance u d It is mainly suppressed by the speed inner loop regulator, and the speed outer loop regulator plays an auxiliary role; the system external disturbance ω d Mainly suppressed by the speed outer loop regulator, and the parameters G of the DC torque motor m (s) is irrelevant. In this way, the purpose of suppressing the internal disturbance and external disturbance of the system in blocks is achieved. Among them, the input angular position θR The angular position difference Δθ from the angular position output by the angle measuring element is obtained after G3(s) R ,ω R After the dual speed loop controller, we get ω L .

[0053] Step 2: Design a dual-speed loop position controller based on the dual-speed loop controller.

[0054] Step 3: Based on the dual-speed loop position controller, the input angular position θ R Perform closed-loop feedback control and output the compensated angular position θ L .

[0055] In this embodiment, the control structure of the dual speed loop position controller is as follows: Figure 3 As shown, we have:

[0056]

[0057] Where G3(s) represents the position regulator transfer function, G n (s) represents the dual speed loop transfer function, G θ (s) represents the transfer function of the position outer loop angle measuring element, and s represents a complex variable.

[0058] In this embodiment, the speed outer loop regulator, the speed inner loop regulator and the position regulator can be designed as follows:

[0059] Define z1, z2 and z3 as the output of the linear extended state observer, the observation error is e1 = z1-x1, and design the following linear extended state observer:

[0060]

[0061] Among them, β i >0(i=1,2,3), represents observer gain; x1=y, represents system output; u represents error compensation control law, and b represents control gain.

[0062] The designed state error feedback control law u0 is as follows:

[0063] u0=k1(r-z1)-k2z2…(6)

[0064] The designed error compensation control law u is as follows:

[0065]

[0066] Among them, k1 and k2 represent the parameters to be adjusted. represents the estimated value of the control gain, and r represents the reference input signal.

[0067] Based on the above embodiment, a specific example is described below.

[0068] (1) Dual speed loop controller design

[0069] The closed-loop characteristics of the speed inner loop are the control object of the position outer loop, and the speed inner loop plays the main role in suppressing disturbances in the system. Based on this analysis, combined with the advantages of cascade control, the following is adopted: Figure 2 The dual-speed loop controller shown in the figure includes a speed inner loop regulator and a speed outer loop regulator, thereby achieving block suppression of disturbances and improving control performance. Therefore, the output angular velocity ω of the dual-speed loop controller can be derived L for:

[0070]

[0071] Design the speed outer loop regulator and the speed inner loop regulator so that G1(s) and G2(s) satisfy:

[0072] ||G c (s)k PWM G2(s)G m (s)||>>1

[0073] ||k PWM G1(s)G2(s)G m (s)G f (s)+G c (s)k PWM G2(s)G m (s)||>>1

[0074] Then we have:

[0075]

[0076] It can be seen that the internal disturbance u of the system d It is mainly suppressed by the speed inner loop regulator, and the speed outer loop regulator plays an auxiliary role; the system external disturbance ω d Mainly suppressed by the speed outer loop regulator, and the parameters G of the DC torque motor m (s) is irrelevant. In this way, the purpose of suppressing the internal disturbance and external disturbance of the system in blocks is achieved. Compared with the traditional single speed loop structure, the dual speed loop disturbance isolation structure proposed in the present invention has better robustness and anti-disturbance.

[0077] (2) Design of dual-speed loop position tracking control scheme for servo system based on anti-disturbance control

[0078] The system's position outer loop takes the speed inner loop structure as the control object, uses an angle measuring element to measure the system's angular position information and feeds it back to the input end to form a position closed loop to achieve target position tracking, such as Figure 3 As shown, G3(s) represents the transfer function of the position regulator. The main purpose of the position regulator is to eliminate position tracking errors and achieve high-precision and fast tracking.

[0079] Based on the above analysis, the present invention designs a multi-loop control structure of dual speed inner loop + position outer loop. Due to the nonlinearity of the system, multiple disturbances, and uncertainty of loads and parameters, the present invention adopts an anti-disturbance control algorithm. In order to reduce the number of controller parameters, the present invention will design a linear extended state observer and a linear state error feedback control law.

[0080] Design a second-order linear active disturbance rejection controller:

[0081]

[0082] in, represents the sum of the internal disturbance and external disturbance of the system, ω represents the external disturbance, and y represents the system output.

[0083] Let x1 = y, And define an expansion state Then the expanded state equation of the system can be obtained as:

[0084]

[0085] in, C = [1 0 0],

[0086] Define z1, z2 and z3 as the output of the linear extended state observer, the observation error is e1 = z1-x1, and design the following linear extended state observer:

[0087]

[0088] The state error feedback control law and error compensation control law are:

[0089] u0=k1(r-z1)-k2z2

[0090]

[0091] (3) Simulation analysis

[0092] In order to verify the effectiveness and anti-disturbance performance of the dual-speed loop position tracking control method of the servo system based on the active disturbance rejection control proposed in the present invention, a simulation experiment is carried out on the servo system. According to the active disturbance rejection control tuning rules, the parameters are designed as shown in Table 1 below:

[0093]

[0094] Table 1, parameter example table

[0095] Figure 4 and Figure 5 The control effect of the angular position and angular velocity of the servo system without any disturbance is described. It can be seen that under the dual-speed loop disturbance suppression control scheme based on self-anti-disturbance control, the position tracking and angular velocity converge to the origin in about 0.08s with high accuracy. It can be concluded that the control scheme designed by the present invention can efficiently meet the position tracking requirements of the servo tracking system and can track the desired target within a limited time.

[0096] In order to verify the anti-interference performance of the designed control structure, u is added to the system at t = 4s. d = 2000 step input disturbance (considered as friction torque disturbance), and at the same time add ω at t = 6s d = 10rad / s angular velocity disturbance (regarded as external disturbance factor), the control performance is as follows Figure 6 and Figure 7 As shown. Figure 6 It can be seen that the inner speed controller can make the system return to the original equilibrium state at around 0.5s, and the outer speed loop controller can make the system return to a stable state at around 0.08s. Figure 7 It can be seen that the inner speed loop mainly suppresses the friction interference inside the system, and the outer speed loop mainly suppresses the influence of external disturbances such as carrier movement, and stability can be achieved in about 0.08s. This shows the effectiveness and rapidity of the dual speed loop disturbance suppression structure, and can achieve high-precision tracking.

[0097] Since the noise interference of the speed measurement element also has a great influence on the control accuracy of the system, in order to verify the designed control structure's suppression of the speed measurement element noise, a white noise interference signal is added to the outer speed loop feedback. The control results are as follows: Figure 8 and Fig. 9 As shown, it can be seen that the servo system can track stably and effectively, with high control accuracy and almost no impact.

[0098] Depend on Figures 4 to 9 It can be seen that although the system is affected by internal friction interference, external disturbance and measurement noise, the dual-speed loop disturbance suppression control scheme based on self-disturbance rejection control designed in the present invention can still ensure finite-time stability, high-precision control effect and tracking process and strong anti-disturbance.

[0099] The above results show that the method of the present invention suppresses internal disturbances and external disturbances respectively, and has better visual axis stability performance; and the strong anti-disturbance and strong robustness of the automatic disturbance rejection control bring stability and better disturbance suppression performance to the control scheme.

[0100] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

[0101] The contents not described in detail in the specification of the present invention belong to the common knowledge of the professionals in this field.

Claims

1. A dual-speed loop position tracking control method for a servo system based on active disturbance rejection control, characterized in that: include: Design dual speed loop controller; Based on the dual-speed loop controller, a dual-speed loop position controller is designed; Based on the dual speed loop position controller, the input angular position θ R Perform closed-loop feedback control and output the compensated angular position θ L .

2. The dual-speed loop position tracking control method of a servo system based on active disturbance rejection control according to claim 1, characterized in that: For the dual speed loop controller, there are: Among them, u d represents the internal disturbance of the system, ω d represents the external disturbance of the system, G c (s) represents the transfer function of the inner loop speed measuring element, G f (s) represents the transfer function of the outer loop speed measuring element, G1(s) represents the transfer function of the outer loop speed regulator, G2(s) represents the transfer function of the inner loop speed regulator, k PWM Indicates the power driver magnification, G m (s) represents the transfer function of the DC torque motor, ω R and ω L denote the input and output angular velocities respectively.

3. The dual-speed loop position tracking control method of the servo system based on active disturbance rejection control according to claim 2, characterized in that: Design the speed outer loop regulator and the speed inner loop regulator so that G1(s) and G2(s) satisfy: Then, formula (1) is simplified to:

4. The dual-speed loop position tracking control method of the servo system based on active disturbance rejection control according to claim 3 is characterized in that: Based on the dual speed loop position controller, the input angular position θ R The closed-loop feedback control is expressed as follows: Where G3(s) represents the position regulator transfer function, G n (s) represents the dual speed loop transfer function, G θ (s) represents the transfer function of the position outer loop angle measuring element, and s represents a complex variable.

5. The dual-speed loop position tracking control method of the servo system based on active disturbance rejection control according to claim 4 is characterized in that: Input angular position θ R The angular position difference Δθ from the angular position output by the angle measuring element is obtained after G3(s) R ,ω R After the dual speed loop controller, we get ω L .

6. The dual-speed loop position tracking control method of a servo system based on active disturbance rejection control according to claim 5, characterized in that: Design the speed outer loop regulator, speed inner loop regulator and position regulator as follows: Define z1, z2 and z3 as the output of the linear extended state observer, the observation error is e1 = z1-x1, and design the following linear extended state observer: Among them, β i >0(i=1,2,3), represents observer gain; x1=y, represents system output; u represents error compensation control law, b represents control gain; The designed state error feedback control law u0 is as follows: u0=k1(r-z1)-k2z2…(6) The designed error compensation control law u is as follows: Among them, k1 and k2 represent the parameters to be adjusted. represents the estimated value of the control gain, and r represents the reference input signal.

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