Servo system control method based on frequency domain self-tuning and linear active disturbance rejection

Abstract

The invention discloses a servo system control method based on frequency domain self-tuning and linear active disturbance rejection, and relates to the technical field of servo control and motor control. Comprising the following steps: based on a mathematical model of a permanent magnet synchronous motor, establishing a double-inertia model suitable for a large-inertia servo system, and constructing an equivalent mathematical expression of an electrical and mechanical transmission system; in a three-stage cascade control architecture composed of a current loop, a speed loop and a position loop, the current loop is used for current adjustment, the speed loop is used for dynamic response adjustment, and the position loop is used for displacement target tracking. Based on a frequency domain performance index and a rule method, PI controller parameters of a speed loop and a position loop are set respectively, and the frequency domain index comprises an open-loop cut-off frequency and a phase margin; and establishing a frequency domain equivalent mapping relation between the PI controller and the LADRC controller. The method has the advantages that the method does not depend on accurate modeling and manual interference, automatic parameter setting can be achieved, non-overshoot dynamic response is achieved, and the remarkable disturbance suppression capacity is shown.

Description

Technical Field

[0001] This invention relates to the field of servo control and motor control technology, and to a servo system control method based on frequency domain self-tuning and linear active disturbance rejection, specifically to a control method for self-tuning and linear active disturbance rejection control of a permanent magnet synchronous motor suitable for large inertia servo systems. Background Technology

[0002] Large-inertia servo systems have become a hot topic in control technology research due to their crucial role in complex load applications such as rocket artillery and tank gun control systems. However, in actual operation, large-inertia servo systems are often accompanied by complex factors such as significant load disturbances, dynamic changes in system inertia, strong coupling nonlinearity, and fluctuations in the external environment. Traditional PID (Proportional Integral Derivative) controllers, due to their high dependence on the accuracy of the controlled system model, reliance on manual experience for parameter tuning, and lack of real-time suppression capability for disturbance changes, struggle to achieve stable, accurate, efficient, and high-dynamic-performance control under such complex conditions.

[0003] Linear Active Disturbance Rejection Control (LADRC) has gained widespread attention in the field of motor control in recent years due to its advantages such as simple structure, strong robustness, and no need for precise modeling of the controlled object. This control strategy estimates the system state and total disturbance in real time through an Extended State Observer (LESO) and constructs a composite control law by combining error feedback, exhibiting good disturbance suppression capability and tracking performance. However, in practical engineering, the core parameters of LADRC still mainly rely on empirical settings, and its key parameters such as control bandwidth and observer bandwidth lack systematic tuning methods. These shortcomings severely restrict its widespread application in industrial scenarios.

[0004] Therefore, how to establish a servo system control method suitable for large inertia servo systems by combining frequency domain control design theory without increasing the modeling burden, and to achieve efficient deployment and robust operation of LADRC controllers, has become a key technical problem that urgently needs to be solved in this field. Summary of the Invention

[0005] The primary objective of this invention is to provide a control method for large inertia servo systems based on frequency domain self-tuning and linear active disturbance rejection, which is efficient, has high tuning efficiency, and excellent disturbance rejection performance without relying on precise modeling. This method addresses the problems in large inertia servo control systems where traditional PID controllers struggle to adapt to disturbance changes, and linear active disturbance rejection controller parameter tuning relies on experience.

[0006] Another objective of this invention is to provide a control system for a servo system control method based on frequency domain self-tuning and linear active disturbance rejection, which can ensure the full realization of the technical effects of the servo system control method.

[0007] The primary objective of this invention is to provide a servo system control method based on frequency domain self-tuning and linear active disturbance rejection, comprising the following steps:

[0008] Step 1: Based on the mathematical model of the permanent magnet synchronous motor, establish a dual-inertia model suitable for large inertia servo systems, and construct the equivalent mathematical expression of the electrical and mechanical transmission system.

[0009] Step 2: In the three-level cascade control architecture consisting of a current loop, a speed loop, and a position loop, the current loop is set for current regulation, the speed loop for dynamic response regulation, and the position loop for displacement target tracking.

[0010] Step 3: Based on frequency domain performance indicators and rule-based methods, tune the PI controller parameters for the speed loop and position loop respectively. Frequency domain indicators include open-loop cutoff frequency and phase margin.

[0011] Step four: Establish the frequency domain equivalent mapping relationship between the PI controller and the LADRC controller, and convert the tuned PI controller parameters into key parameters of the LADRC controller, including the controller bandwidth ω. c With observer bandwidth ω o And the system model parameter b0;

[0012] Step 5: Deploy the configured LADRC controller to the speed loop and position loop to control the operation of the servo system under disturbance and load change conditions;

[0013] In a specific embodiment of the present invention, in step one, considering the dual inertia coupling and transmission elasticity effect between the motor side and the load side, a simplified dual inertia model is used to describe the dynamic characteristics of the system; the input variable is the current signal, and the output is the displacement signal.

[0014] In another specific embodiment of the present invention, in step two, the speed loop and the position loop adopt an LADRC controller. The speed loop adjusts the motor speed and receives the desired speed command output by the position loop to form a coordinated control of the inner and outer loops. The position loop outputs the desired speed according to the displacement error to realize displacement control.

[0015] In another specific embodiment of the present invention, in step three, the speed loop adopts the frequency margin method, and the tuning target of the speed loop PI controller is the open-loop cutoff frequency, which is set in the range of 1 / 10 to 1 / 5 of the current loop bandwidth, the phase margin is controlled in the range of 45° to 60°, and the position loop PI controller parameters are tuned using the overshoot-free Ziegler-Nichols rule method.

[0016] In another specific embodiment of the present invention, in step four, the bandwidth ω of the velocity loop LADRC observer... o Set as controller bandwidth ω c γ v times, γ v The value ranges from 3 to 8. The equivalent mapping relationship of the velocity loop in the frequency domain is constructed based on the principle of low-frequency approximation in the frequency domain as ω. o =k I (2γ v +1) / (k p ·γ v ), ω c =γ v ω o The position loop frequency domain equivalent mapping relationship is based on the maximum phase compensation design principle. The LADRC observer bandwidth is set according to the target open loop cutoff frequency, and the state feedback parameters are calculated in combination with the bandwidth ratio relationship to complete the parameter mapping between LADRC controllers.

[0017] In another specific embodiment of the present invention, the position loop LADRC controller in step four is tuned using the maximum phase compensation design principle, and ω is selected. c,p With ω o,p Bandwidth ratio γ p The value is 0.25, and ω is taken as ω. f =50Hz, LADRC ω after SDMS-DE optimization o,p = 618.89 rad / s, ω c,p =157.08 rad / s, while the ω of DMC-LADRC o,p =603.94 rad / s, ω c,p =161.58rad / s, and position loop simulation experiments were conducted using the above self-tuning parameters.

[0018] In a further specific embodiment of the present invention, in step five, the LADRC controller adopts a first-order extended state observer structure. This first-order extended state observer estimates the disturbance components in the system in real time and feeds them back to the control output channel for compensation, thereby achieving online disturbance suppression.

[0019] Another objective of this invention is achieved as follows: a control system for a servo system control method based on frequency domain self-tuning and linear active disturbance rejection includes a permanent magnet synchronous motor, a displacement sensor, a speed calculation module, and a motor controller. The permanent magnet synchronous motor provides driving torque to the system, and its output shaft is connected to a reducer. The displacement sensor measures the displacement of the servo motor in real time, serving as a control feedback signal. The speed calculation module estimates the speed by differentiating or filtering the displacement signal, which is used as the speed loop feedback input. The motor controller includes a main control module, a power drive module, a signal sampling and processing module, and a communication module. These modules work together to complete motor control and data interaction functions.

[0020] Compared with existing technologies, this invention, due to its aforementioned structure, offers the following advantages: First, it proposes a LADRC parameter tuning method based on frequency domain performance indicators, avoiding the drawback of relying on manual experience for traditional LADRC bandwidth setting and improving the standardization and engineering consistency of controller parameter design. Second, it constructs a frequency domain mapping relationship from PI controller parameters to LADRC controller parameters, enabling the automatic derivation of key LADRC controller parameters from tuned PI parameters, thus achieving rapid controller configuration and automated deployment. Third, by constructing a three-closed-loop decoupled control structure, the LADRC controller is deployed in the velocity loop and position loop respectively, effectively enhancing the system's adaptability to disturbances and structural changes, and improving the robustness and dynamic performance of the large-inertia servo control system. Fourth, the proposed tuning and mapping method does not rely on online modeling or self-learning processes; the controller structure is simple, the deployment process is clear, and it can be directly applied to industrial scenarios with high requirements for response speed and accuracy, such as servo control systems. Fifth, the tuning process has programmable implementation capabilities, is adaptable to embedded platforms, industrial controllers, and other environments, and possesses good portability and mass production capabilities. Attached Figure Description

[0021] Figure 1 This is a flowchart of the method of the present invention;

[0022] Figure 2 This is a schematic diagram of the three-closed-loop control structure of a servo control system.

[0023] Figure 3 Simulation diagrams of the step response of the LADRC velocity loop under different parameters;

[0024] Figure 4 This is a comparison chart of the position response of the servo system under load disturbance.

[0025] Figure 5 A comparison chart of the response performance of the PI controller and the LADRC controller under the speed loop self-tuning parameters;

[0026] Figure 6aThe difference between PI parameters and LADRC parameters is γ v Frequency domain performance comparison chart;

[0027] Figure 6b The observer bandwidth ω between the PI parameters and the LADRC parameters o Frequency domain performance comparison chart;

[0028] Figure 7a A graph showing the position of the LADRC controller under external disturbances;

[0029] Figure 7b This is a graph showing the position error of the LADRC controller under external disturbances.

[0030] Figure 8a A position comparison curve of the servo system under varying load inertia conditions;

[0031] Figure 8b This is a position error curve of the servo system under varying load inertia conditions.

[0032] Figure 8c This is a graph showing the total position disturbance of the servo system under varying load inertia conditions.

[0033] Figure 8d A speed comparison curve of the servo system under varying load inertia conditions;

[0034] Figure 9 The equivalent transfer function block diagram for a first-order LADRC is shown. Detailed Implementation

[0035] The specific embodiments of the present invention are described in detail below with reference to the accompanying drawings. However, the description of the embodiments is not a limitation on the technical solution. Any formal but not substantive changes made based on the concept of the present invention should be considered within the scope of protection of the present invention.

[0036] In the following description, all directional (or orientational) concepts involving up, down, left, right, front, and back refer to the position of the figure being described, and are intended to facilitate public understanding. Therefore, they should not be construed as a special limitation on the technical solution provided by this invention.

[0037] This invention focuses on the application background of large-inertia servo systems driven by permanent magnet synchronous motors (PMSMs). Addressing tuning and disturbance rejection control strategies, it proposes a servo system control method based on frequency domain self-tuning and linear active disturbance rejection. By constructing a mathematical model of the PMSM, a dual-inertia model suitable for large-inertia servo systems is established, and the system's disturbance characteristics are analyzed in depth. Simultaneously, the fundamental classical PID algorithm and the LADRC algorithm with excellent disturbance rejection capabilities are analyzed, constructing a three-closed-loop control structure for the servo system. The phase margin method and the overshoot-free ZN method are used for preliminary PID parameter tuning of the speed and position loops, respectively. Finally, the LADRC control parameters are self-tuned using mapping relationships and the maximum phase compensation method, overcoming the drawback of LADRC tuning's heavy reliance on manual parameter adjustment and achieving high-precision, robust displacement control. The specific steps of this invention are as follows.

[0038] Step 1: Constructing the System Model: Based on the mathematical model of the permanent magnet synchronous motor and combined with the mechanical structure characteristics of the servo system, an electrical and mechanical servo system model suitable for large inertia servo systems is established, considering the effects of dual inertia coupling and flexible transmission. The model analyzes common nonlinear disturbance characteristics in the system, such as backlash effect, friction torque, and flexible transmission, and constructs an equivalent mathematical expression for the electrical and mechanical transmission system.

[0039] The control method described in this invention is applied to the control scenario of a large inertia servo system, forming a high-performance control system for a large inertia servo system operating under complex disturbances. This control system comprises four parts: a permanent magnet synchronous motor, a displacement sensor, a speed calculation module, and a motor controller. The permanent magnet synchronous motor provides driving torque to the system; its output shaft is connected to a reducer, and the motor rotation is converted into linear displacement of the push rod through the reducer. The displacement sensor measures the real-time displacement of the servo motor, serving as the control feedback signal. The speed calculation module estimates the speed by differentiating or filtering the displacement signal, which is used as the speed loop feedback input. The motor controller consists of a main control module, a power drive module, a signal sampling and processing module, an overcurrent protection module, a power management module, and a communication module. These modules work together to complete motor control and data interaction functions.

[0040] The control system is internally constructed as a three-closed-loop cascade structure, see Figure 2The system consists of three layers: the innermost layer is the current loop, which directly controls the motor current to achieve electromagnetic torque regulation; the middle layer is the speed loop, used to adjust the motor speed response performance; and the outermost layer is the position loop, which achieves closed-loop tracking of the final displacement. Both the speed and position loops are equipped with Linear Active Disturbance Rejection Controllers (LADRCs) based on Extended State Observers, providing online disturbance estimation and compensation. The controller outputs control signals to the motor driver via a PWM module, forming a complete closed-loop execution link. This system has a compact structure and clear connections, making it suitable for high-inertia servo system control scenarios and also applicable to other industrial execution tasks requiring high-thrust servo control. The system integrates torque disturbance factors such as backlash, Coulomb friction in friction torque, and elastic torque caused by flexible transmission into a unified load disturbance torque model for the servo system. Furthermore, when analyzing disturbances caused by external loads, the complexity of the internal transmission structure of the servo system is simplified, treating the entire system as a rigid body motion model. The simplified motion equations of the servo system are as follows:

[0041]

[0042] Where J = J m +J l B represents the total inertia of the servo system. m T is the viscous damping coefficient. m T is the output torque of the motor. l Let d be the load disturbance torque, and d be the unmodeled disturbance term of the system. Let ω be the angular acceleration and ω be the mechanical angular velocity. In the specific modeling process, the motor and load parameters are given based on the actual application environment. This model serves as the basis for controller tuning and deployment, ensuring that the objects of subsequent parameter calculations and control verification are consistent, realistic, and reproducible.

[0043] Step 2: Design a dual-loop control structure for the servo control system. In the three-loop architecture, a current loop is set for current regulation, a speed loop for dynamic response regulation, and a position loop for displacement target tracking. The speed loop and position loop adopt LADRC controllers to achieve precise speed regulation and high-precision displacement control.

[0044] The servo outer-loop control system employed in this invention is a relay-based dual-closed-loop structure, comprising a speed control loop and a position control loop for hierarchical adjustment of motor speed and push rod displacement, achieving the closed-loop control objective of guide vane angle. The two controllers employ a cascaded nested structure, with the speed loop receiving output commands from the position loop as a reference, exhibiting excellent hierarchical control characteristics and system response adjustability.

[0045] In the control structure, the innermost layer is the current control loop, which uses a proportional-integral (PI) controller to quickly adjust the q-axis current of the motor. Since the dynamics of the current loop are dominated by purely electrical parameters, it is less affected by mechanical load disturbances, and its bandwidth is much higher than that of the speed loop and position loop. Generally, it does not need to perform self-tuning for external disturbances or load changes. Therefore, this invention does not introduce an additional parameter adjustment mechanism for the current loop.

[0046] In the design of the velocity loop and position loop controller, this invention uses the LADRC algorithm. The motion state equation of PMSM in equation (1) is rewritten as:

[0047]

[0048] in, B is angular acceleration. m K is the coefficient of viscous friction. T i is the torque coefficient. q Let J be the q-axis current and J be the moment of inertia. The disturbance term B caused by viscous friction... m ω m Load torque disturbance term T L And the disturbance term d that is not modeled in the system is uniformly denoted as the total external disturbance f of the system:

[0049]

[0050] The above formula can also be rewritten as:

[0051]

[0052] Wherein, the system model parameter b0 = K T / J can be calculated by identifying parameters and motor electrical parameters. Define the state variable x1 = ω. m System input Let the total disturbance f be denoted as the extended state variable x2. Since f is a time-varying disturbance, assume... h can be estimated using the observer, therefore the state-space equation of the system is:

[0053]

[0054] The matrix form of the permanent magnet synchronous motor model is obtained:

[0055]

[0056] in, C = [1 0].

[0057] Based on the above model, a second-order LESO is designed. The LESO input signal is the measured speed ω of the motor. m Output control quantity u = iq .

[0058] LESO estimates the system states x1 and x2 in real time based on the input signals and outputs disturbance estimates for control loop compensation.

[0059]

[0060] Where z1 is the observed rotational speed, z2 is the estimated total disturbance, and β1 and β2 are the observer error feedback gains. Using the bandwidth method, the observer parameters are designed as follows:

[0061] β1=2ω o ,β2=ω o 2 (8)

[0062] The linear control law can be designed as follows:

[0063]

[0064] Where k1 is the control gain, ω * For a given speed,

[0065] The disturbance compensation amount z2 is limited:

[0066]

[0067] In practical engineering, to meet the requirements of digital control system implementation, a bilinear transform s = (2 / T) is adopted. s The continuous-time model of LESO is discretized using (z-1) / (z+1). Where T... s Let z be the sampling time, and z be the discrete-time variable. After performing a bilinear transformation on LESO's continuous-time model, its discrete-time model can be obtained:

[0068]

[0069] For the position ring, based on the rotor mechanical angle θ m and mechanical angular velocity ω m Relationship Standardize it and introduce unmodeled perturbation factor d p The result was:

[0070]

[0071] Where, θ base b is the base value of the mechanical angle. p =1 / θ base For the position loop model parameters, f p The total disturbance of the position loop includes unmodeled disturbances such as quantization error, measurement error, tracking error, and backlash.

[0072] Choose θ p As the system state x1, the total position loop disturbance f p As the extended state x2, the state equation can be expressed as:

[0073]

[0074] The corresponding second-order LESO is:

[0075]

[0076] The error-based feedback control law is:

[0077]

[0078] in For feedback error, k 1,p The linear control gain of the position loop is also determined by the position loop controller bandwidth ω. cp Tuning, i.e., satisfying k 1,p =ω cp .

[0079] Step 3, PI parameter tuning: The PI controller parameters for the speed loop and position loop are tuned based on the frequency domain performance indicators. The frequency domain indicators include the open-loop cutoff frequency and phase margin. The frequency margin method is used for the speed loop, and the overshoot-free Ziegler-Nichols method is used for the position loop.

[0080] In this invention, controller parameter tuning is based on an understanding of the system's frequency response characteristics. The system model can be obtained through any form of offline identification method, such as existing techniques like relay feedback. This modeling process, as a prerequisite for controller design, does not constitute the innovative content of this invention.

[0081] In step three, frequency response analysis is performed on the system model. Based on the offline identification results, the PI parameters of the speed loop are tuned according to the desired open-loop cutoff frequency and phase margin. In the speed loop controller design, the frequency domain phase margin method is used for PI parameter tuning. The speed loop adopts a traditional PI controller structure. By analyzing the intersection of the system's open-loop amplitude-frequency response and the unit circle, the system's open-loop cutoff frequency ω is set. vc The two core indicators, phase margin γ, serve as the design basis for dynamic performance and stability margin. In the design, the system cutoff frequency is defined by the unity-gain intersection, and the system phase margin is defined as the angle between the frequency response phase and the negative real axis at that frequency. Using complex plane trigonometric relationships, the proportional gain K can be directly calculated. vp With integral gain K vi :

[0082]

[0083] To ensure system speed and engineering stability, the speed loop cutoff frequency is recommended to be set between 1 / 10 and 1 / 5 of the current loop bandwidth. For servo systems, a reference design range of 60Hz to 240Hz is typically chosen, with a phase margin recommended to be controlled between 45° and 60° to achieve better noise immunity and dynamic tracking performance. This design method has a clear theoretical basis, high tuning efficiency, and is suitable for industrial mass deployment scenarios.

[0084] In the design of the position loop controller, considering that the bandwidth of the velocity loop is much higher than the open-loop frequency of the position loop, the inner velocity loop can be approximated as a first-order inertial element, thus simplifying the design model of the position loop. Based on this first-order approximation model, the overshoot-free tuning strategy in the Ziegler-Nichols method is used to configure the parameters of the position loop PI controller. The position gain is tuned in one step through relay experiments, enabling the control system to meet steady-state accuracy requirements while also considering dynamic response characteristics. This tuning process does not rely on trial and error, and the experiment can be automatically performed according to preset rules, exhibiting good consistency and repeatability. Specifically, a critical response experiment is conducted by constructing a relay feedback loop outside the position loop to obtain the critical oscillation period and gain parameters of the system. Based on this, the Tyreus-Luben overshoot-free tuning formula is used to calculate the proportional gain K of the position loop. pp :

[0085]

[0086] Among them, K pc The critical gain of the ZN method ensures that the system maintains rapid adjustment capability without overshoot, thus meeting the high stability requirements of the servo control system.

[0087] This method features clear tuning steps and simple parameter calculation, making it suitable for displacement circuits with low modeling requirements but high control accuracy requirements. The PI controller parameters for the velocity and position loops are not used in the final deployed controller, but rather serve as the frequency domain parameter basis for subsequent LADRC design. These parameters are used to construct the observer bandwidth and feedback gain in the LADRC controller, and are key inputs to the subsequent controller mapping strategy of this invention.

[0088] Step 4: Parameter Mapping to LADRC: Establish a frequency domain equivalent mapping relationship between the PI controller and the LADRC controller. Convert the tuned PI controller parameters into key LADRC controller parameters, including the controller bandwidth ω, according to the frequency domain mapping relationship. c With observer bandwidth ω o And the system model parameter b0. The mapping relationship is ω. o =k I(2γ v +1) / (k p ·γ v ), ω c =γ v ω o .

[0089] Step four establishes an equivalent open-loop transfer function relationship between the PI controller and the LADRC in the frequency domain, constructing a mapping mechanism for deriving the core parameters of the LADRC from the tuned PI parameters. To improve the disturbance rejection capability and response stability of large-inertia servo control systems under complex operating conditions, this invention proposes a parameter mapping method for Linear Active Disturbance Rejection Controllers (LADRC) for engineering applications, based on the completion of PI controller frequency domain tuning. This method, based on frequency domain approximation, establishes the correspondence between the frequency response characteristics of the traditional PI controller and the core parameters of the LADRC controller through analysis, realizing the automatic conversion from a PI controller to an LADRC controller, which is one of the main technical innovations of this invention.

[0090] In the speed loop controller design, based on the principle of frequency response approximation, the control performance of the LADRC controller in the low-to-mid frequency range is kept equivalent to that of the original PI controller. The proportional and integral parameters of the PI controller are converted into observer bandwidth and state feedback coefficients using analytical formulas, ensuring that the system achieves good dynamic characteristics and disturbance robustness without increasing bandwidth burden. Specifically, in the speed loop design, the LADRC controller adopts a first-order extended state observer structure. The transfer function obtained from the Laplace transform of the differential equation is:

[0091]

[0092] Where b0 represents the system model parameters.

[0093] The system transfer function can be represented in the form of a block diagram, such as... Figure 9 The function C1(s) on the feedback channel in the graph can be simplified as follows:

[0094]

[0095] For a control transfer function with a structure like C1(s), it can be compared with the transfer function of a traditional PI controller, yielding the following relationship:

[0096]

[0097] Its response characteristics in the low-to-mid frequency range can be approximated as a series combination of a PI controller and an inertial element, so let C1(s)≈G c (s), the parameters are adjusted using the bandwidth method, β1=2ω o , l1=ω c And set the control rate bandwidth ω c and observer bandwidth ω o The bandwidth ratio between them is γ v , i.e., ω c =γ v ω o This approximation characteristic can then be used to further derive the control bandwidth ω in LADRC from the tuned PI parameters. c and observer bandwidth ω o parameter:

[0098]

[0099] Where k p k is the proportional gain parameter. I This is the integral gain. This invention proposes to use the control law bandwidth γ... v Set it to be between 0.2 and 1 of the observer bandwidth.

[0100] Continue organizing k p and k I From this relationship, we can obtain the system model parameter b0:

[0101]

[0102] The formalization of this parameter mapping process allows for the direct calculation of key parameters of the LADRC, such as the observer bandwidth and state feedback gain, given the PI parameters. This mapping process features an explicit expression and eliminates the need for trial and error or online optimization during tuning, significantly improving the tuning efficiency and consistency of the controller. It is particularly suitable for deployment in applications with high reliability requirements, such as large-inertia servo control systems.

[0103] In position loop design, considering that the position loop mainly adopts a proportional control structure, it is impossible to directly map PI parameters through frequency domain response. This invention proposes a design method based on the phase response characteristics of the LADRC feedback channel, using maximum phase compensation frequency alignment. The method sets the LADRC observer bandwidth according to the target open-loop cutoff frequency and calculates the state feedback parameters based on the bandwidth ratio to maximize the system's phase margin at key frequency points, enhancing disturbance suppression and system stability. This mapping process can be constructed as a set of explicit mathematical functions, possessing a clear calculation path and programmable implementation capabilities. It supports efficient automatic migration of controller parameters from traditional PID to LADRC, suitable for batch tuning and rapid iterative update requirements in engineering deployments. Specifically, by adjusting the maximum phase compensation ω of the LADRC controller... f The point is set at the expected open-loop cutoff frequency ω. po Nearby, and adjust the control rate ω c With observer ω oThe bandwidth ratio γ between p This allows for the attainment of maximum phase margin at that frequency, thereby enhancing the system's steady-state accuracy and dynamic robustness.

[0104] Ultimately, this invention realizes a control strategy for automatically tuning LADRC parameters based on frequency domain indices, suitable for large-inertia servo systems. This system uses a traditional PI controller as an intermediary, constructing a mapping relationship between velocity loop PI parameters and LADRC parameters through a frequency domain response approximation method. Combined with the maximum phase margin design principle of the position loop, it completes the entire controller parameter generation process. This method is particularly suitable for engineering environments where on-site modeling is not possible or online optimization is not feasible, and can be widely applied to systems such as hydraulic automation that require high response speed and control accuracy.

[0105] Step 5: Deploy the LADRC controller and run it: Deploy the configured LADRC controller to the speed loop and position loop, and realize disturbance estimation and compensation by extending the state observer to achieve high stability and high precision closed-loop position control of the servo motor under complex disturbance and load change conditions.

[0106] Step five involves loading the LADRC controller parameters obtained through frequency domain mapping into the controller, completing the initialization configuration of the Extended State Observer (LESO) and the state error feedback control law. During system operation, the LESO estimates the controlled object's state variables and total disturbance in real time, and the control law dynamically generates adjustment commands to drive the motor. The controller requires no online modeling or self-learning mechanism, nor does it require manual parameter tuning during runtime, maintaining a stable and rapid response under disturbances such as friction and load fluctuations. This method achieves automatic parameter design through frequency domain mapping, and with reasonable configuration of ω... c With γ v It can achieve a dynamic response with almost no overshoot, significantly improve disturbance suppression capability, and is suitable for large inertia servo control.

[0107] Based on the frequency domain tuning results, LADRC is deployed in the velocity loop and position loop respectively, constructing a three-level closed-loop structure of current loop-velocity loop-position loop. All parameters are determined through offline frequency domain analysis, eliminating the need for online model identification, self-learning, or manual tuning at runtime, thus exhibiting strong engineering applicability and replicability.

[0108] The deployed LADRC controller consists of an extended state observer and an error feedback control law. It can estimate system state variables and synthesize disturbance information in real time during system operation. Without introducing additional disturbance modeling, it can automatically compensate for non-modeled dynamic factors such as friction and load changes, thereby significantly improving the system's disturbance rejection capability and operational stability.

[0109] In its implementation, the speed loop employs a first-order extended state observer, which dynamically adjusts the motor's acceleration and deceleration behavior based on disturbance estimation results. The position loop utilizes a separate independent observer structure to estimate the push rod displacement state and its disturbance information in real time, and accurately generates displacement control commands through a composite control law. This clearly hierarchical and tightly coordinated control structure ensures that the large-inertia servo control system maintains excellent dynamic performance and high robustness during long-term operation, making it suitable for automation control applications of permanent magnet synchronous motors with high reliability and accuracy requirements.

[0110] Example:

[0111] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0112] To verify the effectiveness of the control method and system based on frequency domain self-tuning and linear active disturbance rejection proposed in this invention, the following simulation experiment was designed. The system was built on the Matlab / Simulink platform, and the controller underwent parameter tuning and response simulation in the Simulink environment. The simulation model has a modular structure and can be directly deployed with the configuration logic of the field controller. The simulation experiment follows... Figure 1 The control strategy flowchart shown is implemented in conjunction with the five key steps of this invention.

[0113] Figure 1 The diagram shows the overall framework of the control strategy of this invention, which includes: taking a large inertia servo control system as the control object, constructing a three-closed-loop control structure, tuning PID parameters using frequency domain performance indicators, mapping them to LADRC controller parameters, and finally completing the control deployment and disturbance rejection verification of LADRC.

[0114] Figure 2 The diagram shows the three-loop structure of the control system, consisting of the innermost current loop, the middle velocity loop, and the outermost position loop. A fixed PI controller is used for the current loop, while a PID controller and a LADRC controller are used for comparative experiments in the velocity and position loops, respectively.

[0115] The controller tuning effect was verified through simulation. Figure 3 The figure shows the simulation results of speed step tracking of the LADRC controller under different control parameter configurations. The simulation shows that under the set controller bandwidth parameters, the system can achieve fast response and stable tracking. The output curve reaches the target value in a short time without obvious overshoot, and has good dynamic response capability.

[0116] Figure 4The simulation process of the speed response of the control system under applied load disturbance is illustrated. The simulation results show that the system maintains stable operation after disturbance injection, and the controller can achieve disturbance compensation and restore speed tracking state in a short time, demonstrating good disturbance suppression capability and system dynamic recovery performance.

[0117] This embodiment further maps the tuned PI controller parameters to the key bandwidth parameters of the LADRC controller using a frequency domain equivalent method. Table 1 shows the tuning results of PI and LADRC under the mapping relationship.

[0118] Table 1 Simulation results of self-tuning parameters

[0119]

[0120] Figure 5 The simulation response diagrams of the LADRC controller obtained through frequency domain mapping and the directly tuned PI controller under a speed step command are shown. The simulation is set with a speed step of 400 r / min and a system open-loop cutoff frequency of 150 Hz. The key parameters of the LADRC controller are generated through frequency domain formula mapping and correspond to the parameters of the traditionally tuned PI controller. Table 2 summarizes the speed step response results of PI and LADRC under self-tuning parameters.

[0121] Table 2 Simulation results of velocity step

[0122]

[0123]

[0124] Simulation results show that the LADRC controller using parameter mapping has a response speed comparable to the PI controller, while its extended state observer can estimate and compensate for disturbances and unmodeled dynamics online. Furthermore, the LADRC controller configured through frequency domain mapping exhibits excellent dynamic characteristics during step response. The control system achieves fast response without overshoot, smooth control process, maintains low-amplitude velocity error under disturbance conditions, and possesses rapid recovery capability. Compared with control strategies using traditional tuning methods, the LADRC controller enhances its adaptability to disturbance changes while maintaining stable performance, making it suitable for high-precision position adjustment tasks requiring long-term operation.

[0125] Figure 6a and Figure 6bThe comparison of the amplitude-frequency response curves between PI and LADRC parameters is illustrated, verifying the consistency of the two controllers in response characteristics under equivalent mapping. The figure shows that the performance of the two algorithms is similar in the low-to-mid-frequency range, but the amplitude-frequency response of LADRC decays faster in the high-frequency range. Therefore, it can be concluded that LADRC has better disturbance suppression and high-frequency measurement noise immunity than the PI controller, making it more suitable for applications of large-inertia servo control systems. This verifies the feasibility of the mapping method in maintaining controller performance and provides a theoretical basis for the automated tuning of LADRC control parameters.

[0126] When deploying the LADRC controller and performing push-stick control, the LADRC design for the position loop adopts the maximum phase compensation design principle, selecting ω. c,p With ω o,p Bandwidth ratio γ p The value is 0.25, and ω is taken as ω. f =50Hz, LADRC ω after SDMS-DE optimization o,p =618.89, ω c,p =157.08, while the ω of DMC-LADRC o,p =603.94, ω c,p =161.58, and position loop simulation experiments were conducted using the aforementioned self-tuning parameters. In this embodiment, the constructed LADRC controller is embedded into the speed loop and position loop of the servo control system, forming a dual-loop cascaded control structure with self-disturbance rejection capability. The LADRC controller contains an extended state observer, used to dynamically estimate disturbance factors, modeling errors, and external load changes in the system, and achieves precise system control through a disturbance compensation mechanism. After the controller is deployed, system-level simulation verification is performed. Table 3 summarizes the position step experiment results.

[0127] Table 3 Simulation results of position step jump

[0128]

[0129] Figure 7a The figure shows the displacement tracking response curve of the servo system under a step input. The figure demonstrates that the controller can complete closed-loop regulation in a short time, with stable output and no overshoot, indicating that the LADRC controller has excellent fast response capability. Figure 7bThe diagram illustrates the system's displacement error response curve under an applied external disturbance torque. With a disturbance injected at 0.2 seconds, the LADRC controller quickly estimates and compensates for the disturbance, causing the error to converge rapidly and the system to maintain stable operation. The simulation response curves after deploying the LADRC controller demonstrate the system's velocity and position tracking performance under disturbance. It can be seen that the LADRC controller can quickly suppress and maintain tracking accuracy under load disturbances or parameter changes, exhibiting better control performance than traditional PI schemes.

[0130] To further test the adaptability of the proposed method under varying load parameters, the load rotational inertia variation was introduced into the simulation model to simulate the uncertain load changes during the control of a large-inertia servo system. Table 4 summarizes the response data from the sinusoidal tracking experiment.

[0131] Table 4 Simulation results of sinusoidal tracking with variable inertia

[0132]

[0133] Figure 8a The diagram illustrates the position comparison curves of the control system under varying load inertia conditions. Figure 8b The diagram illustrates the position error curve of the control system under varying load inertia conditions. Figure 8c The diagram illustrates the total position disturbance curve of the control system under varying load inertia conditions. Figure 8d The diagram illustrates the speed comparison curves of the control system under varying load inertia conditions. The comparison shows that under the condition of fixed controller parameters, the system can still maintain stable operation and the output response is smooth and oscillating. This indicates that the deployed LADRC controller has good parameter robustness and adaptability to changes in system structure, and is suitable for continuous adjustment tasks of large inertia servo control systems under uncertain load scenarios.

[0134] The control strategy constructed in this embodiment has been verified through multi-scenario simulations, including typical operating conditions such as step response, external disturbances, and load parameter changes. It consistently achieves stable control and continuous tracking of the system output, and its control performance meets the dynamic response requirements of the turbine push rod under high-precision position adjustment. The controller parameters can be automatically generated through frequency domain mapping, eliminating the need for manual tuning and physical trial-and-error during deployment. This makes it suitable for complex industrial environments with frequent changes in operating conditions, exhibiting strong deployability and control consistency. In summary, this embodiment demonstrates that the detection method described in this invention is effective and achieves the invention's objectives.

Claims

1. A servo system control method based on frequency domain self-tuning and linear active disturbance rejection, characterized in that, Includes the following steps: Step 1: Based on the mathematical model of the permanent magnet synchronous motor, establish a dual-inertia model suitable for large inertia servo systems, and construct the equivalent mathematical expression of the electrical and mechanical transmission system. Step 2: In the three-level cascade control architecture consisting of a current loop, a speed loop, and a position loop, the current loop is set for current regulation, the speed loop for dynamic response regulation, and the position loop for displacement target tracking. Step 3: Based on frequency domain performance indicators and rule-based methods, tune the PI controller parameters for the speed loop and position loop respectively. Frequency domain indicators include open-loop cutoff frequency and phase margin. Step four: Establish the frequency domain equivalent mapping relationship between the PI controller and the LADRC controller, and convert the tuned PI controller parameters into key parameters of the LADRC controller, including the controller bandwidth ω. c With observer bandwidth ω o And the system model parameter b0; Step 5: Deploy the configured LADRC controller to the speed loop and position loop to control the operation of the servo system under disturbance and load change conditions.

2. The servo system control method based on frequency domain self-tuning and linear active disturbance rejection as described in claim 1, characterized in that, In step one, considering the dual-inertia coupling and transmission elasticity effect between the motor side and the load side, a simplified dual-inertia model is used to describe the dynamic characteristics of the system; the input variable is the current signal, and the output is the displacement signal.

3. The servo system control method based on frequency domain self-tuning and linear active disturbance rejection as described in claim 1, characterized in that, In step two, the speed loop and position loop use an LADRC controller. The speed loop adjusts the motor speed and receives the desired speed command output by the position loop, forming a coordinated control between the inner and outer loops. The position loop outputs the desired speed based on the displacement error to achieve displacement control.

4. The servo system control method based on frequency domain self-tuning and linear active disturbance rejection as described in claim 1, characterized in that, In step three, the speed loop uses the frequency margin method, and the tuning target of the speed loop PI controller is the open-loop cutoff frequency, which is set in the range of 1 / 10 to 1 / 5 of the current loop bandwidth. The phase margin is controlled between 45° and 60°. The position loop PI controller parameters are tuned using the overshoot-free Ziegler-Nichols rule method.

5. The servo system control method based on frequency domain self-tuning and linear active disturbance rejection according to claim 1, characterized in that, In step four, the bandwidth ω of the velocity loop LADRC observer... o Set as controller bandwidth ω c γ v times, γ v The value ranges from 3 to 8. The equivalent mapping relationship of the velocity loop in the frequency domain is constructed based on the principle of low-frequency approximation in the frequency domain as ω. o =k I (2γ v +1) / (k p ·γ v ), ω c =γ v ω o ; The position loop frequency domain equivalent mapping relationship is based on the maximum phase compensation design principle. The LADRC observer bandwidth is set according to the target open-loop cutoff frequency, and the state feedback parameters are calculated in combination with the bandwidth ratio relationship to complete the parameter mapping between LADRC controllers.

6. The servo system control method based on frequency domain self-tuning and linear active disturbance rejection according to claim 5, characterized in that, In step four, the position loop LADRC controller is tuned using the maximum phase compensation design principle, selecting ω... c,p With ω o,p Bandwidth ratio γ p Given 0.25, take ω f =50Hz, LADRC ω after SDMS-DE optimization o,p = 618.89 rad / s, ω c,p =157.08 rad / s, while the ω of DMC-LADRC o,p = 603.94 rad / s, ω c,p =161.58rad / s, and position loop simulation experiments were conducted using the above self-tuning parameters.

7. The servo system control method based on frequency domain self-tuning and linear active disturbance rejection as described in claim 1, characterized in that, In step five, the LADRC controller adopts a first-order extended state observer structure. This first-order extended state observer estimates the disturbance components in the system in real time and feeds them back to the control output channel for compensation, thereby achieving online disturbance suppression.

8. The control system used in the servo system control method based on frequency domain self-tuning and linear active disturbance rejection according to any one of claims 1 to 7 includes a permanent magnet synchronous motor, a displacement sensor, a speed calculation module, and a motor controller. The permanent magnet synchronous motor provides driving torque to the system, and its output shaft is connected to a reducer. The displacement sensor measures the displacement of the servo motor in real time, serving as a control feedback signal. The speed calculation module estimates the speed by differentiating or filtering the displacement signal, which is used as the speed loop feedback input. The motor controller includes a main control module, a power drive module, a signal sampling and processing module, and a communication module. Each module works together to complete the motor control and data interaction functions.

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