High-precision control method for aero-engine electric actuator

Abstract

The application belongs to the technical field of fast anti-disturbance control under complex disturbance, and provides a high-precision control method for an aero-engine electric actuator. A three-phase permanent magnet synchronous motor and a ball screw are combined together through a rigid connection mode, and the control problem of the electric cylinder is equivalent to the control problem of the motor. In combination with a backstepping control technology and a finite-time observation technology, fast lumped disturbance estimation and compensation are provided through a finite-time disturbance estimator, higher steady-state precision is realized, and the electric cylinder realizes input instruction tracking well through the backstepping method to ensure deterministic transient performance.

Description

Technical Field

[0001] This invention relates to the field of rapid anti-disturbance control technology under complex interference, and in particular to a high-precision control method for electric actuators of aero-engines. Background Technology

[0002] Aero-engine drive mechanisms are shifting from traditional hydraulic drives to electric drives. While providing the same output torque, the new electric cylinders eliminate complex hydraulic oil supply lines and the need for essential components like solenoid valves found in hydraulic cylinder systems. Power is supplied by lightweight cables, effectively reducing engine weight and improving the actuator's compatibility with multi-electric engines. In future multi-electric engine configurations, after integrating the aircraft's electrical energy, traditional hydraulic cylinders utilize electrical energy secondaryly through hydraulic oil, while electric cylinders directly apply electrical energy, reducing energy conversion steps and effectively improving the efficiency of the aircraft's limited electrical energy. Furthermore, compared to traditional hydraulic cylinders, electric cylinders are smaller and more compact, and better isolated from external influences. They possess advantages such as simple structure, high precision, fast response, and high stability, providing better steady-state and transient performance.

[0003] Currently, electric cylinders have become a mainstream trend in the field of aero-engines. Airbus A320 and Boeing 787 aircraft have already replaced some traditional low-load hydraulic actuators with electric cylinder technology, offering irreplaceable advantages in engine weight reduction, operating costs, and maintenance expenses. In the design of a new generation of small turbofan aero-engines in my country, traditional A1 / A2 and A8 / A9 hydraulic actuators were replaced with electric cylinders. However, traditional hydraulic cylinder motion control algorithms are not suitable for electric cylinder control. Furthermore, because aero-engines often operate in complex environments with high temperature, high pressure, and high load, and are also affected by weather and other factors, engine airflow can experience unpredictable fluctuations, causing the actuators to continuously endure various unknown disturbances. When designing electric cylinder control algorithms, the impact of disturbances should be considered as much as possible, and methods for rapid estimation and compensation should be introduced. In the disturbance rejection control process of electric cylinders, traditional observers and parameter adaptive methods have many limitations, such as the inability to accurately model disturbances and their uncertainties, and significant lag in the integration process, failing to adequately meet the requirements for rapid disturbance suppression. Currently, in the field of electric cylinder motion control technology, traditional PID controllers are still used in engineering. Balancing overshoot and transient performance is difficult, which undoubtedly increases the difficulty of developing control algorithms. Therefore, there is an urgent need to invent a technology that can guarantee high-precision motion control performance. Summary of the Invention

[0004] Electric cylinders in aero engines typically employ a three-phase permanent magnet synchronous motor and a ball screw structure. Essentially, the rigid connection means that electric cylinder control is equivalent to motor control. Motor control usually uses vector control, transforming the complex three-phase AC quantities into a two-dimensional DC control problem (d-axis and q-axis). When the d-axis current is zero, motion control of the motor and even the ball screw is achieved by controlling the q-axis current alone. Furthermore, the current loop response frequency of the motor is much higher than the actual motion frequency of the ball screw; this invention directly approximates the current loop as a proportional element.

[0005] To achieve higher control precision for electric cylinders, the technical solution of this invention is as follows:

[0006] A high-precision control method for an electric actuator in an aircraft engine includes the following steps:

[0007] S1: Mechanism modeling of electric cylinders;

[0008] S1.1: Define the load displacement x of the electric cylinder L m, velocity The lead is hm, the rotation angle of the motor is θrad, and the rotational angular velocity is ω. r rad / s; The electric cylinder adopts a motor and ball screw structure, with the motor and ball screw rigidly connected. The control of the electric cylinder is equivalent to the control of the motor.

[0009] The relationships between the load displacement and rotation angle, and between the speed and angular velocity of the electric cylinder are as follows:

[0010]

[0011] S1.2: Given the output electromagnetic torque model of the motor:

[0012]

[0013] In the formula, T e Electromagnetic torque, measured in N·m, p n This represents the number of pole pairs of the motor. L is the magnetic flux. d L q The inductance coefficients for the d-axis and q-axis are respectively, i d i q These are the currents along the d-axis and q-axis, respectively, in amperes (A).

[0014] S1.3: Construct a motor rotation model;

[0015]

[0016] In the formula, B f=B / J, where J is the moment of inertia of the motor and its load, in kg·m 2 B is the coefficient of viscous friction, with units of N·rad·s. The reference current signal is in amperes (A), and d represents the lumped interference, as follows:

[0017]

[0018] In the formula, T L It is the load torque, in N·m, and g represents the uncertainty of other parameters;

[0019] S1.4: Combining steps S1.1-S1.3, the motion model of the electric cylinder is constructed as follows:

[0020]

[0021] In the formula,

[0022] S2: Design a finite-time disturbance estimator for q-axis lumped disturbances. Perform calculations and processing;

[0023] S2.1: In aero-engines, the electric cylinder operates under finite load conditions. Based on actual data, the upper bound of the lumped disturbance along the q-axis and the upper bound of the first derivative of the lumped disturbance are set, as shown in the following formula:

[0024]

[0025] In the formula, ∈1, ∈2>0 are two bounded constants;

[0026] S2.2: Define the speed of the electric cylinder Observed variables q-axis lumped interference The estimated value The electric cylinder speed and q-axis lumped interference are observed by the following formula:

[0027]

[0028]

[0029]

[0030] In the formula, λ1, λ2, and L are given positive real numbers, and the function sgn * (★)=|★| * sign(★);

[0031] S3: After obtaining the finite-time disturbance estimator, when the lumped disturbance satisfies equation (6), it indicates that the lumped disturbance is accurately observed within a finite time. The lumped disturbance includes all parameter uncertainties, external disturbance torque, and unmodeled dynamics; given the desired command x d First derivative and its second derivative Then, a backstepping controller based on finite-time disturbance estimation is designed using the backstepping method;

[0032] S3.1: Define the tracking error z1 = x L -x d The derivative is as follows:

[0033]

[0034] Define virtual error The virtual control input is constructed as follows:

[0035]

[0036] In the formula, k1 is the feedback control gain. For the reference motion speed, substituting into the virtual control equations (9) to (8) yields the following equation:

[0037]

[0038] S3.2: The derivative with respect to the virtual error z2 is as follows:

[0039]

[0040] Based on the finite-time disturbance estimator in step S2, design the control input. as follows:

[0041]

[0042] In the formula, k2 is the speed feedback control gain; substituting into equation (11) to equation (10) yields the following equation:

[0043]

[0044] The backstepping controller based on finite-time disturbance estimation was designed and iteratively calculated until the system tracking error converged to zero.

[0045] This technical solution can provide a complete closed-loop convergence theorem for an aero-engine electric cylinder system, as detailed below.

[0046] The invention is supported by mathematical theory. For the electric cylinder system of an aero-engine, i.e., the motion model of the electric cylinder (5), a finite-time disturbance estimator (7.1) to (7.3) and a backstepping controller (12) based on the finite-time disturbance estimation are designed. If there is a lumped disturbance, and the assumption (6) is satisfied, the lumped disturbance can be accurately observed in a finite time, and the system tracking error exponent converges to zero. The lumped disturbance includes parameter uncertainty, external disturbance torque, and other unmodeled dynamics.

[0047] The theoretical design consists of two steps. The first step is to ensure that the observation error of the homogeneous differential equation converges precisely to zero within a finite time. The second step is to ensure that the tracking error of the electric cylinder control system converges exponentially to zero through the Lyapunov function.

[0048] S4.1: Note the finite-time disturbance estimator (7.1)~(7.3) and the motion model (5) of the electric cylinder. The difference between the two is as follows:

[0049]

[0050]

[0051] According to the boundedness of the disturbance derivative:

[0052]

[0053]

[0054] Clearly, by selecting appropriate parameters λ1, λ2, and L, finite-time precise observations of velocity and lumped disturbances can be achieved.

[0055]

[0056] Next, we prove how to achieve exponential convergence of the tracking error. Given the Lyapunov function... The derivative is as follows:

[0057]

[0058] From equation (16) and the finite-time disturbance estimator (7.1) to (7.3), it can be seen that after a finite time T1, i.e. when t≥T1, Therefore, the following equation holds:

[0059]

[0060] Obviously, equation (18) can be derived as follows:

[0061] |V(t)|≤e -2kt V(0), (19)

[0062] In the formula, k = min{k1,k2}, and V(0) represents the initial value of V(t). At this time, the tracking error z1 converges exponentially to zero, that is:

[0063]

[0064] The exponential convergence of the tracking error and the finite-time accurate estimation performance of the disturbance observer have been demonstrated.

[0065] The beneficial effects of this invention are as follows: By equating the control problem of an electric cylinder to the control problem of a motor, and combining backstepping control technology and finite-time disturbance estimation technology, the finite-time disturbance estimator provides fast lumped disturbance estimation and compensation, achieving higher steady-state accuracy; the backstepping method ensures deterministic transient performance, enabling the electric cylinder to effectively track input commands. Attached Figure Description

[0066] Figure 1 The control flowchart for the electric cylinder of an aero-engine and its finite-time disturbance estimator;

[0067] Figure 2 Simulation diagram of the expected displacement trajectory and actual output of the ball screw in the electric cylinder;

[0068] Figure 3 Simulation diagrams of the desired and actual speeds of the ball screw in an electric cylinder;

[0069] Figure 4 Simulation diagram of the actual reference control current generated by the q-axis of the electric cylinder motor;

[0070] Figure 5 Simulation diagram showing the given disturbance and its real-time estimated value for the electric cylinder. Detailed Implementation

[0071] In practice, the electric cylinder combines a three-phase permanent magnet synchronous motor and a ball screw via a rigid connection, so the control problem of the electric cylinder is equivalent to the control problem of the motor. Based on traditional three-phase motor vector control technology, coordinate transformation is performed on the permanent magnet synchronous motor, and finally, a DC motor control strategy can be used to control the AC motor, thereby achieving motion control of the ball screw. Building upon this, this invention aims to provide a new control algorithm that combines backstepping control technology and finite-time observation technology. A finite-time disturbance estimator provides fast lumped disturbance estimation and compensation, achieving higher steady-state accuracy; the backstepping method ensures deterministic transient performance, enabling the electric cylinder to effectively track input commands.

[0072] The invention will be further described below with reference to the accompanying drawings, and the process is as follows: Figure 1As shown, this implementation case relies on a certain type of turbofan aero-engine under development. A mechanism simulation model of the electric cylinder is built based on actual physical parameters, demonstrating the usage process of the invention in detail. Simulation diagrams of system performance and interference suppression performance are also provided to facilitate a better understanding of the algorithm of this invention.

[0073] S1: Physical parameters of the electric cylinder.

[0074] The displacement range of the electric cylinder actuator is x L Maximum running speed ∈[0,0.3]m Load torque T L ∈[-10,10] N·m. Other parameters are selected as follows: h = 0.02m, J = 0.003kg·m 2 p n =4, L d =0.01, L q =0.01.

[0075] S2: Selection of reference trajectory and initial value. The reference trajectory is: x L = -0.25cos(πt) + 0.25m, the initial value of the electric cylinder is: x L (0) = 0.03m, The initial values ​​for the finite-time disturbance estimator are selected as follows:

[0076] S3: Parameter design of the backstepping controller and finite-time disturbance estimator. The parameters of the backstepping controller are: k1 = k2 = 50; the parameters of the observer are: λ1 = 10, λ2 = 10, L = 4.

[0077] S4: Introduce external interference. The selected external interference is: That is, the reference input current of the actual system is:

[0078] S5: According to Figure 5 The good effect of the invented finite-time disturbance estimator can be clearly seen. Its active estimated trajectory converges to the true value of the disturbance within a finite time. In addition, the designed backstepping controller can also achieve good exponential stability of the tracking error.

Claims

1. A high-precision control method for an electric actuator of an aero-engine, characterized in that, The steps include the following: S1: Mechanism modeling of electric cylinders; S1.1: Define the load displacement x of the electric cylinder L m, velocity The lead is hm, the rotation angle of the motor is θrad, and the rotational angular velocity is ω. r rad / s; The electric cylinder adopts a motor and ball screw structure, with the motor and ball screw rigidly connected. The control of the electric cylinder is equivalent to the control of the motor. The relationships between the load displacement and rotation angle, and between the speed and angular velocity of the electric cylinder are as follows: S1.2: Given the output electromagnetic torque model of the motor: In the formula, T e Electromagnetic torque, measured in N·m, p n This represents the number of pole pairs of the motor. L is the magnetic flux. d L q The inductance coefficients for the d-axis and q-axis are respectively, i d i q These are the currents along the d-axis and q-axis, respectively, in amperes (A). S1.3: Construct a motor rotation model; In the formula, J is the moment of inertia of the motor and its load, measured in kg·m. 2 B is the coefficient of viscous friction, with units of N·rad·s. The reference current signal is in amperes (A), and d represents the lumped interference, as follows: In the formula, T L It is the load torque, in N·m, and g represents the uncertainty of other parameters; S1.4: Combining steps S1.1-S1.3, the motion model of the electric cylinder is constructed as follows: In the formula, S2: Design a finite-time disturbance estimator for q-axis lumped disturbances. Perform calculations and processing; S2.1: In aero-engines, the electric cylinder operates under finite load conditions. Based on actual data, the upper bound of the lumped disturbance along the q-axis and the upper bound of the first derivative of the lumped disturbance are set, as shown in the following formula: In the formula, ∈1 and ∈2>0 are two bounded constants; S2.2: Define the speed of the electric cylinder Observed variables q-axis lumped interference The estimated value The electric cylinder speed and q-axis lumped interference are observed by the following formula: In the formula, λ1, λ2, and L are given positive real numbers, and the function sgn * (★)=|★| * sign(★); S3: After obtaining the finite-time disturbance estimator, when the lumped disturbance satisfies equation (6), it indicates that the lumped disturbance is accurately observed within a finite time. The lumped disturbance includes all parameter uncertainties, external disturbance torque, and unmodeled dynamics; given the desired command x d First derivative and its second derivative Then, a backstepping controller based on finite-time disturbance estimation is designed using the backstepping method; S3.1: Define the tracking error z1 = x L -x d The derivative is as follows: Define virtual error The virtual control input is constructed as follows: In the formula, k1 is the feedback control gain. For the reference motion speed, substituting into the virtual control equations (9) to (8) yields the following equation: S3.2: The derivative with respect to the virtual error z2 is as follows: Based on the finite-time disturbance estimator in step S2, design the control input. as follows: In the formula, k2 is the speed feedback control gain; substituting into equation (11) to equation (10) yields the following equation: The backstepping controller based on finite-time disturbance estimation was designed and iteratively calculated until the system tracking error converged to zero.

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