Parameter tuning method for lag-lead compensation in a single closed-loop control system for a finite angle motor position

Abstract

This application provides a parameter tuning method for lag-lead compensation in a single closed-loop position control system for a finite angle motor, belonging to the field of motor control technology. The method includes constructing a third-order linear differential equation from the input voltage to the output speed and angular displacement of the finite angle motor, performing simplification and Laplace transform to obtain the finite angle motor transfer function; determining the system open-loop gain, calculating the cutoff frequency of the uncompensated system, and adjusting the open-loop gain to make the cutoff frequency of the uncompensated system greater than the given system cutoff frequency; calculating the attenuation coefficient, corner frequency, and transfer function of the lag compensation device; calculating the lead coefficient, corner frequency, and transfer function of the lead compensation device; and obtaining the open-loop transfer function of the finite angle motor single closed-loop position control system after lag-lead compensation based on the transfer functions of the lag and lead compensation devices. This scheme reduces system complexity and cost, and improves system steady-state performance and motor position control accuracy.

Description

Technical Field

[0001] This application relates to the field of motor control technology, and in particular to a parameter tuning method for lag-lead correction in a single closed-loop control system for the position of a finite angle motor. Background Technology

[0002] With the continuous development of aviation technology, the performance requirements for aero-engines are constantly increasing. The increasing control functions and precision of aero-engines place ever higher demands on the control system. The main tasks of the control system include precise control of physical quantities such as fuel flow, air mass flow, and turbine clearance. Among these, fuel flow control is the most critical task. The fuel metering device is an important component of the aero-engine power control system, serving as the actuator of the engine fuel flow control system. It is responsible for ensuring the minimum pressure of fuel supply, accurately metering fuel flow to the combustion chamber, and limiting the fuel flow range. Finite-angle motors (FEMs) possess the characteristics of simple structure, finite angle range, high torque ratio, low cost, and high reliability. Under the technical requirements of high precision, fast response, and high reliability for fuel metering devices in aero-engine control systems, the use of FEM drives has become one of the mainstream solutions for fuel metering devices. FEMs often employ dual closed-loop control schemes (position loop and current loop) or triple closed-loop control schemes (current, speed, and position). However, using multi-loop control schemes often increases the complexity and debugging difficulty of the control system, and the cost of the control system is also increased to collect the motor phase current. Summary of the Invention

[0003] In view of this, the embodiments of this application provide a parameter tuning method for lag-lead correction of a single closed-loop control system for the position of a finite angle motor. This method has low requirements for the main frequency of the controller chip and does not require the acquisition of the phase current of the finite angle motor, thereby reducing the cost of the control system and exhibiting good stability, speed and robustness.

[0004] This application provides a parameter tuning method for lag-lead compensation in a single-loop position control system for a finite angle motor. The control system adopts a single-loop position structure and includes a finite angle motor, a position controller, a position sensor, and a power amplifier. The position controller employs lag-lead compensation. The parameter tuning method for lag-lead compensation includes:

[0005] A third-order linear differential equation is constructed between the input voltage and the output speed angular displacement of a finite angle motor. The third-order linear differential equation is then simplified and subjected to Laplace transform to obtain the transfer function of the finite angle motor. Determine the system open-loop gain based on the system's steady-state error requirements; The open-loop logarithmic amplitude-frequency characteristic of the uncorrected system is obtained based on the open-loop gain. The cutoff frequency of the uncorrected system is calculated based on the relationship between the cutoff frequency of the uncorrected system and the corner frequency of the finite angle motor. The open-loop gain is then adjusted so that the cutoff frequency of the uncorrected system is greater than the given cutoff frequency of the system. Based on the relationship between the corner frequency of the lag compensator, the cutoff frequency given by the system, the corner frequency of the finite angle motor, and the corner frequency of the lead compensator, as well as the logarithmic amplitude-frequency characteristic of the system after compensation at the cutoff frequency, the attenuation coefficient of the lag compensator is obtained. The corner frequency of the lag compensator is determined based on the attenuation coefficient of the lag compensator, the time constant of the inertial element of the lag compensator, and the given cutoff frequency of the system. The transfer function of the hysteresis compensator is obtained based on the corner frequency of the hysteresis compensator. Based on the phase margin requirement of the corrected system at the given cutoff frequency, the lead coefficient of the lead compensator is calculated. The turnaround frequency of the advance compensation device is calculated based on the advance coefficient of the advance compensation device and the turnaround frequency of the finite angle motor. Based on the corner frequency of the lead compensator, the transfer function of the lead compensator is obtained. Based on the transfer functions of the lag compensator and the lead compensator, the open-loop transfer function of the lag-lead compensator system for single closed-loop position control of a finite angle motor is obtained.

[0006] According to a specific implementation of this application, the expression of the third-order linear differential equation between the input voltage and the output speed angular displacement of the finite angle motor is as follows: , Among them, L a R is the inductance of the armature of a finite-angle motor. a f is the resistance of the armature of a finite-angle motor. m It is the total viscous friction coefficient referred to the shaft of a motor with a finite rotation angle, J. m It is the total moment of inertia referred to the shaft of the finite-angle motor, C. m For a finite angle motor, θ is the torque coefficient. m (·) represents the output angular displacement of the finite-rotation motor, t represents time, and K represents the displacement. s For the stiffness of the return spring after power failure, C e u is the back electromotive force coefficient of a finite angle motor. a (·) represents the input voltage of the finite angle motor; The simplified expression of the third-order linear differential equation is as follows: , Among them, T mK is the electromechanical time constant of the motor. a This is the transmission coefficient of the motor; The expression for the transfer function of the finite angle motor is: , Where s is the complex frequency variable in the Laplace transform, and G a (·) is the transfer function of a finite-angle motor, U a (·) represents the input armature voltage of the finite angle motor.

[0007] According to a specific implementation of an embodiment of this application, the open-loop gain of the system is: , Where K is the system open-loop gain. This is the steady-state error given by the system.

[0008] According to a specific implementation of an embodiment of this application, the step of obtaining the open-loop logarithmic amplitude-frequency characteristic of the uncorrected system based on the open-loop gain, and calculating the cutoff frequency of the uncorrected system based on the relationship between the cutoff frequency of the uncorrected system and the cornering frequency of the finite-angle motor, includes: The open-loop logarithmic magnitude-frequency characteristic of the uncorrected system is obtained based on the open-loop gain, and the expression is: , Where, ω c0 Let L0(·) be the cutoff frequency of the uncompensated system, L0(·) be the open-loop logarithmic amplitude-frequency response of the uncompensated system, j be the imaginary unit, and G0(·) be the uncompensated system. m The turning frequency of a finite angle motor; when At that time, based on the open-loop gain, the expression for the open-loop logarithmic magnitude-frequency characteristic of the uncorrected system is obtained, resulting in: , ; when At that time, based on the open-loop gain, the expression for the open-loop logarithmic magnitude-frequency characteristic of the uncorrected system is obtained, resulting in: , , Where dB is the amplitude unit.

[0009] According to a specific implementation of an embodiment of this application, obtaining the attenuation coefficient of the lag compensator based on the relationship between the corner frequency of the lag compensator, the cutoff frequency given by the system, the corner frequency of the finite angle motor, and the corner frequency of the lead compensator, as well as the logarithmic amplitude-frequency characteristic of the compensated system at the cutoff frequency, includes: The logarithmic magnitude-frequency response of the corrected system at the cutoff frequency is calculated as follows: , in, This is the second corner frequency of the hysteresis correction device. The first corner frequency of the hysteresis correction device. The cutoff frequency given by the system, This is the first corner frequency of the lead compensator. L is the second corner frequency of the lead compensator, L(·) is the logarithmic amplitude-frequency characteristic of the system at the cutoff frequency after compensation, and G(·) is the compensation system. when At that time, or when When corrected, the expression for the logarithmic amplitude-frequency characteristic of the system at the cutoff frequency simplifies to: , get: , Where b is the attenuation coefficient of the hysteresis correction device.

[0010] According to a specific implementation of an embodiment of this application, the hysteresis correction device corner frequency includes a second hysteresis correction device corner frequency and a first hysteresis correction device corner frequency. The expression for the second corner frequency of the hysteresis compensator is: , The expression for the first corner frequency of the hysteresis compensator is: , Where T1 is the time constant of the inertial element of the hysteresis correction device.

[0011] According to a specific implementation of this application, the expression for the transfer function of the hysteresis correction device is: , Among them, G lag (·) represents the transfer function of the hysteresis correction device.

[0012] According to a specific implementation of an embodiment of this application, the expression for the lead coefficient of the lead correction device is: , Where a is the lead coefficient of the lead compensator; The corner frequency of the lead compensator includes a first corner frequency and a second corner frequency, and the expression for the first corner frequency is as follows: , The expression for the second corner frequency of the lead compensation device is: , Where T2 is the time constant of the inertial element of the lead correction device.

[0013] According to a specific implementation of an embodiment of this application, the expression for the transfer function of the lead compensation device is: , Among them, G lead (·) represents the transfer function of the lead compensator.

[0014] According to a specific implementation of this application, the expression for the open-loop transfer function of the single closed-loop position control system of the finite angle motor after lag-lead compensation is as follows: , Wherein, G(s) is the open-loop transfer function of the single closed-loop position control system of the finite angle motor after lag-lead compensation.

[0015] Beneficial effects: The parameter tuning method for lag-lead compensation in the single closed-loop position control system of the finite angle motor in this application proposes a single closed-loop position control scheme for the finite angle motor, which reduces the complexity and cost of the control system; the proposed parameter tuning method for lag-lead compensation in the single closed-loop position control of the finite angle motor ensures that the system has a large phase margin after compensation. Under the premise of ), the low frequency band can be appropriately raised, which improves the steady-state performance of the system and realizes high-precision control of the position of the finite angle motor; the proposed lag-lead compensation parameter tuning method for single closed-loop position control of finite angle motor makes the asymptote of the open-loop logarithmic amplitude-frequency characteristic of the compensated system have a slope of -20dB / dec in the mid-frequency band and occupy a relatively wide frequency range. Therefore, its closed-loop system dynamic response exhibits good stability and speed; simultaneously, it results in a large phase angle (greater than -120°) in the mid-frequency range of the corrected system's open-loop logarithmic phase frequency response curve. The bandwidth range of ) is Even if the system's cutoff frequency shifts significantly due to parameter changes, the system can still maintain a high phase margin, thus maintaining good stability and dynamic performance, resulting in good robustness of the corrected system. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a structural diagram of a single closed-loop control system for a finite angle motor position according to an embodiment of the present invention; Figure 2 This is an equivalent electrical schematic diagram of a finite-angle motor according to an embodiment of the present invention; Figure 3 The transfer function block diagram of a lag-lead compensation system for a single closed-loop position control of a finite angle motor according to an embodiment of the present invention is shown below. Figure 4 The following is a result diagram of a single closed-loop position control system for a finite angle motor after lag-lead correction according to an embodiment of the present invention: (a) is a schematic diagram of the asymptote of the open-loop logarithmic amplitude-frequency characteristic, and (b) is a schematic diagram of the open-loop logarithmic phase-frequency characteristic. Figure 5 Bode plot of open-loop transfer function of a single closed-loop control system for a finite angle motor position designed according to a lag-lead compensation parameter tuning method of an embodiment of the present invention, wherein (a) is the open-loop logarithmic amplitude-frequency characteristic plot and (b) is the open-loop logarithmic phase-frequency characteristic plot; Figure 6 The following are the results of the system after conventional lag-lead compensation: (a) is a schematic diagram of the asymptote of the open-loop logarithmic amplitude-frequency characteristic, and (b) is a schematic diagram of the open-loop logarithmic phase-frequency characteristic. Figure 7 Bode plot of the open-loop transfer function of the same finite angle motor position single closed-loop control system designed using the conventional lag-lead compensation parameter tuning method, where (a) is the open-loop logarithmic amplitude-frequency response plot and (b) is the open-loop logarithmic phase-frequency response plot. Detailed Implementation

[0018] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0019] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0020] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this application, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0021] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this application. The illustrations only show the components related to this application and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0022] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0023] This application provides a parameter tuning method for lag-lead compensation in a single-loop position control system for a finite angle motor. The control system adopts a single-loop position structure and includes a finite angle motor, a position controller, a position sensor, and a power amplifier. The position controller employs lag-lead compensation. The parameter tuning method for lag-lead compensation includes: A third-order linear differential equation is constructed between the input voltage and the output speed angular displacement of a finite angle motor. The third-order linear differential equation is then simplified and subjected to Laplace transform to obtain the transfer function of the finite angle motor. Determine the system open-loop gain based on the system's steady-state error requirements; The open-loop logarithmic amplitude-frequency characteristic of the uncorrected system is obtained based on the open-loop gain. The cutoff frequency of the uncorrected system is calculated based on the relationship between the cutoff frequency of the uncorrected system and the corner frequency of the finite angle motor. The open-loop gain is then adjusted so that the cutoff frequency of the uncorrected system is greater than the given cutoff frequency of the system. Based on the relationship between the corner frequency of the lag compensator, the cutoff frequency given by the system, the corner frequency of the finite angle motor, and the corner frequency of the lead compensator, as well as the logarithmic amplitude-frequency characteristic of the system after compensation at the cutoff frequency, the attenuation coefficient of the lag compensator is obtained. The corner frequency of the lag compensator is determined based on the attenuation coefficient of the lag compensator, the time constant of the inertial element of the lag compensator, and the given cutoff frequency of the system. The transfer function of the hysteresis compensator is obtained based on the corner frequency of the hysteresis compensator. Based on the phase margin requirement of the corrected system at the given cutoff frequency, the lead coefficient of the lead compensator is calculated. The turnaround frequency of the advance compensation device is calculated based on the advance coefficient of the advance compensation device and the turnaround frequency of the finite angle motor. Based on the corner frequency of the lead compensator, the transfer function of the lead compensator is obtained. Based on the transfer functions of the lag compensator and the lead compensator, the open-loop transfer function of the lag-lead compensator system for single closed-loop position control of a finite angle motor is obtained.

[0024] Specifically, refer to Figure 1 This paper presents a block diagram of a single-loop position control system for a finite angle motor, which mainly consists of a finite angle motor, a position controller, a position sensor, and a power amplifier. The control system employs a single-loop position structure, where the position controller uses a lag-lead compensation algorithm. This results in a simple control system structure, low frequency requirements for the controller chip, and no need to collect phase current data from the finite angle motor, thus reducing the cost of the control system.

[0025] In one embodiment, the expression for the third-order linear differential equation between the input voltage and the output speed angular displacement of the finite-angle motor is: , Among them, L a R is the inductance of the armature of a finite-angle motor. a f is the resistance of the armature of a finite-angle motor. m It is the total viscous friction coefficient referred to the shaft of a motor with a finite rotation angle, J. m It is the total moment of inertia referred to the shaft of the finite-angle motor, C. m For a finite angle motor, θ is the torque coefficient. m(·) represents the output angular displacement of the finite-rotation motor, t represents time, and K represents the displacement. s For the stiffness of the return spring after power failure, C e u is the back electromotive force coefficient of a finite angle motor. a (·) represents the input voltage of the finite angle motor; The simplified expression of the third-order linear differential equation is as follows: , Among them, T m Let be the electromechanical time constant of the motor. ,in The resistance of the armature of a finite-angle motor, To account for the total moment of inertia referred to the shaft of the finite-angle motor, The total viscous friction coefficient is applied to the shaft of a motor with a finite rotation angle. It is the back electromotive force coefficient of a finite angle motor (V / (rad / s)). It is the torque coefficient (Nm / A) of a finite angle motor; K a This is the transmission coefficient of the motor. ; The expression for the transfer function of the finite angle motor is: , Where s is the complex frequency variable in the Laplace transform, and G a (·) is the transfer function of a finite-angle motor, U a (·) represents the input armature voltage of the finite angle motor.

[0026] In specific implementation, refer to Figure 2 The diagram shows the equivalent electrical schematic of a finite-angle motor, where the armature voltage is... θ is the input quantity (input voltage of a finite angle motor). m (·) represents the output angular displacement of a finite-angle motor, and M represents the motor. These are the resistance and inductance of the armature of a finite-angle motor, respectively. These are the total viscous friction coefficient, total moment of inertia, and load torque (external load on the motor) referred to the motor shaft with a finite rotation angle.

[0027] The voltage balance equations for the motor armature circuit are as follows: , In the formula, It is the current in the armature of the motor. It is the back electromotive force generated in the armature when the motor rotates, and its magnitude is directly proportional to the rotational speed, that is: In the formula, It is the back electromotive force coefficient (V / (rad / s)). ω represents the angular velocity (rad / s) of a finite-angle motor.

[0028] The electromagnetic torque generated by the armature current is: , In the formula, It is the electromagnetic torque (Nm) generated by the armature current. It is the motor torque coefficient (Nm / A).

[0029] The torque balance equation for the motor shaft is: , In the formula, It is the stiffness (Nm / rad) of the return spring after power failure.

[0030] In practical engineering, the rotation angle of a finite-angle motor is used. As output: , By combining the above equations and eliminating intermediate variables, After processing, the input voltage of the finite angle motor can be obtained. To the angular displacement output of the limited-rotation motor The third-order linear differential equation between them: ; In this embodiment, due to the inductance of the armature winding of the finite angle motor Since the effect is relatively small, its influence can usually be ignored; and the effect of the de-energized return spring can also be ignored, therefore, the above formula can be simplified to the following form: , In the formula, This is the electromechanical time constant of the motor (in seconds). ; This is the transmission coefficient of the motor. .

[0031] Under zero initial conditions, perform a Laplace transform on the above equation and consider... The effect of the system is expressed in angular displacement. We can obtain:

[0032] In the formula This is the transfer function for a finite-angle motor.

[0033] In one embodiment, the following indicators of the corrected system are given based on the actual control quality requirements of the finite-angle motor: 1) When the ramp input At that time, steady-state error ; 2) Open-loop system cutoff frequency ; 3) Phase margin ; in, e is the function value of the input signal as a function of time. ss The steady-state error is given by ωc, the cutoff frequency of the open-loop system, and γ is the phase margin. Based on the above-mentioned indicator requirements, the parameters of the lag-lead correction device are tuned.

[0034] Furthermore, the open-loop gain of the system is: , Where K is the system open-loop gain. This is the steady-state error given by the system.

[0035] In practice, the open-loop gain of the system is determined based on the system's steady-state error requirements. The corrected system in this embodiment With uncalibrated systems All are type I. Based on the steady-state error calculation method for a type I system under typical input signals, it can be seen that the ramp input... When the steady-state error of the system is ,Right now Generally take ,recommend The value range is 3.1 × 10. -4 ~0.001.

[0036] Furthermore, the step of obtaining the open-loop logarithmic amplitude-frequency characteristic of the uncorrected system based on the open-loop gain, and calculating the cutoff frequency of the uncorrected system according to the relationship between the cutoff frequency of the uncorrected system and the corner frequency of the finite-angle motor, includes: like Figure 4 As shown in Figure (a), the open-loop logarithmic magnitude-frequency characteristic of the uncorrected system is obtained based on the open-loop gain, and the expression is: , Where, ω c0 Let L0(·) be the cutoff frequency of the uncompensated system, L0(·) be the open-loop logarithmic amplitude-frequency response of the uncompensated system, j be the imaginary unit, and G0(·) be the uncompensated system. m The turning frequency of a finite angle motor; when At that time, that is The expression for the open-loop logarithmic magnitude-frequency characteristic of the uncorrected system is obtained based on the open-loop gain. The "√" in the formula is then used to express this characteristic. "Omitted, we get:" , From this expression, we get: ; when At that time, that is Based on the open-loop gain, the expression for the open-loop logarithmic magnitude-frequency characteristic of the uncorrected system is obtained. Omit the "1" in the equation, and we get: , From this expression, we can obtain: , Where dB is the amplitude unit; In this embodiment, it is necessary to ensure If this condition is not met, the open-loop gain needs to be increased. So that Preferred, The range of values ​​is .

[0037] Furthermore, the step of obtaining the attenuation coefficient of the lag compensator based on the relationship between the corner frequency of the lag compensator, the given cutoff frequency of the system, the corner frequency of the finite angle motor, and the corner frequency of the lead compensator, as well as the logarithmic amplitude-frequency characteristic of the compensated system at the cutoff frequency, includes: The logarithmic magnitude-frequency response of the corrected system at the cutoff frequency is calculated as follows: , in, This is the second corner frequency of the hysteresis correction device. , The first corner frequency of the hysteresis correction device. T1 is the time constant of the inertial element of the lag compensation device. The cutoff frequency given by the system, This is the first corner frequency of the lead compensator. , This is the second corner frequency of the lead compensation device. T2 is the time constant of the inertial element of the lead compensator, L(·) is the logarithmic amplitude-frequency characteristic of the system after compensation at the cutoff frequency, and G(·) is the compensation system. when At that time, or when When corrected, the expression for the logarithmic amplitude-frequency characteristic of the system at the cutoff frequency simplifies to: , get: , Where b is the attenuation coefficient of the hysteresis correction device. .

[0038] Specifically, when At that time, due to ,Right now , , At this point, the formula The square root of the " " "as well as" Item omitted; due to ,Right now , At this time and Omit the "1" in the equation, and we get: , From this formula, we can see that: ; when At that time, that is , , , At this time , , and The item “1” in the text is omitted; because ,Right now At this time "in "Omitted, we get:" , From this formula, we can see that: .

[0039] In one embodiment, the corner frequencies of the hysteresis compensator include a second corner frequency and a first corner frequency. When using a hysteresis compensator for series correction, its high-frequency amplitude attenuation characteristics are primarily utilized to avoid the maximum hysteresis angle occurring at the cutoff frequency of the corrected system. Nearby. Therefore, when selecting the parameters of the hysteresis compensator, the second corner frequency of the hysteresis compensator should be set to... much smaller Then the expression for the second corner frequency of the hysteresis compensator is obtained as follows: , The expression for the first corner frequency of the hysteresis compensator is: , Where T1 is the time constant of the inertial element of the hysteresis correction device.

[0040] Furthermore, the expression for the transfer function of the hysteresis correction device is: , Among them, G lag (·) represents the transfer function of the hysteresis correction device.

[0041] Furthermore, the expression for the lead coefficient of the lead correction device is as follows: , Where 'a' is the lead coefficient of the lead compensator. ; The corner frequency of the lead compensator includes a first corner frequency and a second corner frequency, and the expression for the first corner frequency is as follows: , The expression for the second corner frequency of the lead compensation device is: , Where T2 is the time constant of the inertial element of the lead correction device.

[0042] In this embodiment, to ensure that the corrected system maintains a slope of -20dB / dec in the mid-frequency band, the first corner frequency of the lead compensator is chosen as... Furthermore, changes in the parameters of a finite-angle motor (such as uncertainties in the model parameters or changes over time) can lead to... If a certain range of shift occurs, in order to still ensure that the corrected system maintains a slope of -20dB / dec in the mid-frequency range, the first corner frequency of the lead compensator can also be taken as... ; The phase margin of the corrected system at the cutoff frequency is: , In the formula, The phase frequency characteristics of the system after correction of single closed-loop position control for a finite angle motor at the cutoff frequency.

[0043] As can be seen from the above, the second corner frequency of the lag correction device After correction, the system stop frequency If there is an 11th harmonic, the impact of the lag compensator on the phase margin of the corrected system will not exceed -6°, that is: , but: , Depend on We can obtain: , Pick ; This leads to the second corner frequency of the lead compensator: .

[0044] Furthermore, the expression for the transfer function of the lead compensation device is: , Among them, G lead (·) represents the transfer function of the lead compensator.

[0045] In one embodiment, the transfer function of the position controller is: , In the formula, Pass functions to the position controller. For the gain of the position controller; The open-loop transfer function of an uncorrected single-closed-loop position control system for a finite angle motor is: , In the formula, The open-loop transfer function for an uncorrected single-closed-loop position control system of a finite-angle motor. ,in For the gain of the power amplifier, This is the gain of the position sensor.

[0046] Furthermore, refer to Figure 3 , Figure 3 middle For finite angle motor angle commands, This refers to the disturbance voltage generated by the external load. The expression for the open-loop transfer function of the single closed-loop position control system of the finite angle motor after lag-lead compensation is: , Wherein, G(s) is the open-loop transfer function of the single closed-loop position control system of the finite angle motor after lag-lead compensation.

[0047] The asymptote of the typical open-loop logarithmic amplitude-frequency characteristic of the finite angle motor single-closed-loop position control lag-lead compensation system completed according to the above steps. Open-loop logarithmic phase frequency characteristics Each as Figure 4 The solid curve in figure (a) and Figure 4 The solid curve in Figure (b) is shown. Figure 4 In Figure (b) for at cutoff frequency The frequency points in the nearby frequency band where the phase begins to be greater than -120°, for at cutoff frequency The frequency point where the phase begins to fall below -120° in the nearby frequency band. Asymptotes of the open-loop logarithmic amplitude-frequency response of an uncorrected single-loop position control system for a finite angle motor. Open-loop logarithmic phase frequency characteristics Each as Figure 4 The dashed curve in figure (a) and Figure 4 The dashed curve in Figure (b) shows the logarithmic amplitude-frequency characteristic of the finite angle motor. like Figure 4 As shown by the dashed-dot curve in Figure (a), due to the finite-angle motor transfer function Open-loop transfer function of a single closed-loop position control system for a finite angle motor The only difference is the gain, therefore the logarithmic phase frequency characteristic of a finite angle motor is... Open-loop logarithmic phase frequency characteristics of a single closed-loop position control system for a finite angle motor Same, such as Figure 4 The dashed curve in Figure (b) is shown.

[0048] Low frequency band usually refers to The asymptote at the first corner frequency of the lag compensator (i.e., The frequency band to the left of the equation is entirely determined by the integral element and open-loop gain. The more negative the slope (the larger the absolute value of the negative number) in the low-frequency band, the higher the position, the more integral elements are involved, and the greater the open-loop gain. Under stable closed-loop system conditions, this results in smaller steady-state error and higher steady-state accuracy. In this embodiment, the lag-lead compensation system for the single closed-loop position control of the finite angle motor ensures phase margin. Under the premise of ensuring the stability of the closed-loop system, appropriately raise the low frequency band (compared to) and (in the low-frequency band), which improves the steady-state performance of the system.

[0049] Mid-frequency band refers to at cutoff frequency In the nearby frequency band, this characteristic primarily reflects the stability and speed of the dynamic response of the closed-loop system. Generally speaking, Size and corresponding frequency It is closely related to the slope. The more negative the slope, the better. The smaller (the larger the absolute value of a negative number). Place, The slope of the curve versus the phase margin The impact is greatest the farther away. place slope pair The smaller the impact, the better. Qualitatively speaking, if The curve has a mid-frequency slope of -20 dB / dec and occupies a relatively wide frequency range, therefore the phase margin is... If the angle is relatively large (close to 90°), the system overshoot will be small. Conversely, if the mid-frequency range has a slope of -40dB / dec and covers a wide frequency range, the phase margin will be large. Even at very small angles (close to 0°), the system's stability and speed become very poor. Therefore, to ensure satisfactory dynamic performance of the system, it is desirable to... Crossing the 0dB line with a slope of -20dB / dec while maintaining a relatively wide mid-frequency range. For example... Figure 4 As shown by the solid curve in Figure (a), the asymptote of the open-loop logarithmic amplitude-frequency characteristic of the single closed-loop position control system for the finite angle motor designed in this embodiment after lag-lead compensation. The curve in the mid-frequency band ( The slope in the surrounding area is -20 dB / dec, and it occupies a relatively wide frequency range. Therefore, its closed-loop system dynamic response exhibits good stability and speed; such as Figure 4 As shown by the solid curve in Figure (b), the open-loop logarithmic phase frequency characteristic of the single closed-loop position control system for the finite angle motor designed in this embodiment after lag-lead compensation is shown. The curve in the mid-frequency band ( The surrounding area has a large phase angle (the smaller the absolute value of the negative number), that is, a phase angle greater than -120° (i.e., phase margin). The bandwidth range of ) is This means that even if the system's cutoff frequency shifts significantly due to parameter changes (such as changes in open-loop gain, uncertainties in model parameters, or changes over time), the system can still maintain a high phase margin, thereby maintaining good stability and dynamic performance. Therefore, the corrected system in this embodiment has good robustness.

[0050] High-frequency characteristics are typically composed of elements with small time constants, and their corner frequencies are far from the cutoff frequency. Therefore, it has little impact on the system's dynamic performance. However, the amplitude in the high-frequency band directly reflects the system's ability to suppress high-frequency signals at the input. The lower the decibel value in the high-frequency band, the greater the attenuation effect of the system on high-frequency signals, meaning the stronger the system's resistance to high-frequency interference. For example... Figure 4 As shown by the solid curve in Figure (a), the asymptote of the open-loop logarithmic amplitude-frequency characteristic of the single closed-loop position control system for the finite angle motor designed in this embodiment after lag-lead compensation. The slope of the curve in the high-frequency range is -40dB / dec, which maintains good attenuation capability for high-frequency signals.

[0051] The open-loop transfer function of the finite angle motor single closed-loop position control system with lag-lead compensation described in this embodiment is as follows: , Its Byrd diagram Figure 5 As shown, (a) is the open-loop logarithmic magnitude frequency response diagram, and (b) is the open-loop logarithmic phase frequency response diagram. The open-loop gain of the corrected system is shown in the figure. Cutoff frequency The mid-frequency slope is -20dB / dec, and it occupies a relatively wide frequency range. Multiples; phase margin The phase angle in the mid-frequency band is greater than -120° (i.e., phase margin). The bandwidth range of ) is Therefore, the system corrected using this embodiment has higher steady-state accuracy, better stability and speed in its closed-loop dynamic response, and better robustness.

[0052] The asymptote of the typical open-loop logarithmic amplitude-frequency characteristic of a single closed-loop position control system for a finite angle motor after conventional lag-lead compensation. Open-loop logarithmic phase frequency characteristics Each as Figure 6 The solid curve in graph (a) and Figure 6 The solid curve in graph (b) is shown. Figure 6 In Figure (b) for at cutoff frequency The frequency points in the nearby frequency band where the phase begins to be greater than -120°, for at cutoff frequency The frequency points in the nearby frequency band where the phase begins to be less than -120°, This is the cutoff frequency of the conventional lag-lead compensation design result. Parameter tuning is carried out according to the same control quality requirements for the finite angle motor described above, so the low-frequency range is the same as in this embodiment. However, in the mid-frequency range, the cutoff frequency of the conventional lag-lead compensation design result does not meet the design specifications. This is mainly because the design results of conventional lag-lead compensation show a region with a slope of 0dB / dec in the mid-frequency range, which leads to a smaller cutoff frequency and a deterioration in the system's speed. Additionally, the open-loop logarithmic phase frequency characteristic of the system after conventional lag-lead compensation... The curve has a large phase angle in the mid-frequency range (the smaller the absolute value of the negative number), that is, a phase angle greater than -120° (i.e., phase margin). The bandwidth range of ) is Therefore, the robustness of the conventional lag-lead compensation system is worse than that of the compensation system described in this embodiment.

[0053] The open-loop transfer function of a single closed-loop position control system for the same finite angle motor using conventional lag-lead compensation is: , Its Byrd diagram Figure 7 As shown, (a) is the open-loop logarithmic magnitude frequency response diagram, and (b) is the open-loop logarithmic phase frequency response diagram. The open-loop gain of the corrected system is shown in the figure. Cutoff frequency The mid-frequency band exhibits a region with a slope close to 0 dB / dec; phase margin The phase angle in the mid-frequency band is greater than -120° (i.e., phase margin). The bandwidth range of ) is The conventional lag-lead compensation method can achieve higher steady-state accuracy, but its closed-loop dynamic response speed and robustness are inferior to the system compensated by the method described in this embodiment. One important reason is that the conventional lag-lead compensation does not consider the relative positional relationship between the lead compensation cutoff frequency, the cutoff frequency of the uncompensated system, and the cutoff frequency of the compensated system, nor the resulting changes in the shape of the compensated system.

[0054] Therefore, the solution proposed in this application has the following beneficial effects: the invention proposes a single closed-loop position control scheme for a finite angle motor, which reduces the complexity and cost of the control system; the proposed lag-lead correction parameter tuning method for the single closed-loop position control of the finite angle motor ensures that the system has a large phase margin after correction. Under the premise of ), the low frequency band can be appropriately raised, which improves the steady-state performance of the system and realizes high-precision control of the position of the finite angle motor; the proposed lag-lead compensation parameter tuning method for single closed-loop position control of finite angle motor makes the asymptote of the open-loop logarithmic amplitude-frequency characteristic of the compensated system have a slope of -20dB / dec in the mid-frequency band and occupy a relatively wide frequency range. Therefore, its closed-loop system dynamic response has good stability and speed; the proposed lag-lead compensation parameter tuning method for single closed-loop position control of finite angle motor makes the open-loop logarithmic phase frequency characteristic curve of the compensated system have a large phase angle in the mid-frequency range, that is, the phase angle is greater than -120° (phase margin). The bandwidth range of ) is Even if the system's cutoff frequency shifts significantly due to parameter changes, the system can still maintain a high phase margin, thus maintaining good stability and dynamic performance, resulting in good robustness of the corrected system.

[0055] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A parameter tuning method for lag-lead compensation in a single closed-loop control system for the position of a finite angle motor, characterized in that, The control system adopts a single closed-loop position structure. The control system includes a finite-angle motor, a position controller, a position sensor, and a power amplifier. The position controller employs lag-lead compensation, and the parameter tuning method for the lag-lead compensation includes: A third-order linear differential equation is constructed between the input voltage and the output speed angular displacement of a finite angle motor. The third-order linear differential equation is then simplified and subjected to Laplace transform to obtain the transfer function of the finite angle motor. Determine the system open-loop gain based on the system's steady-state error requirements; The open-loop logarithmic amplitude-frequency characteristic of the uncorrected system is obtained based on the open-loop gain. The cutoff frequency of the uncorrected system is calculated based on the relationship between the cutoff frequency of the uncorrected system and the corner frequency of the finite angle motor. The open-loop gain is then adjusted so that the cutoff frequency of the uncorrected system is greater than the given cutoff frequency of the system. Based on the relationship between the corner frequency of the lag compensator, the cutoff frequency given by the system, the corner frequency of the finite angle motor, and the corner frequency of the lead compensator, as well as the logarithmic amplitude-frequency characteristic of the system after compensation at the cutoff frequency, the attenuation coefficient of the lag compensator is obtained. The corner frequency of the lag compensator is determined based on the attenuation coefficient of the lag compensator, the time constant of the inertial element of the lag compensator, and the given cutoff frequency of the system. The transfer function of the hysteresis compensator is obtained based on the corner frequency of the hysteresis compensator. Based on the phase margin requirement of the corrected system at the given cutoff frequency, the lead coefficient of the lead compensator is calculated. The turnaround frequency of the advance compensation device is calculated based on the advance coefficient of the advance compensation device and the turnaround frequency of the finite angle motor. Based on the corner frequency of the lead compensator, the transfer function of the lead compensator is obtained. Based on the transfer functions of the lag compensator and the lead compensator, the open-loop transfer function of the lag-lead compensator system for single closed-loop position control of a finite angle motor is obtained.

2. The parameter tuning method for lag-lead compensation in a single closed-loop control system for a finite angle motor position according to claim 1, characterized in that, The expression for the third-order linear differential equation between the input voltage and the output speed angular displacement of the finite angle motor is as follows: ， Among them, L a R is the inductance of the armature of a finite-angle motor. a f is the resistance of the armature of a finite-angle motor. m It is the total viscous friction coefficient referred to the shaft of a motor with a finite rotation angle, J. m It is the total moment of inertia referred to the shaft of the finite-angle motor, C. m For a finite angle motor, θ is the torque coefficient. m (·) represents the output angular displacement of the finite-rotation motor, t represents time, and K represents the displacement. s For the stiffness of the return spring after power failure, C e u is the back electromotive force coefficient of a finite angle motor. a (·) represents the input voltage of the finite angle motor; The simplified expression of the third-order linear differential equation is as follows: ， Among them, T m K is the electromechanical time constant of the motor. a This is the transmission coefficient of the motor; The expression for the transfer function of the finite angle motor is: ， Where s is the complex frequency variable in the Laplace transform, and G a (·) is the transfer function of a finite-angle motor, U a (·) represents the input armature voltage of the finite angle motor.

3. The parameter tuning method for lag-lead compensation in a single closed-loop control system for a finite angle motor position according to claim 2, characterized in that, The open-loop gain of the system is: ， Where K is the system open-loop gain. This is the steady-state error given by the system.

4. The parameter tuning method for lag-lead compensation of a single closed-loop control system for a finite angle motor position according to claim 3, characterized in that, The process of obtaining the open-loop logarithmic amplitude-frequency characteristic of the uncorrected system based on the open-loop gain, and calculating the cutoff frequency of the uncorrected system according to the relationship between the cutoff frequency of the uncorrected system and the cornering frequency of the finite-angle motor, includes: The open-loop logarithmic magnitude-frequency characteristic of the uncorrected system is obtained based on the open-loop gain, and the expression is: ， Where, ω c0 Let L0(·) be the cutoff frequency of the uncompensated system, L0(·) be the open-loop logarithmic amplitude-frequency response of the uncompensated system, j be the imaginary unit, and G0(·) be the uncompensated system. m The turning frequency of a finite angle motor; when At that time, based on the open-loop gain, the expression for the open-loop logarithmic magnitude-frequency characteristic of the uncorrected system is obtained, resulting in: ， ； when At that time, based on the open-loop gain, the expression for the open-loop logarithmic magnitude-frequency characteristic of the uncorrected system is obtained, resulting in: ， ， Where dB is the amplitude unit.

5. The parameter tuning method for lag-lead compensation of a single closed-loop control system for a finite angle motor position according to claim 4, characterized in that, The attenuation coefficient of the lag compensator is obtained based on the relationship between the corner frequency of the lag compensator, the given cutoff frequency of the system, the corner frequency of the finite angle motor, and the corner frequency of the lead compensator, as well as the logarithmic amplitude-frequency characteristic of the system at the cutoff frequency after compensation. This includes: The logarithmic magnitude-frequency response of the corrected system at the cutoff frequency is calculated as follows: ， in, This is the second corner frequency of the hysteresis correction device. The first corner frequency of the hysteresis correction device. The cutoff frequency given by the system, This is the first corner frequency of the lead compensator. L is the second corner frequency of the lead compensator, L(·) is the logarithmic amplitude-frequency characteristic of the system at the cutoff frequency after compensation, and G(·) is the compensation system. when At that time, or when When corrected, the expression for the logarithmic amplitude-frequency characteristic of the system at the cutoff frequency simplifies to: ， get: , Where b is the attenuation coefficient of the hysteresis correction device.

6. The parameter tuning method for lag-lead compensation of a single closed-loop control system for a finite angle motor position according to claim 5, characterized in that, The hysteresis correction device's corner frequency includes a second corner frequency and a first corner frequency. The expression for the second corner frequency of the hysteresis compensator is: ， The expression for the first corner frequency of the hysteresis compensator is: ， Where T1 is the time constant of the inertial element of the hysteresis correction device.

7. The parameter tuning method for lag-lead compensation of a single closed-loop control system for a finite angle motor position according to claim 6, characterized in that, The expression for the transfer function of the hysteresis correction device is: ， Among them, G lag (·) represents the transfer function of the hysteresis correction device.

8. The parameter tuning method for lag-lead compensation of a single closed-loop control system for a finite angle motor position according to claim 7, characterized in that, The expression for the lead coefficient of the lead correction device is: ， Where a is the lead coefficient of the lead compensator; The corner frequency of the lead compensator includes a first corner frequency and a second corner frequency, and the expression for the first corner frequency is as follows: ， The expression for the second corner frequency of the lead compensation device is: ， Where T2 is the time constant of the inertial element of the lead correction device.

9. The parameter tuning method for lag-lead compensation of a single closed-loop control system for a finite angle motor position according to claim 8, characterized in that, The expression for the transfer function of the lead compensation device is: ， Among them, G lead (·) represents the transfer function of the lead compensator.

10. The parameter tuning method for lag-lead compensation of a single closed-loop control system for a finite angle motor position according to claim 9, characterized in that, The expression for the open-loop transfer function of the single closed-loop position control system of the finite angle motor after lag-lead compensation is as follows: ， Wherein, G(s) is the open-loop transfer function of the single closed-loop position control system of the finite angle motor after lag-lead compensation.

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