Multi-time scale disturbance accurate compensation method based on disturbance observer

Abstract

The invention provides a multi-time scale disturbance accurate compensation method based on a disturbance observer, and belongs to the technical field of engineering system control. Firstly, a system discrete dynamic model is established based on a disturbance observer and a discrete time analysis method, and design constraints of an object model and observer bandwidth in computer implementation are overcome; calculating an inner-loop transfer function between the external interference input and the acceleration output, including establishing an open-loop transfer function, determining an inner-loop regulation factor to design a phase lead / lag compensator, and synthesizing the compensator to meet the stability requirement of the system; and finally, analyzing the stability of the robust motion control system based on the disturbance observer by utilizing a generalized Bode integral theorem, and ensuring that the system can still keep stable response under the condition that the disturbance bandwidth is increased. According to the invention, through discrete time analysis and a disturbance observer, multi-time scale disturbance is accurately compensated, and the stability and robustness of engineering control such as an unmanned system are enhanced.

Description

Technical Field

[0001] The present invention relates to the technical field of engineering system control, and in particular to a multi-time scale disturbance accurate compensation method based on a disturbance observer. Background Art

[0002] In many engineering systems such as unmanned systems and spacecraft, the uncertainty of the control object and the influence of external disturbances are inevitable. In order to describe the changes in the tracking performance of the system under external disturbances, robust control technology has been proposed to improve the stability and robustness of the controller under the conditions of object uncertainty and external disturbances. Scholars have proposed many methods in the field of robust control for anti-interference, including Control, sliding mode control (SMC) and robust parameter control, etc. For the modern control field, the robustness and stability of the system under disturbance conditions have become key goals.

[0003] Robust control technology can be divided into two categories: suppressing interference through feedback control and eliminating interference through feedforward control. The method of suppressing interference through feedback control usually involves a more complex controller, which is difficult to respond quickly under strong interference conditions. For the method of eliminating interference through feedforward control, the robustness of the system is more intuitively achieved by feedforward compensating the disturbance signal. However, this feedforward compensation method is difficult to apply in practice because the disturbance quantity in the engineering system is unknown and unmeasurable. To solve this problem, scholars have proposed a precise disturbance compensation method based on a dynamic disturbance observer, which uses measurable states and known objects to dynamically estimate disturbances, thereby improving the robustness of the control system under unknown disturbance conditions.

[0004] The control method based on dynamic disturbance observer (DOB) has become a popular robust control tool due to its simplicity and effectiveness. It can be used to estimate the uncertainty and external disturbance of objects in the control system. At present, scholars have proposed a variety of research methods around robust control based on dynamic disturbance observer, including the use of continuous time analysis and synthesis methods to analyze robust control systems, and the use of optimal object shaping, Kalman filter and other methods to deal with the system instability caused by the increase in disturbance estimation bandwidth. However, the above methods still have shortcomings in the dynamic analysis of robust motion controllers and in dealing with the increase in disturbance bandwidth.

[0005] (1) Dynamic analysis of robust motion controllers: Continuous-time analysis methods are difficult to explain some dynamic behaviors of control methods based on disturbance observers implemented by computers, such as poor stability and poor performance. To this end, the present invention overcomes the design constraints of the object model and observer bandwidth brought by computers based on discrete-time analysis methods, thereby being able to effectively analyze the dynamic behaviors of control methods based on disturbance observers.

[0006] (2) In dealing with the increase of disturbance bandwidth: As the disturbance bandwidth increases, the control method based on disturbance observer will show underdamped or unstable response. Although this problem has been studied based on methods such as optimal object shaping and Kalman filter, the impact of measurement state on the robustness and stability of DOB control system has not been given.

[0007] In summary, many current technical means have considered the disturbance compensation problem based on dynamic disturbance observers, but their processing capabilities for dynamic behavior analysis and disturbance bandwidth increase faced in the robust control system process are limited. Therefore, the present invention proposes a multi-time scale disturbance accurate compensation method based on disturbance observers to solve the above-mentioned deficiencies in the prior art. Summary of the invention

[0008] The purpose of the present invention is to provide a multi-time scale disturbance accurate compensation method based on a disturbance observer. The discrete time analysis method can effectively analyze the dynamic behavior of the control method based on the disturbance observer, such as anti-interference robustness and control performance stability; as well as the control performance advantage. Under the condition of disturbance, the acceleration measurement state shows good performance in the robustness and stability of the control system based on DOB, and effectively copes with the underdamped or unstable response problems caused by the increase of disturbance bandwidth. It provides an effective solution for the uncertainty of control objects and the influence of external disturbances in engineering systems such as unmanned systems and spacecraft, and improves the stability and robustness of the control system.

[0009] To achieve the above object, the present invention provides a multi-time scale disturbance accurate compensation method based on a disturbance observer, comprising the following steps: Step S1, establishing a system discrete dynamic model based on a disturbance observer and a discrete time analysis method; Step S2, calculating the inner loop transfer function between the external disturbance input and the acceleration output based on the system discrete dynamic model established in step S1; Step S21, establishing an open-loop transfer function; Step S22, determining an inner loop adjustment factor to design a phase lead / lag compensator; Step S23, establishing an inner loop transfer function and synthesizing a phase lead / lag compensator to meet system stability requirements; Step S3: Analyze the stability of the robust motion control system based on disturbance observer by using the generalized Bode integral theorem.

[0010] Preferably, in step S1, a system discrete dynamic model is established based on a disturbance observer and a discrete time analysis method, including: (1); in, express The acceleration state at the moment; represents uncertain inertia; express The inverse of represents the uncertainty factor; express Input of acceleration measurement link of DOB control system at the moment; express The disturbance amount at the moment; Represents the acceleration measurement output; represents a complex variable, express time; Indicates sampling time; represents the nominal factor; It represents the acceleration measurement link input of the DOB control system; represents the nominal inertia; express The discrete form of Indicates the acceleration measurement status, represents the noise external input; Indicates the bandwidth of the DOB control system.

[0011] Preferably, in step S21, establishing an open-loop transfer function includes: (2); in, represents the open-loop transfer function; Represents the inner loop regulatory factor.

[0012] Preferably, in step S22, determining the inner loop adjustment factor to design a phase lead / lag compensator includes: Without considering the dynamic process of speed measurement, and The transfer function between is expressed as: (3); in, and denote the controlled object and the expected value of the controlled object respectively; Formula (3) indicates that by adjusting the inner loop adjustment factor , the DOB control system is designed as a phase lead / lag compensator.

[0013] Preferably, in step S23, an inner loop transfer function is established, and a phase lead / lag compensator is synthesized to meet the system stability requirement, including: Based on the established system discrete dynamic model, the calculation results of the inner loop transfer function between the external disturbance input and the acceleration output are obtained: (4); in, represents a phase lead / lag compensator; represents the sensitivity function of the inner control loop; represents the amount of interference input; represents the complementary sensitivity function of the inner control loop; represents external noise input; The phase lead / lag compensator is established as: (5).

[0014] Preferably, in step S3, the stability of the robust motion control system based on the disturbance observer is analyzed using the generalized Bode integral theorem, including: (6); in, represents the complex exponential function, Indicates plural, Indicates the angular velocity of the DOB control system; ; express The Bode integral form of .

[0015] Therefore, the present invention adopts the above-mentioned multi-time scale disturbance accurate compensation method based on disturbance observer, and the beneficial technical effects are as follows: (1) Advantages of the analytical method: The discrete-time analytical method overcomes the design constraints of the object model and observer bandwidth brought by the computer, and can effectively analyze the dynamic behavior of the control method based on the disturbance observer, such as the anti-disturbance robustness of the control system and the stability of the control performance.

[0016] (2) Advantages in control performance: Considering that as the disturbance bandwidth increases, the control method based on the disturbance observer will show underdamped or unstable response. By using the multi-time scale disturbance accurate compensation method based on the disturbance observer, it can be seen that under the condition of disturbance, the acceleration measurement state has better performance in robustness and stability of the DOB-based control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 The present invention is a flowchart of a method for accurate compensation of multi-time-scale disturbances based on a disturbance observer. DETAILED DESCRIPTION

[0018] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0019] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0020] Embodiment 1 The idea of ​​realizing the purpose of the present invention is: since the continuous time analysis method is difficult to explain some dynamic behaviors of the control method based on the disturbance observer implemented by the computer, such as poor stability and poor performance, it is necessary to introduce a discrete time analysis method to overcome the design constraints of the object model and observer bandwidth brought by the computer, so as to effectively analyze the dynamic behavior of the control method based on the disturbance observer. In addition, under the condition of increasing the disturbance bandwidth, the control method based on the disturbance observer will show an underdamped or unstable response. Therefore, it is necessary to analyze the robustness and stability of the DOB control system.

[0021] To this end, the idea of ​​the present invention is to use a discrete time analysis method to reduce the unstable response based on the disturbance observer while considering the increase of the disturbance bandwidth, so as to meet the requirements of accurate compensation of control system disturbances under multiple time scales. The specific process of the method of accurate compensation of multiple time scale disturbances based on the disturbance observer of the present invention is shown in Figure 1 .

[0022] The specific steps of the multi-time scale disturbance accurate compensation method based on disturbance observer of the present invention include the following: 1. Discrete dynamic model of the system.

[0023] like Figure 1 As shown, ZOH is the zero-order holder of the system. is the sampling time, and denote the continuous and discrete time domains, respectively, is a complex variable. At the kth moment, ,and . and They represent the expected input of the DOB control system and the input of the acceleration measurement link respectively. The DOB control system can be modeled as follows in discrete time: (1); in, express The acceleration state at the moment; represents uncertain inertia; express The inverse of represents the uncertainty factor; express Input of acceleration measurement link of DOB control system at the moment; express The disturbance amount at the moment; Represents the acceleration measurement output; represents a complex variable, express time; Indicates sampling time; represents the nominal factor; It represents the acceleration measurement link input of the DOB control system; represents the nominal inertia; express The discrete form of Indicates the acceleration measurement status, represents the noise external input; Indicates the bandwidth of the DOB control system.

[0024] 2. Calculation of inner loop transfer function.

[0025] 201. Establish an open-loop transfer function: Open loop transfer function Expressed as (2); in, represents the open-loop transfer function; Represents the inner loop regulatory factor.

[0026] 202. Inner Loop Regulatory Factor : In this system, the dynamic process of speed measurement is not considered. and The transfer function between them can be expressed as (3); in, and denote the controlled object and the expected value of the controlled object respectively; This formula means that by adjusting the factors in the inner loop , DOB can be designed as a phase lead / lag compensator, thereby improving the phase margin and stability of the robust control system.

[0027] 203. Establish the inner loop transfer function: Based on the system discrete dynamic model established in the previous stage, the calculation results of the inner loop transfer function between the external disturbance input and the acceleration output can be obtained.

[0028] (4); in, represents a phase lead / lag compensator; represents the sensitivity function of the inner control loop; represents the amount of interference input; represents the complementary sensitivity function of the inner control loop; Represents external noise input.

[0029] 204. Further, a phase lead / lag compensator is established as: (5); According to the inner loop transfer function established in step 203, it can be seen that when the nominal inertia and thrust coefficient are properly adjusted, the phase lead (lag) compensator In the inner loop, it is synthesized to satisfy .

[0030] By increasing To improve the phase margin of the robust motion control system, the inner loop transfer function is stable to all parameters of the nominal controlled object and bandwidth variations of the DOB. and With the increase of , the frequency response value of the system sensitivity function will decrease, which will help improve the robustness of the control system to disturbances.

[0031] 3. Stability analysis of DOB compensation method.

[0032] The stability of the DOB-based robust motion control system is analyzed using the generalized Bode integral theorem. The Bode integral equation is: (6); in, represents the complex exponential function, Indicates plural, Indicates the angular velocity of the DOB control system; ; express The Bode integral form of .

[0033] Since in formula (6), as and As the robustness to low-frequency disturbances increases, the value on the right side of the equal sign becomes smaller. Therefore, when the robustness to low-frequency disturbances increases, the Bode integral equation holds true, and no high-sensitivity peak appears. In summary, the DOB based on acceleration measurement will not be affected by the waterbed effect. Although the high-sensitivity peak will not appear in the robust and precise compensation control process based on DOB, the noise is less suppressed during the acceleration measurement process. Therefore, in the multi-time-scale disturbance precise compensation method based on the disturbance observer, the DOB bandwidth and phase margin of the established controller are only affected by the noise in the acceleration measurement system.

[0034] It is worth noting that the contents not elaborated in detail in the present invention are all prior art and are well known to those skilled in the art.

[0035] Therefore, the present invention adopts the above-mentioned multi-time scale disturbance precise compensation method based on disturbance observer, and the discrete time analysis method can effectively analyze the dynamic behavior of the control method based on disturbance observer, such as anti-interference robustness and control performance stability; as well as control performance advantages. Under the condition of disturbance, the acceleration measurement state shows better performance in the robustness and stability of the control system based on DOB, and effectively copes with the underdamped or unstable response problems caused by the increase of disturbance bandwidth, and provides an effective solution for the uncertainty and external disturbance influence of the control objects in engineering systems such as unmanned systems and spacecraft, thereby improving the stability and robustness of the control system.

[0036] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A multi-time scale disturbance accurate compensation method based on disturbance observer, characterized in that: The following steps are involved: Step S1, establishing a system discrete dynamic model based on a disturbance observer and a discrete time analysis method; Step S2, calculating the inner loop transfer function between the external disturbance input and the acceleration output based on the system discrete dynamic model established in step S1; Step S21, establishing an open-loop transfer function; Step S22, determining an inner loop adjustment factor to design a phase lead / lag compensator; Step S23, establishing an inner loop transfer function and synthesizing a phase lead / lag compensator to meet system stability requirements; Step S3: Analyze the stability of the robust motion control system based on disturbance observer by using the generalized Bode integral theorem.

2. The method for accurate compensation of multi-time-scale disturbances based on disturbance observer according to claim 1, characterized in that: In step S1, a system discrete dynamic model is established based on a disturbance observer and a discrete time analysis method, including: （1）； in, express The acceleration state at the moment; represents uncertain inertia; express The inverse of represents the uncertainty factor; express Input of acceleration measurement link of DOB control system at the moment; express The disturbance amount at the moment; Represents the acceleration measurement output; represents a complex variable, express time; Indicates sampling time; represents the nominal factor; It represents the acceleration measurement link input of the DOB control system; represents the nominal inertia; express The discrete form of Indicates the acceleration measurement status, represents the noise external input; Indicates the bandwidth of the DOB control system.

3. The method for accurate compensation of multi-time-scale disturbances based on disturbance observer according to claim 2, characterized in that: In step S21, an open-loop transfer function is established, including: （2）； in, represents the open-loop transfer function; Represents the inner loop regulatory factor.

4. The method for accurate compensation of multi-time-scale disturbances based on disturbance observer according to claim 3 is characterized in that: In step S22, an inner loop adjustment factor is determined to design a phase lead / lag compensator, including: Without considering the dynamic process of speed measurement, and The transfer function between is expressed as: （3）； in, and denote the controlled object and the expected value of the controlled object respectively; Formula (3) indicates that by adjusting the inner loop adjustment factor , the DOB control system is designed as a phase lead / lag compensator.

5. The method for accurate compensation of multi-time-scale disturbances based on disturbance observer according to claim 4, characterized in that: In step S23, an inner loop transfer function is established and a phase lead / lag compensator is synthesized to meet the system stability requirement, including: Based on the established system discrete dynamic model, the calculation results of the inner loop transfer function between the external disturbance input and the acceleration output are obtained: （4）； in, represents a phase lead / lag compensator; represents the sensitivity function of the inner control loop; represents the amount of interference input; represents the complementary sensitivity function of the control inner loop; represents external noise input; The phase lead / lag compensator is established as: （5）。 6. The method for accurate compensation of multi-time-scale disturbances based on disturbance observer according to claim 5, characterized in that: In step S3, the stability of the robust motion control system based on the disturbance observer is analyzed by using the generalized Bode integral theorem, including: （6）； in, represents the complex exponential function, Indicates plural, Indicates the angular velocity of the DOB control system; ; express The Bode integral form of .

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