A mobile robot servo motor active disturbance rejection position control method

Abstract

The application relates to a mobile robot servo motor active disturbance rejection position control method, and belongs to the technical field of servo motor control.The application quickly estimates position, speed and main body lumped disturbance through a front-stage observer, takes the front-stage disturbance estimation value as the known input of a rear-stage observer, performs secondary fine estimation on the residual disturbance, thereby reducing the bandwidth pressure of the single-stage observer, and giving consideration to the stability under large disturbance and the observation precision under small disturbance;secondly, a smoothing Ifal function composed of inverse hyperbolic sine functions and sine functions is used to replace a traditional fal function, the continuity of a small error interval and a segmented boundary is improved, nonlinear gain mutation, disturbance estimation chattering and q-axis reference current fluctuation are reduced;finally, the two-stage disturbance estimation results are superposed and fed forwardly compensated, and a linear state error feedback is combined to generate a torque current instruction, so that the permanent magnet synchronous motor realizes rapid disturbance recovery and high-precision position control under the condition of load mutation.

Description

Technical Field

[0001] This invention relates to the field of servo motor control technology, and in particular to a method for self-disruption-resistant position control of a servo motor for a mobile robot. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are characterized by high power density, high operating efficiency, and fast torque response, and are widely used in high-precision servo control systems for mobile robot joints. During operation, mobile robots often experience frequent starts and stops, low-speed operation, and rapid load changes, making their position control performance susceptible to sudden load torque fluctuations and motor parameter perturbations. Traditional three-loop control of position, speed, and current often employs PI controllers, relying primarily on tracking errors to generate feedback control quantities, lacking direct observation and active compensation capabilities for unknown disturbances. Active disturbance rejection control (ADRC), through a tracking differentiator, extended state observer, and state error feedback control law, unifies parameter mismatch, external loads, and unmodeled dynamics into a lumped disturbance, which is then estimated and compensated for in real time. This provides an effective technical approach for achieving high-precision position tracking, rapid disturbance recovery, and steady-state position maintenance for PSMs in mobile robots.

[0003] Traditional error feedback control typically adjusts only after position deviation occurs, making it difficult to suppress rapidly changing internal and external disturbances in a timely manner. Therefore, it is necessary to improve the control system's ability to observe, accurately estimate, and actively compensate for lumped disturbances in real time. Existing research on active disturbance rejection position control (ADRC) for permanent magnet synchronous motors mainly focuses on the design of extended state observer structures and nonlinear error correction functions.

[0004] Furthermore, existing non-cascaded active disturbance rejection control (ADRC) schemes typically employ only a single linear or nonlinear extended state observer, treating load torque, parameter perturbations, friction, and unmodeled dynamics as a unified lumped disturbance for estimation and compensation. While this scheme is structurally simple, the single-stage observer must simultaneously estimate position, velocity, and all disturbances, making its disturbance observation performance susceptible to bandwidth limitations. With low bandwidth, tracking of sudden load changes and rapid time-varying disturbances lags, leading to untimely disturbance compensation, increased position deviation, and prolonged recovery time. Increasing bandwidth, while accelerating disturbance estimation, amplifies error noise, causing high-frequency fluctuations in both velocity and disturbance estimates. Additionally, single-stage linear observers lack nonlinear gain adjustment capabilities, limiting the accuracy of estimation for small residual disturbances; single-stage nonlinear observers, under large disturbances, may be affected by parameter configuration and nonlinear gain variations. Therefore, non-cascaded schemes struggle to simultaneously achieve stability under large disturbances, estimation accuracy under small disturbances, and high-frequency noise suppression capabilities.

[0005] Furthermore, most existing active disturbance rejection position control schemes use the traditional FAL function to correct observation errors. While this function exhibits the characteristic of "large gain for small errors and small gain for large errors," the transition between the linear segment of small errors and the power segment of large errors at the boundary is not smooth enough, and the first derivative is usually not continuous. When encoder errors or mechanical vibrations cause the observation error to fluctuate repeatedly near the boundary point, the nonlinear correction gain is prone to abrupt changes, resulting in high-frequency fluctuations in the velocity estimate, residual disturbance estimate, and q-axis reference current. Simultaneously, the nonlinear exponent and linear interval of the traditional FAL function are coupled. Reducing the linear interval to improve the accuracy of small-error observations can easily amplify measurement noise; while expanding the linear interval can reduce chattering, it reduces the sensitivity to detect small disturbances. Summary of the Invention

[0006] This invention overcomes the shortcomings of the prior art and provides a method for self-disruption-resistant position control of servo motors for mobile robots.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows: This invention provides a method for self-disturbance rejection position control of a servo motor for a mobile robot, comprising the following steps: Using a vector control method with zero q-axis current, a position control model for a permanent magnet synchronous motor is constructed in a synchronous rotating coordinate system. An extended state model of the position control system is constructed by combining current loop tracking error, permanent magnet flux variation, rotational inertia variation, load torque variation, friction, and unmodeled dynamics. Construct the fastest control synthesis function, use the position output and velocity output of the tracking differentiator in the kth operation cycle to construct the discrete state update equation, and use the discrete state update equation to change the tracking speed of the tracking differentiator to the given position signal; A cascaded observation structure is constructed by using a front-stage third-order linear extended state observer and a rear-stage third-order improved nonlinear extended state observer. The front-stage third-order linear extended state observer is used to conduct preliminary observations of position, velocity and main disturbance. The residual disturbance that the preceding third-order linear extended state observer failed to accurately estimate was observed by using the improved third-order nonlinear extended state observer. The reference state output by the tracking differentiator is combined with the estimated state obtained by the extended state observer using state error feedback to generate the basic control quantity of the system. The LSEF is selected to generate the basic control quantity, and the total disturbance estimate output by the cascaded extended state observer is used for compensation.

[0008] Furthermore, in the self-disturbance rejection position control method for servo motors in mobile robots, a vector control mode with zero q-axis current is adopted. A position control model for a permanent magnet synchronous motor is constructed in a synchronous rotating coordinate system. An extended state model of the position control system is constructed by combining current loop tracking error, permanent magnet flux variation, rotational inertia variation, load torque variation, friction, and unmodeled dynamics. Specifically: Using a vector control method with zero q-axis current, a position control model for a permanent magnet synchronous motor is constructed in a synchronous rotating coordinate system. Based on the position control model of the permanent magnet synchronous motor, the second-order dynamic equation of the mechanical angular position is obtained. Define the actual gain from current to mechanical angular acceleration, and reconstruct the second-order dynamic equation of the mechanical angular position by combining the current loop tracking error, permanent magnet flux variation, rotational inertia variation, load torque variation, friction, and unmodeled dynamics. By reconstruction, the second-order dynamic equation of the reconstructed mechanical angular position is obtained, and the extended state model of the position control system is constructed by combining the actual gain from the current to the mechanical angular acceleration.

[0009] Furthermore, in the active disturbance rejection position control method for servo motors in mobile robots, a fastest control synthesis function is constructed. A discrete state update equation is built using the position and velocity outputs of the tracking differentiator in the kth operation cycle. This discrete state update equation is then used to change the tracking speed of the tracking differentiator to the given position signal. Specifically, this includes: The fastest control synthesis function is constructed, and a second-order nonlinear tracking differentiator based on the fastest control synthesis function fhan is adopted. The position given signal first passes through the tracking differentiator to generate smooth position reference value and reference velocity value. The position output and velocity output in the kth operation cycle are calculated using a tracking differentiator. Based on the position output and velocity output in the kth operation cycle, the discrete state update equation of the second-order nonlinear tracking differentiator is constructed. Based on the discrete state update equation of the second-order nonlinear tracking differentiator, the tracking speed of the tracking differentiator to the given position signal is changed by adjusting the speed factor.

[0010] Furthermore, in the active disturbance rejection position control method for servo motors in mobile robots, a pre-stage third-order linear extended state observer is used to perform preliminary observations of position, velocity, and main body disturbances, specifically including: Define the position observation error of the preceding third-order linear extended state observer, and define the preceding third-order linear extended state observer and set the bandwidth of the preceding observer. The three poles of the observer are configured in preset positions to generate a pre-characteristic polynomial, and the gain of the pre-observer is obtained based on the characteristic polynomial.

[0011] Furthermore, in the active disturbance rejection position control method for servo motors in mobile robots, a second observation is performed using a subsequent third-order improved nonlinear extended state observer to detect the residual disturbances that the preceding third-order linear extended state observer failed to accurately estimate. Specifically: Define the position observation error of the subsequent stage, and at the same time, construct the third-order improved nonlinear extended state observer of the subsequent stage, set the bandwidth of the preceding stage observer, and use the fal function to perform nonlinear correction on the observation error; In the range below the preset error threshold, a weighted combination of inverse hyperbolic sine function and sine function is introduced. The characteristics of continuous, smooth and approximately linear near the origin of inverse hyperbolic sine function and sine function are utilized to smooth the error. If the error threshold is exceeded, continue to use the power nonlinear function. Utilize the continuity of the piecewise function with the preset function value and the first derivative to obtain the equation. Then, use the fitting method to solve for the weight coefficients. By replacing the fal nonlinear function in the subsequent nonlinear extended state observer with the improved smooth nonlinear function Ifal, the improved NLESO is obtained.

[0012] Furthermore, in the active disturbance rejection position control method for servo motors in mobile robots, the reference state output by the tracking differentiator is combined with the estimated state obtained by the extended state observer using state error feedback to generate the basic control quantity of the system. The LSEF is selected to generate the basic control quantity, and compensation is performed using the total disturbance estimate output by the cascaded extended state observer. Specifically, this includes: By combining the reference state output by the tracking differentiator with the estimated state obtained by the extended state observer using state error feedback, the basic control quantity of the system is generated. The target mechanical position command is input into the tracking differentiator, and the sudden position command is smoothed through the fastest control synthesis function to obtain the smoothed position reference value and the reference mechanical angular velocity. The actual mechanical angular position of the permanent magnet synchronous motor is acquired, and the position feedback signal is input into the front-stage third-order linear extended state observer and the rear-stage third-order improved nonlinear extended state observer; The motor position, mechanical angular velocity, and main body lumped disturbance are initially estimated by using a front-stage third-order linear extended state observer and a rear-stage third-order improved nonlinear extended state observer to obtain disturbance estimates, and compensation is performed based on the disturbance estimates.

[0013] Furthermore, in the active disturbance rejection position control method for servo motors in mobile robots, compensation is performed based on the disturbance estimate, specifically including: The disturbance estimate is used as the known disturbance input to improve the NLESO stage, and the observation error is corrected by the improved smoothing nonlinear function Ifal, to further obtain the mechanical angular position estimate, mechanical angular velocity estimate and the previous stage residual disturbance estimate; The basic control quantity is calculated using linear state error feedback. At the same time, the estimated value of the main disturbance of the preceding stage is superimposed with the estimated value of the residual disturbance of the following stage to obtain the total disturbance estimate, which is then fed forward from the basic control quantity for compensation. The q-axis reference current is then obtained through conversion, while the d-axis reference current is set to 0. The difference between the d-axis and q-axis reference currents and the actual d-axis and q-axis currents obtained through coordinate transformation is calculated, and the d-axis and q-axis reference voltages are obtained through two current proportional-integral controllers. Six drive signals, PWM1 to PWM6, are generated by inverse Park transform and space vector pulse width modulation to control the three-phase inverter to drive the permanent magnet synchronous motor.

[0014] This invention addresses the shortcomings of the prior art and has the following beneficial effects: To address the problems of limited perturbation estimation bandwidth, difficulty in balancing observation accuracy and noise suppression in existing non-cascaded extended state observers, as well as the unsmooth piecewise boundaries, complex parameter tuning, and susceptibility to high-frequency chattering in traditional fal functions, the core objective of this invention is to specifically resolve these contradictions. First, a cascaded structure combining a front-stage linear extended state observer and a rear-stage improved nonlinear extended state observer is constructed. The front-stage observer quickly estimates the position, velocity, and main lumped disturbance. Then, the disturbance estimate from the front stage is used as the known input for the rear-stage observer to perform a second, refined estimate of the remaining disturbance, thereby reducing the bandwidth pressure on a single-stage observer and balancing stability under large disturbances with observation accuracy under small disturbances. Second, a smoothed Ifal function composed of an inverse hyperbolic sine function and a weighted sine function is used to replace the traditional FAL function, improving the continuity of the small error interval and piecewise boundaries, and reducing nonlinear gain abrupt changes, disturbance estimation chattering, and q-axis reference current fluctuations. Finally, the disturbance estimation results from the two stages are superimposed and fed forward compensation is performed. Combined with linear state error feedback, torque current commands are generated to achieve rapid disturbance recovery and high-precision position control of the permanent magnet synchronous motor under load abrupt changes. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other embodiments can be obtained from these drawings without creative effort.

[0016] Figure 1The first overall structural diagram of the strategy block diagram of the active disturbance rejection position control method for permanent magnet synchronous motors based on an improved extended state observer is shown. Figure 2 The second overall structural diagram shows the strategy block diagram of the active disturbance rejection position control method for permanent magnet synchronous motors based on an improved extended state observer; Figure 3 Position tracking curves and position tracking error curves of permanent magnet synchronous motors under no-load conditions, using a three-closed-loop PI control strategy and a CL-NLADRC control strategy; Figure 4 The permanent magnet synchronous motor starts under no-load conditions under sinusoidal position command, and when 50% of the rated load (0.15 N·m) is suddenly applied at t=0.5"s, the position tracking curve and position tracking error curve obtained by using the three closed-loop PI control strategy and CL-NLADRC control strategy are shown. Figure 5 The position tracking curve and position tracking error curve are obtained by using a three-closed-loop PI control strategy and a CL-NLADRC control strategy to start the permanent magnet synchronous motor under no-load conditions under a sinusoidal position command and to suddenly apply a rated load of 0.3 N·m at t=0.5"s". Detailed Implementation

[0017] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0018] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0019] To address the shortcomings of existing technologies, this invention provides a method for active disturbance rejection (ADR) position control of a permanent magnet synchronous motor (PMSM) for mobile robots based on an improved cascaded extended state observer. An improved cascaded linear-nonlinear ADRC (CL-NLADRC) structure is designed using a cascaded extended state observer structure, reducing the high-frequency chattering problem inherent in traditional nonlinear error functions. The front stage employs a linear extended state observer (LESO) for stable observation of motor position, speed, and overall lumped disturbances; the rear stage uses an improved NLESO for secondary observation of residual disturbances that the front-stage observer failed to accurately estimate. This achieves high-precision motor position tracking and improves the system's overall suppression capability against large load disturbances, parameter changes, and small disturbance residuals.

[0020] To facilitate understanding of the technical objectives, implementation schemes, and advantages of this invention, the technical content of this invention will now be described in detail with reference to relevant accompanying drawings and examples. The main parameters of the motor used in this invention are listed in the table below. The implementation steps and working process of the control strategy are described in detail below.

[0021] ; This invention preferably employs a surface-mounted permanent magnet synchronous motor, and uses... The vector control method is used. In the synchronous rotating coordinate system, the position control model of the permanent magnet synchronous motor is as follows: ; ; ; ; In the formula The total moment of inertia of the motor and load referred to the motor shaft ( ); The coefficient of viscous friction ( ); For load torque ( ); This includes cogging torque, Coulomb friction, mechanical clearance, and other unmodeled mechanical disturbances. The mechanical angular position (rad); The mechanical angular velocity (rad / s); for d Shaft current (A); for q Shaft current (A); for d Shaft voltage (V); for q Shaft voltage (V); For permanent magnet flux linkage (Wb); Stator resistance (Ω); For stator inductance (H); It is an extreme logarithm. It is the q-axis inductance; It is the d-axis inductance; Electromagnetic torque (N·m) is the driving torque generated by the motor.

[0022] Combining these equations, we obtain the second-order dynamic equation for the mechanical angular position: ; in, Let be the mechanical angular acceleration (rad / s²), which is the second derivative of the mechanical angular position with respect to time. It is a polar logarithm (dimensionless). Note: The previous section used... , here written as Both have the same meaning: the number of magnetic pole pairs of the motor rotor. It represents the mechanical angular velocity (rad / s).

[0023] Define the actual gain from current to mechanical angular acceleration. for: ; Considering current loop tracking error, permanent magnet flux variation, rotational inertia variation, load torque variation, friction, and unmodeled dynamics, the second-order dynamic equation for the mechanical angular position can be rewritten in the standard form of active disturbance rejection control: ; in, The total disturbance represents the sum of all uncertainties and known dynamics both inside and outside the system. Set the q-axis current value (command value).

[0024] As can be seen from the above, lumped disturbances include not only external load torque, but also friction, parameter perturbations, current tracking errors, inverter nonlinearity, and unmodeled mechanical disturbances. Therefore, this invention does not require the separate establishment of precise mathematical models for each of these disturbances, but instead utilizes a cascaded extended state observer to uniformly observe and compensate for them.

[0025] Based on the construction method of the extended state observer in the active disturbance rejection controller, the extended state model of the position control system can be obtained as follows: ; in, The rate of change of the lumped disturbance is assumed to be bounded within the normal operating range of the motor. For second-order position objects, position, velocity, and lumped disturbance need to be estimated simultaneously; therefore, both the front-end and rear-end observers employ a third-order structure. It is the system's state variable, representing the system's output, i.e., the mechanical angular position. , It is the second state variable of the system, representing the first derivative of the system output, i.e., the mechanical angular velocity. (or ). —The third state variable of the system (extended state) represents the total disturbance of the system, that is, the extended state observer will It is treated as a new state variable for real-time estimation, therefore . , as well as These represent the derivatives of each state variable with respect to time. This is the system output, i.e., the position signal actually measured by the sensor.

[0026] A classic active disturbance rejection controller (ADRC) consists of an ESO, a tracking differentiator (TD), and a state error feedback (SEF). The CL-NLADRC structure used in this invention is shown in the diagram below. Figure 2 .

[0027] This invention employs a synthesis function based on the fastest control. A second-order nonlinear tracking differentiator, with a given position signal. First, a tracking differentiator is used to generate a smooth position reference value. and reference speed value The fastest control synthesis function is expressed as: ; In the formula, and These are the position error variable and velocity state variable of the tracking differentiator, respectively. This is the speed factor, used to adjust how fast the tracking differentiator tracks position commands; To track the discrete operation step size of the differentiator; , , , , , , and These are all intermediate variables and require no explanation. It is a symbolic function. For linear / nonlinear boundary thresholds.

[0028] The target mechanical position setpoint of the permanent magnet synchronous motor is denoted as . The tracking differentiator in the first... The position output and velocity output of each operation cycle are denoted as follows: and The discrete state update equation of the second-order nonlinear tracking differentiator is: ; By adjusting the speed factor It can change the tracking speed of the tracking differentiator for a given position signal. The larger, track The faster the speed, but the larger the size... May lead to And the q-axis reference current changes too quickly; If the value is too small, it will prolong the transition time of position commands. Parameter It is usually taken as the discrete sampling period of the position controller. For the first The target mechanical position given value (original command). For the first Reference value for the position at the next moment. For the first Reference value for the speed at the next moment. For the first shoot The function outputs a virtual acceleration command.

[0029] ESO (Electronic Disturbance Rejection) is a core component of the Active Disturbance Rejection Control System. Its function is to estimate the position, mechanical angular velocity, and lumped disturbance of the permanent magnet synchronous motor in real time based on the mechanical angular position feedback and control input. This invention employs a cascaded observation structure consisting of a front-stage third-order linear extended state observer and a rear-stage improved third-order nonlinear extended state observer. The front-stage linear extended state observer is used for preliminary observation of position, velocity, and main disturbances; the rear-stage improved nonlinear extended state observer is used for secondary observation of residual disturbances that the front-stage observer failed to accurately estimate.

[0030] Define the position observation error of the preceding linear extended state observer. for: ; in, This is the estimated mechanical angular position of the motor by the preceding observer.

[0031] The preceding third-order linearly extended state observer is represented as: ; In the formula, Location estimate The rate of change (rad / s). It is equal to the velocity estimate. Subtract error With gain The product of these factors enables real-time correction of the position estimate; Speed ​​estimate The rate of change (rad / s²). This is the pre-stage estimate of the motor's mechanical angular position; This is a preliminary estimate of the mechanical angular velocity; This is an estimate of the lumped disturbance of the main body of the system; , and These represent the error correction gains of the preceding linearly extended state observer. The bandwidth method is used to configure the gain of the preceding linearly extended state observer. Let the bandwidth of the preceding observer be... The three poles of the observer are configured at Then its characteristic polynomial is: ; Where s is the complex frequency variable in the Laplace transform.

[0032] Therefore, the gain of the pre-stage observer is: ; To further estimate the perturbation observation residuals of the preceding linear extended state observer, this invention sets up a subsequent third-order nonlinear extended state observer. The subsequent position observation error is defined. for: ; in, This is the estimated value of the mechanical angular position of the motor by the subsequent observer.

[0033] The subsequent third-order nonlinear extended state observer is represented as ; In the formula, This is an estimate of the angular position of the subsequent mechanical stage; This is an estimate of the angular velocity of the subsequent mechanical stage; This is an estimate of the residual perturbation of the preceding extended state observer; , and For the gain of the subsequent nonlinear extended state observer; , and It is a non-linear exponent; The small error interval of the nonlinear function; This is a nonlinear error function. Location estimate The rate of change (rad / s). Speed ​​estimate The rate of change (rad / s²). For the remaining disturbance estimate The rate of change (rad / s³).

[0034] The gain of the subsequent improved nonlinear extended state observer can also be initially configured using the bandwidth method. Let the bandwidth of the subsequent observer be... Then we have: ; Traditional nonlinear extended state observers typically employ The function performs nonlinear correction for observation errors. Traditional The function is represented as: ; In the formula, This refers to the observation error of the extended state observer; It is a non-linear exponent, which usually satisfies ; These are the boundary values ​​of the linear interval with small errors. This represents the boundary value of the linear interval with small errors. When and hour, To achieve "large error, small gain" and prevent overshoot; when and hour, To achieve "medium error, appropriate gain".

[0035] Tradition The function exhibits a nonlinear characteristic of "large gain for small errors and small gain for large errors." When the error is small, a larger equivalent gain can improve the steady-state estimation accuracy of the observer; when the error is large, the power function can limit the growth rate of the error correction, preventing the control quantity from becoming too large. However, traditional... The function still has certain limitations in practical digital control systems. The first derivatives of the two segments of the function are usually discontinuous at the boundary point. When the observation error changes repeatedly near the boundary point, the equivalent gain is prone to abrupt changes, resulting in high-frequency fluctuations in the observer output.

[0036] To avoid high-frequency chattering, this invention, while retaining its characteristic of "fast correction of large-error nonlinearity," improves and enhances the function structure in the small-error range, denoted as... Specifically, within a small error range, a weighted combination of an inverse hyperbolic sine function and a sine function is introduced. The continuous, smooth, and approximately linear characteristics of the inverse hyperbolic sine function and the sine function near the origin are used to smooth out small errors. Within a large error range, a power-order nonlinear function is continued to be used to ensure the convergence speed when there are sudden load changes and rapid state changes.

[0037] ; In the formula, It is a non-linear exponent. The output value of the improved nonlinear error function. , and These are the function combination coefficients within the small error interval; The expression for the inverse hyperbolic sine function is: ; Using piecewise functions Since the function value at point A is continuous and the first derivative is continuous, the following equation is obtained: ; These conditions require that the function does not have any jumps at the breakpoints. Is the function in The function value on the left (at the end of the small error region). Is the function in The function value on the right (at the beginning of the large error region). Is the function in The value of the first derivative on the left (to ensure the slope is continuous). Is the function in The value of the first derivative on the right side.

[0038] Is the function in The function value on the negative side (requiring symmetry about the origin). Is the function in The positive and negative function values, Is the function in The derivative value on the negative side. Is the function in positive derivative The weighting coefficients are obtained by using a fitting method. and The calculation formula is: ; Replacing the fal nonlinear function in the subsequent nonlinear extended state observer with the improved smoothing nonlinear function Ifal, we obtain the improved NLESO as follows: ; The improved NLESO can maintain the fast convergence performance with large errors while improving the smoothness of the small error interval and the accuracy of residual perturbation estimation.

[0039] State Error Feedback (SEF) combines the reference state output by the tracking differentiator with the estimated state obtained by the extended state observer to generate the basic control quantity of the system. SEF can be divided into Linear State Error Feedback (LSEF) and Nonlinear State Error Feedback (NLSEF). NLSEF typically uses a nonlinear function to combine position and velocity errors. While it can change the feedback gain according to the error magnitude, it involves a nonlinear exponent, a linear interval, and multiple feedback gains, making parameter tuning complex. Furthermore, the output control signal may exhibit unsmoothness when the error changes or passes through the piecewise region of the nonlinear function, leading to fluctuations and oscillations in the q-axis reference current. In contrast, LSEF uses a linearly weighted combination of position and velocity errors, which is more conducive to parameter tuning of the permanent magnet synchronous motor control system of the mobile robot. Therefore, this invention chooses LSEF to generate the basic control quantity and combines it with the total disturbance estimate output by the cascaded extended state observer for compensation. Its expression is: ; formula, and These are the position error feedback gain and the velocity error feedback gain, respectively. The basic control variables generated for LSEF; Position tracking error (unit: rad). It represents the position reference value after smoothing by the tracking differentiator (TD). The optimal estimate of the position by the subsequent nonlinear ESO. The deviation between the two. This error is the most critical input quantity for position feedback control. This represents the velocity tracking error (unit: rad / s). It indicates the smoothed velocity reference at the output of the tracking differentiator. The optimal estimate of speed from the subsequent ESO stage. The deviation between the two. This error provides information about the system's damping. The base control quantity (in rad / s²) generated for Linear State Error Feedback (LSEF). It is essentially a virtual acceleration command, representing the "desired acceleration" to be applied based solely on position and velocity errors without considering disturbance compensation.

[0040] The strategy block diagram of the active disturbance rejection position control method for permanent magnet synchronous motors based on an improved extended state observer is shown below. Figure 1 First, send the target mechanical position command. The input tracking differentiator (TD) performs smoothing planning on abrupt position commands using the fastest control synthesis function to obtain smoothed position reference values. and reference mechanical angular velocity Secondly, the encoder acquires the actual mechanical angular position of the permanent magnet synchronous motor and inputs the position feedback signal into the front-stage linear extended state observer (LESO) and the rear-stage improved nonlinear extended state observer (NLESO). The front-stage LESO performs preliminary estimations of the motor position, mechanical angular velocity, and overall lumped disturbance, obtaining disturbance estimates. ; then, As a known perturbation input, the NLESO stage is improved, and an improved smoothing nonlinear function is utilized. After correcting for observation errors, the estimated mechanical angular position is obtained. Estimated mechanical angular velocity and the estimated residual disturbance of the preceding stage Linear State Error Feedback (LSEF) is based on and Calculate the basic control quantity, and simultaneously add the estimated values ​​of the preceding main disturbance and the estimated values ​​of the subsequent residual disturbance to obtain the total disturbance estimate. And feedforward compensation from the basic control quantity, and then through The q-axis reference current was obtained by conversion. At the same time, set the d-axis reference current Finally, the difference between the d-axis reference current and the actual d-axis current obtained after coordinate transformation is calculated, and the difference is used to obtain the d-axis reference voltage through two current proportional-integral controllers. Then, six drive signals from PWM1 to PWM6 are generated through inverse Park transformation and space vector pulse width modulation (SVPWM) to control the three-phase inverter to drive the permanent magnet synchronous motor.

[0041] The above theory will be verified through simulation experiments: The given target position instruction is ,like Figure 3 The figures show (a) the position tracking curve and (b) the position tracking error curve of a permanent magnet synchronous motor under no-load conditions, obtained using a three-loop PI control strategy and a CL-NLADRC control strategy. As can be seen from the figures, both control methods can track the position command, but the three-loop PI control exhibits significant phase lag, with a maximum tracking error of approximately 0.6 rad. The CL-NLADRC control curve shows a higher degree of overlap with the given curve, with a maximum error of approximately 0.15 rad, demonstrating better dynamic tracking accuracy.

[0042] Figure 4 To enable the permanent magnet synchronous motor to start under no-load conditions under a sinusoidal position command, and in When a 50% increase in rated load (0.15 N·m) is suddenly applied, the position tracking curves (a) and position tracking error curves (b) are obtained using a three-loop PI control strategy and a CL-NLADRC control strategy. After the sudden load change, the position errors of both control methods show a short-term increase. The peak error of the three-loop PI control is approximately 0.43 rad, and the recovery process is slower. The peak error of the CL-NLADRC control is approximately 0.23 rad, and it can recover to the original tracking state more quickly, indicating that it has a stronger load disturbance suppression capability.

[0043] Figure 5 To enable the permanent magnet synchronous motor to start under no-load conditions under a sinusoidal position command, and in When a rated load of 0.3 N·m is suddenly applied, the position tracking curves (a) and (b) position tracking error curves are obtained using a three-loop PI control strategy and a CL-NLADRC control strategy. As the load amplitude increases, the position deviation of the three-loop PI control increases significantly, with an instantaneous peak error of approximately 0.88 rad and a relatively long recovery time. The peak error of the CL-NLADRC control strategy is approximately 0.58 rad, and the error decays faster after a sudden load change. The results show that the proposed control method still exhibits good tracking accuracy and robustness under rated load impact. In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or components can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the various components shown or discussed can be through some interfaces, and the indirect coupling or communication connection between devices or units can be electrical, mechanical, or other forms.

[0044] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units. They may be located in one place or distributed across multiple network units. Some or all of the units may be selected to achieve the purpose of this embodiment according to actual needs.

[0045] In addition, in the various embodiments of the present invention, each functional unit can be integrated into one processing unit, or each unit can be a separate unit, or two or more units can be integrated into one unit; the integrated unit can be implemented in hardware or in the form of hardware plus software functional units.

[0046] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0047] Alternatively, if the integrated units of this invention are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this invention, or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROM, RAM, magnetic disks, or optical disks.

[0048] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention 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 the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for self-disturbance rejection position control of a servo motor for a mobile robot, characterized in that, Includes the following steps: Using a vector control method with zero q-axis current, a position control model for a permanent magnet synchronous motor is constructed in a synchronous rotating coordinate system. An extended state model of the position control system is constructed by combining current loop tracking error, permanent magnet flux variation, rotational inertia variation, load torque variation, friction, and unmodeled dynamics. Construct the fastest control synthesis function, use the position output and velocity output of the tracking differentiator in the kth operation cycle to construct the discrete state update equation, and use the discrete state update equation to change the tracking speed of the tracking differentiator to the given position signal; A cascaded observation structure is constructed by using a front-stage third-order linear extended state observer and a rear-stage third-order improved nonlinear extended state observer. The front-stage third-order linear extended state observer is used to conduct preliminary observations of position, velocity and main disturbance. The residual disturbance that the preceding third-order linear extended state observer failed to accurately estimate was observed by using the improved third-order nonlinear extended state observer. The reference state output by the tracking differentiator is combined with the estimated state obtained by the extended state observer using state error feedback to generate the basic control quantity of the system. The LSEF is selected to generate the basic control quantity, and the total disturbance estimate output by the cascaded extended state observer is used for compensation.

2. The self-disturbance rejection position control method for a servo motor of a mobile robot according to claim 1, characterized in that, A vector control method with zero q-axis current is adopted. A position control model for the permanent magnet synchronous motor is constructed in a synchronous rotating coordinate system. An extended state model of the position control system is built by incorporating current loop tracking error, permanent magnet flux variation, moment of inertia variation, load torque variation, friction, and unmodeled dynamics. Specifically: Using a vector control method with zero q-axis current, a position control model for a permanent magnet synchronous motor is constructed in a synchronous rotating coordinate system. Based on the position control model of the permanent magnet synchronous motor, the second-order dynamic equation of the mechanical angular position is obtained. Define the actual gain from current to mechanical angular acceleration, and reconstruct the second-order dynamic equation of the mechanical angular position by combining the current loop tracking error, permanent magnet flux variation, rotational inertia variation, load torque variation, friction, and unmodeled dynamics. By reconstruction, the second-order dynamic equation of the reconstructed mechanical angular position is obtained, and the extended state model of the position control system is constructed by combining the actual gain from the current to the mechanical angular acceleration.

3. The self-disturbance rejection position control method for a servo motor of a mobile robot according to claim 1, characterized in that, Construct the fastest control synthesis function, and use the position output and velocity output of the tracking differentiator in the kth operation cycle to build a discrete state update equation. Use this discrete state update equation to change the tracking speed of the tracking differentiator to the given position signal. Specifically, this includes: The fastest control synthesis function is constructed, and a second-order nonlinear tracking differentiator based on the fastest control synthesis function fhan is adopted. The position given signal first passes through the tracking differentiator to generate smooth position reference value and reference velocity value. The position output and velocity output in the kth operation cycle are calculated using a tracking differentiator. Based on the position output and velocity output in the kth operation cycle, the discrete state update equation of the second-order nonlinear tracking differentiator is constructed. Based on the discrete state update equation of the second-order nonlinear tracking differentiator, the tracking speed of the tracking differentiator to the given position signal is changed by adjusting the speed factor.

4. The self-disturbance rejection position control method for a servo motor of a mobile robot according to claim 1, characterized in that, Preliminary observations of position, velocity, and main disturbances are conducted using a pre-stage third-order linear extended state observer, specifically including: Define the position observation error of the preceding third-order linear extended state observer, and define the preceding third-order linear extended state observer and set the bandwidth of the preceding observer. The three poles of the observer are configured in preset positions to generate a pre-characteristic polynomial, and the gain of the pre-observer is obtained based on the characteristic polynomial.

5. The self-disturbance rejection position control method for a servo motor of a mobile robot according to claim 1, characterized in that, The residual perturbation that the preceding third-order linear extended state observer failed to accurately estimate is observed using a subsequent third-order improved nonlinear extended state observer. Specifically: Define the position observation error of the subsequent stage, and at the same time, construct the third-order improved nonlinear extended state observer of the subsequent stage, set the bandwidth of the preceding stage observer, and use the fal function to perform nonlinear correction on the observation error; In the range below the preset error threshold, a weighted combination of inverse hyperbolic sine function and sine function is introduced. The characteristics of continuous, smooth and approximately linear near the origin of inverse hyperbolic sine function and sine function are utilized to smooth the error. If the error threshold is exceeded, continue to use the power nonlinear function. Utilize the continuity of the piecewise function with the preset function value and the first derivative to obtain the equation. Then, use the fitting method to solve for the weight coefficients. By replacing the fal nonlinear function in the subsequent nonlinear extended state observer with the improved smooth nonlinear function Ifal, the improved NLESO is obtained.

6. The self-disturbance rejection position control method for a servo motor of a mobile robot according to claim 1, characterized in that, The reference state output from the tracking differentiator is combined with the estimated state obtained from the extended state observer using state error feedback to generate the system's basic control input. The LSEF is selected to generate the basic control input, which is then compensated for using the total disturbance estimate output from the cascaded extended state observer. Specifically, this includes: By combining the reference state output by the tracking differentiator with the estimated state obtained by the extended state observer using state error feedback, the basic control quantity of the system is generated. The target mechanical position command is input into the tracking differentiator, and the sudden position command is smoothed through the fastest control synthesis function to obtain the smoothed position reference value and the reference mechanical angular velocity. The actual mechanical angular position of the permanent magnet synchronous motor is acquired, and the position feedback signal is input into the front-stage third-order linear extended state observer and the rear-stage third-order improved nonlinear extended state observer; The motor position, mechanical angular velocity, and main body lumped disturbance are initially estimated by using a front-stage third-order linear extended state observer and a rear-stage third-order improved nonlinear extended state observer to obtain disturbance estimates, and compensation is performed based on the disturbance estimates.

7. A method for self-disturbance rejection position control of a servo motor for a mobile robot according to claim 6, characterized in that, Compensation is performed based on the estimated disturbance value, specifically including: The disturbance estimate is used as the known disturbance input to improve the NLESO stage, and the observation error is corrected by the improved smoothing nonlinear function Ifal, to further obtain the mechanical angular position estimate, mechanical angular velocity estimate and the previous stage residual disturbance estimate; The basic control quantity is calculated using linear state error feedback. At the same time, the estimated value of the main disturbance of the preceding stage is superimposed with the estimated value of the residual disturbance of the following stage to obtain the total disturbance estimate, which is then fed forward from the basic control quantity for compensation. The q-axis reference current is then obtained through conversion, while the d-axis reference current is set to 0. The difference between the d-axis and q-axis reference currents and the actual d-axis and q-axis currents obtained through coordinate transformation is calculated, and the d-axis and q-axis reference voltages are obtained through two current proportional-integral controllers. Six drive signals, PWM1 to PWM6, are generated by inverse Park transform and space vector pulse width modulation to control the three-phase inverter to drive the permanent magnet synchronous motor.

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