Control system stability analysis method and device and computer readable storage medium

Abstract

The invention discloses a control system stability analysis method and device based on a numerical model and a computer readable storage medium, and mainly aims to analyze the stability of a control system by constructing open-loop numerical frequency characteristics of the control system and applying a Nyquist stability criterion. The numerical value frequency characteristics are obtained through signal input and output correlation analysis, meanwhile, the invention provides a mode for verifying the correctness of a controller, the numerical value frequency characteristics of a controlled object and controller parameters are used for calculating and controlling the open-loop frequency characteristics of a system, the open-loop frequency characteristics and the open-loop frequency characteristics directly constructed by system input and output are mutually verified, and the correctness of the controller is verified. According to the method, by disconnecting the controller and the controlled object, it is ensured that the experiment process is safe, free of out-of-control risks, visual and effective, and potential operation errors in a digital control system can be checked through comparison of theoretical calculation results and actual measurement results.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing and automatic control, and in particular to a control system stability analysis method, device and computer-readable storage medium. Background Art

[0002] In the process of control system design and analysis, the stability of the system is one of the key indicators, which directly affects the reliability and safety of the system. The design and implementation of the controller has a direct impact on the design and implementation of the control system. To ensure the stable operation of the system, the open-loop frequency characteristic analysis of the control system has become an important task. At present, many control systems rely on the relationship between input and output for frequency characteristic analysis. With the help of frequency response curves and stability criteria (such as Nyquist criterion), engineers can intuitively evaluate the response and stability of the system at different frequencies. However, when analyzing the performance of the control system in actual engineering, in most cases, the system stability margin is analyzed by using the controlled object model obtained through identification and the ideal controller model, and there is a lack of verification means for the actual execution effect of the controller.

[0003] The design and implementation of the controller usually adopts hardware platforms such as microprocessors, DSPs (digital signal processors) or FPGAs. The controller executes the control law through a discrete calculation method, combining the sampling theorem and the quantization process to convert the continuous signal into a discrete signal. The stability, accuracy and response speed of the system depend to a large extent on the sampling period, quantization accuracy and execution effect of the control algorithm. As a result, during the verification process of complex systems, the actual control effect of the controller may not meet the design indicators due to execution problems, affecting the system performance.

[0004] Therefore, how to combine numerical models and controller parameters in system analysis and verify the correctness of controller execution through frequency characteristics has become a key issue in control system design and implementation. Summary of the invention

[0005] The purpose of the present invention is to overcome the shortcomings and deficiencies of the above-mentioned prior art and provide a control system stability analysis method, device and computer-readable storage medium. The present invention evaluates the system stability by constructing an open-loop numerical frequency characteristic and combining the Nyquist stability criterion, and ensures the safety and effectiveness of the experimental process on the basis of verifying the execution effect of the controller, thereby solving many limitations in traditional analysis methods.

[0006] The present invention is achieved through the following technical solutions:

[0007] A control system stability analysis method based on a numerical model is used to analyze the stability of the control system and verify the correctness of the controller operation in the control system, including the following steps:

[0008] Design excitation signals according to the system operating point and noise characteristics, conduct identification experiments, and obtain the input and output signals of the controlled object and the output signal of the controller;

[0009] Calculate the numerical frequency characteristics of the controlled object according to the input and output signals of the controlled object;

[0010] Calculate the open-loop numerical frequency characteristics of the control system based on the input of the controlled object and the output signal of the controller;

[0011] Calculate the open-loop numerical frequency characteristics of the control system based on the numerical frequency characteristics of the controlled object and the controller parameters;

[0012] According to the open-loop numerical frequency characteristics, the stability of the control system is analyzed using the Nyquist stability criterion;

[0013] Compare the two numerical frequency characteristics to see if they are consistent to verify whether the controller execution effect meets the preset requirements.

[0014] The components of the control system described in the present invention include but are not limited to: sensors, digital controllers, actuators and controlled objects. To simplify the system description, the digital controller and the actuator are collectively referred to as the controller, and the sensor and the controlled object are collectively referred to as the controlled object. During the normal operation of the control system, the controller receives the command signal and the feedback signal as input, the output of the controller is the execution signal, the input of the controlled object is the execution signal, and the output is the feedback signal. A closed loop is formed.

[0015] In the stability analysis test proposed by the present invention, the input of the controller is only the feedback signal, and the output is the open-loop response signal, which is used to calculate the open-loop numerical frequency characteristics. The input of the controlled object is the designed excitation signal, and the output is the object response signal, which is used to obtain the numerical frequency characteristics of the controlled object. By disconnecting the connection between the controller and the controlled object, the experimental process is ensured to be safe and stable, and the control system is prevented from being out of control.

[0016] The excitation signal is composed of multiple signal combinations or segments to ensure comprehensive excitation of the controlled object at different frequencies and dynamic ranges, thereby accurately analyzing its dynamic characteristics. These excitation signals include but are not limited to the following:

[0017] Pseudo-random signal: By generating a series of signal sequences with random characteristics, pseudo-random signals can excite the system over a wide frequency range and are suitable for frequency response characteristic analysis in system identification.

[0018] Logarithmic swept frequency signal: This signal changes frequency logarithmically on the time axis, which can effectively cover the frequency response from low frequency to high frequency. It is particularly suitable for capturing subtle dynamic changes of the system in different frequency bands, especially for systems with a large frequency span.

[0019] Linear swept frequency signal: The signal frequency increases or decreases linearly over time, providing uniform frequency coverage. It is suitable for linear systems or for comprehensive excitation of systems with relatively uniform frequency response.

[0020] DC signal: DC signal is used to adjust the system operating point and help obtain the frequency response of the system under different operating conditions.

[0021] In some implementations of the control system stability analysis method, the first set of equations is:

[0022]

[0023]

[0024] Where u(i) is the input signal, y(i) is the output signal, L is the total length of the input and output signals, and R uu (K) is the autocorrelation sequence of the input signal, R yu (K) is the cross-correlation sequence between the input signal and the output signal, DFT is discrete Fourier transform, The numerical frequency characteristics obtained by correlation analysis of the input and output signals are the spectrum of the test object.

[0025] In some implementations of the control system stability analysis method, the second set of equations is:

[0026]

[0027] Where GM is the amplitude margin and PM is the phase margin.

[0028] ω m is the frequency at which the phase of the numerical frequency characteristic reaches -180°, that is

[0029] ω c is the frequency when the amplitude of the numerical frequency characteristic reaches 1, that is

[0030] When GM and PM are positive, the system is stable. At the same time, PM can also be used to evaluate dynamic characteristics. The larger the phase margin, the smaller the overshoot of the system. For a typical second-order system, the phase margin PM and the damping ratio ξ have an approximate formula ξ≈PM / 100.

[0031] An embodiment of the present invention also provides a control system stability analysis device, including a storage unit and a processing unit, wherein the storage unit stores a computer program that can be executed by the processing unit, and when the processing unit executes the computer program, the steps of the position signal delay compensation method as described above are implemented.

[0032] An embodiment of the present invention further provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the position signal delay compensation method described above are implemented.

[0033] Compared with the prior art, the present invention has the following advantages and effects:

[0034] The present invention constructs an open-loop numerical frequency characteristic of a control system and applies the Nyquist stability criterion to analyze the stability of the control system. The numerical frequency characteristic is obtained by analyzing the correlation between signal input and output. At the same time, the present invention proposes a method for verifying the correctness of a controller. The open-loop frequency characteristic of the control system is calculated using the numerical frequency characteristic of the controlled object and controller parameters, and the open-loop frequency characteristic directly constructed by the system input and output is mutually verified. The method disconnects the connection between the controller and the controlled object to ensure the safety of the experimental process and the risk of loss of control. The method is intuitive and effective. Potential operation errors in the digital control system can be checked by comparing the theoretical calculation results with the measured results. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a flow chart of a control system stability analysis method provided in an embodiment of the present invention.

[0036] Figure 2 It is a schematic diagram of the principle of the control system stability analysis method of the present invention.

[0037] Figure 3 It is a schematic diagram of the principle of the control system stability analysis method provided by an embodiment of the present invention.

[0038] Figure 4 It is a test result diagram of the control system stability analysis method provided by an embodiment of the present invention.

[0039] Figure 5 It is a test result diagram of the control system stability analysis method provided by an embodiment of the present invention.

[0040] Figure 6 It is a schematic diagram of a control system stability analysis device provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0041] The present invention is further described in detail below in conjunction with specific embodiments.

[0042] like Figures 1-2 As shown, the present invention discloses a control system stability analysis method, which can be implemented by the following steps:

[0043] Design excitation signals according to the system operating point and noise characteristics, conduct identification experiments, and obtain the input and output signals of the controlled object and the output signal of the controller;

[0044] Calculate the numerical frequency characteristics of the controlled object according to the input and output signals of the controlled object;

[0045] Calculate the open-loop numerical frequency characteristics of the control system based on the input of the controlled object and the output signal of the controller;

[0046] Calculate the open-loop numerical frequency characteristics of the control system based on the numerical frequency characteristics of the controlled object and the controller parameters;

[0047] According to the open-loop numerical frequency characteristics, the stability of the control system is analyzed using the Nyquist stability criterion;

[0048] Compare the two numerical frequency characteristics to see if they are consistent to verify whether the controller execution effect meets the preset requirements.

[0049] When analyzing the performance of control systems in actual projects, in most cases, the system stability margin is analyzed using the controlled object model obtained through identification and the ideal controller model, and there is a lack of means to verify the actual execution effect of the controller. In response to the above problems, the present invention proposes a control system stability analysis method based on a numerical model, which evaluates the system stability by constructing an open-loop numerical frequency characteristic and combining the Nyquist stability criterion. At the same time, through the special connection form between the controller and the controlled object, the safety and effectiveness of the experimental process are guaranteed on the basis of verifying the execution effect of the controller, thereby solving many limitations of traditional analysis methods.

[0050] Figure 3 The figure shows a schematic diagram of the control system embodiment of the present invention. The controller of the laser galvanometer motor control system includes an output feedback controller and a state feedback controller. In the method of the present patent, the original negative feedback loop is changed to positive feedback during testing, and the controller output is disconnected from the galvanometer motor input.

[0051] Step S1: Design an excitation signal. The excitation signal used in this embodiment is a pseudo-random signal, which is a signal widely used in system identification and testing. It is a binary sequence that approximates white noise and can simulate the characteristics of a random signal. It is often used to excite a system to analyze the frequency response characteristics of the system.

[0052] Step S2: Perform identification experiments to obtain the input and output signals of the controlled object and the output signal of the controller, such as Figure 3 As shown, the input signal u of the controlled object is a pseudo-random signal, and the output signal y of the controlled object and the controller is collected at the same time. 1 ,y 2 .

[0053] Calculate the numerical frequency characteristics of the controlled object based on the input and output signals of the controlled object

[0054] Step S3: Calculate the open-loop numerical frequency characteristics of the control system according to the numerical frequency characteristics of the controlled object and the controller parameters. The numerical frequency characteristics calculation equation group is:

[0055]

[0056] Where u(i) is the input signal, y(i) is the output signal, L is the total length of the input and output signals, and R uu (K) is the autocorrelation sequence of the input signal, R yu (K) is the cross-correlation sequence between the input signal and the output signal, DFT is discrete Fourier transform, The numerical frequency characteristics obtained by correlation analysis of the input and output signals are the spectrum of the test object.

[0057] like Figure 4 The numerical frequency characteristics of the controlled object are shown as follows: Figure 5 Shown is the open loop numerical frequency characteristic.

[0058] Step S4: According to the open-loop numerical frequency characteristics, the Nyquist stability criterion is used to analyze the stability of the control system, and the two numerical frequency characteristics are compared to see whether they are consistent to check whether the controller execution effect meets the preset requirements.

[0059] The stability analysis criterion equation group is:

[0060]

[0061] Where GM is the amplitude margin and PM is the phase margin.

[0062] ω m is the frequency at which the phase of the numerical frequency characteristic reaches -180°, that is

[0063] ω c is the frequency when the amplitude of the numerical frequency characteristic reaches 1, that is

[0064] When GM and PM are positive, the system is stable. At the same time, PM can also be used to evaluate dynamic characteristics. The larger the phase margin, the smaller the overshoot of the system. For a typical second-order system, the phase margin PM and the damping ratio ξ have an approximate formula ξ≈PM / 100.

[0065] For example Figure 5 The measured open-loop numerical frequency characteristics shown use the Nyquist stability criterion, and the amplitude margin is obtained to be 482.6DB, the phase margin is 82.2°, and the system is stable.

[0066] The open-loop numerical frequency characteristics of the control system are calculated based on the numerical frequency characteristics of the controlled object and the controller parameters. The calculation equation group is:

[0067]

[0068] in is the numerical frequency characteristic of the controller equivalent transfer function, which can be directly obtained by obtaining the frequency response of the controller transfer function. is the numerical frequency characteristic of the controlled object, is the theoretical open-loop numerical frequency characteristic obtained by calculation.

[0069] like Figure 5 As shown in the figure, the theoretical open-loop numerical frequency characteristics and the measured open-loop numerical frequency characteristics have a good fitting effect, which shows that the actual effect of the controller is consistent with the theory and there is no abnormality in the execution process.

[0070] like Figure 6 As shown, an embodiment of the present invention further provides a control system stability analysis device, wherein the control system stability analysis device 200 includes a storage unit 210 and a processing unit 220, wherein the storage unit 210 stores a computer program that can be executed by the processing unit 220, and when the processing unit 220 executes the computer program, the steps of the control system stability analysis device as described above are implemented.

[0071] The embodiment of the present invention further provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the parameter self-adjustment method described above are implemented. The computer-readable storage medium in this embodiment belongs to the same concept as the above-mentioned controller stability analysis method, and its implementation process is detailed in the corresponding method embodiment, and the technical features in the method embodiment are correspondingly applicable in the device embodiment, and will not be repeated here.

[0072] As described above, the present invention can be better implemented.

[0073] The implementation methods of the present invention are not limited to the above-mentioned embodiments, and any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principles of the present invention shall be equivalent replacement methods and shall be included in the protection scope of the present invention.

Claims

1. A control system stability analysis method based on a numerical model, used to analyze the stability of the control system and verify the correctness of the controller operation in the control system, characterized by The following steps are involved: Design excitation signals according to the system operating point and noise characteristics, conduct identification experiments, and obtain the input and output signals of the controlled object and the output signal of the controller; Calculate the numerical frequency characteristics of the controlled object according to the input and output signals of the controlled object; Calculate the open-loop numerical frequency characteristics of the control system based on the input of the controlled object and the output signal of the controller; Calculate the open-loop numerical frequency characteristics of the control system based on the numerical frequency characteristics of the controlled object and the controller parameters; According to the open-loop numerical frequency characteristics, the stability of the control system is analyzed using the Nyquist stability criterion; Compare the two numerical frequency characteristics to see if they are consistent, to verify whether the controller execution effect meets the preset.

2. The control system stability analysis method based on numerical model according to claim 1 is characterized in that: The excitation signal is composed of a combination or segmentation of a pseudo-random signal, a logarithmic frequency sweep signal, a linear frequency sweep signal, and a direct current signal.

3. The control system stability analysis method based on numerical model according to claim 2 is characterized in that: The calculation equations of the numerical frequency characteristics are: Where u(i) is the input signal; y(i) is the output signal; L is the total length of input and output signals; R uu (K) is the autocorrelation sequence of the input signal; R yu (K) is the cross-correlation sequence between the input signal and the output signal; DFT is discrete Fourier transform; The numerical frequency characteristics obtained by correlation analysis of the input and output signals are the spectrum of the test object.

4. The control system stability analysis method based on numerical model according to claim 3 is characterized in that: When the output signal substituted into the calculation is the output of the controlled object, what is calculated is the numerical frequency characteristic of the controlled object. When the output signal substituted into the calculation is the output of the controller, what is calculated is the open-loop numerical frequency characteristic of the control system.

5. The control system stability analysis method based on numerical model according to claim 4 is characterized in that: The stability evaluation is performed using numerical frequency characteristics combined with the Nyquist stability criterion to ensure that the system performance meets the predetermined steady-state and dynamic requirements.

6. The control system stability analysis method based on numerical model according to claim 5 is characterized in that: The stability margin calculation equation group is: Where GM is the amplitude margin and PM is the phase margin; ω m is the frequency at which the phase of the numerical frequency characteristic reaches -180°, that is ω c is the frequency when the amplitude of the numerical frequency characteristic reaches 1, that is 7. The control system stability analysis method based on numerical model according to claim 6 is characterized in that: The input of the controlled object is an excitation signal; The output of the controlled object is the input of the controller; There is a circuit between the output of the controller and the input of the controlled object.

8. The control system stability analysis method based on numerical model according to claim 7 is characterized in that: The input of the controller includes a feedback signal and a state signal of the controlled object; The feedback signal is measured by a sensor; The state signal is directly measured by a sensor or obtained through an algorithm such as a state observer.

9. A control system stability analysis device, characterized in that: It comprises a memory and a processor, wherein the memory is used to store program instructions, and the processor is used to call the program instructions to execute the control system stability analysis method based on the numerical model as claimed in any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that: The storage medium stores a computer program, and when the computer program is executed by the processor, the steps of the control system stability analysis method based on the numerical model as claimed in any one of claims 1 to 8 are implemented.

Images