A rocket rudder system control method based on internal mode and extended state observer

Abstract

The application relates to a rocket rudder system control method based on an internal mode and an extended state observer, a permanent magnet synchronous motor is used as a driving motor of a rocket rudder system, a mathematical model of a permanent magnet synchronous motor is established in a two-phase rotation (dq) coordinate system, an internal mode-based state feedback controller is designed for a position loop and a speed loop of the motor, an extended state observer is designed for a current loop of the motor, and a final controller is obtained; the internal mode control method is a global control method, does not need to assume the size of a control signal and a disturbance signal, enhances the steady-state performance of the position loop and the speed loop, and improves the robustness of the rudder system; meanwhile, the extended state observer is designed for the current loop to observe total disturbance of the current loop, enhances the anti-disturbance ability of the current loop, improves the dynamic performance of the rudder system, and solves the problem that load torque disturbance and parameter perturbation affect the position tracking performance of the rudder in the rocket running process.

Description

Technical Field

[0001] This invention relates to the field of rocket electric servo control, and more specifically to a rocket servo system control method based on an internal model and an extended state observer. Background Technology

[0002] Rocket servo systems are classic position servo systems. The system controls the rocket's attitude by manipulating the rotation angle of the servo motor to control the deflection of the control surfaces. Compared to hydraulic servo motors, electric servo motors are increasingly widely used in the aerospace field due to their simpler structure, smaller size, and higher reliability. Permanent magnet synchronous motors (PMSMs), as currently popular AC motors, have advantages such as fast response speed, high efficiency, and large torque-to-inertia ratio, and are gradually becoming the mainstream motor in electric servo systems and are widely used in high-performance position servo systems. PID control, as a classic linear control method, is widely used in the control of PMSMs. However, PMSMs are not only multi-input multi-output nonlinear systems, but are also susceptible to load torque disturbances and parameter variations. In such cases, PID control struggles to achieve satisfactory control performance; that is, in actual operation, disturbances and parameter perturbations affect the servo motor's position control performance. Summary of the Invention

[0003] To overcome the shortcomings of current servo system control technology, this invention provides a rocket servo system control method based on an internal model and expansion state observer.

[0004] To achieve the above-mentioned objectives, the present invention adopts the following technical solution: a rocket servo system control method based on an internal model and an extended state observer, comprising the following steps:

[0005] S1. Using a permanent magnet synchronous motor as the drive motor of the rocket servo system, establish a mathematical model of the permanent magnet synchronous electric servo motor in a two-phase rotating (dq) coordinate system.

[0006] S2. Design a state feedback controller based on internal model for the position loop and velocity loop of an electric servo motor;

[0007] S21. It is assumed that the steering control signal and the interference signal are generated by an external system.

[0008] S22. Write the position and velocity equations for the mathematical model of the electric servo motor.

[0009] S23. Solve for the minimal polynomial of the external system matrix and construct the internal model;

[0010] S24. Combine the position and velocity equations and internal model of the electric servo motor mathematical model to obtain the augmented system;

[0011] S25. Design a state feedback controller based on internal model;

[0012] S3. Design an extended state observer for the current loop of the electric servo motor, and obtain the final controller:

[0013] S31. Write the current loop equation;

[0014] S32. Design an extended state observer to observe unknown dynamics;

[0015] S33, Design i q Current loop controller and i d Current loop controller.

[0016] Furthermore, in step S1, the mathematical modeling of the drive motor in the two-phase rotating (dq) coordinate system is as follows:

[0017]

[0018]

[0019]

[0020]

[0021] Where θ r For the servo rotor position, ω r For servo motor speed, u d For the d-axis voltage, u q Let i be the q-axis voltage. d For d-axis current, i q Let L be the q-axis current, L be the stator inductance, and T be the q-axis current. L R is the load torque. s Where J is the stator resistance, B is the moment of inertia, and Φ is the coefficient of viscous friction. v The permanent magnet flux linkage is p, the number of pole pairs of the motor is p, and the electromagnetic torque is T. e =1.5pΦ v ;

[0022] Furthermore, in step S2, it is assumed that the rudder control signal θ d It is a sinusoidal signal with frequency w, and the load torque interference T L These are constant signals, and they can all be generated by the following external systems:

[0023]

[0024] Where v = [v1 v2 v3] T Let A1 be the external system variable and A1 be the external system matrix. The derivative of v;

[0025] Let x1 = θ r x2=ω r , Stator current i q It can be used as a reference signal for the q-axis current loop. Since it is also the control input for both the position loop and the velocity loop, the position and velocity equations of the electric servo motor mathematical model can be written in the following form:

[0026]

[0027] Where x = (x1 x2) T , The derivative of x;

[0028] The minimal polynomial for solving the external system matrix A1 is λ. 3 +w 2 If λ is used, then an internal model of the following form can be constructed:

[0029]

[0030] Where η is the internal model variable. The derivative of η e = θ r -v1 represents the servo position tracking error;

[0031] Let x a =col(x,η), combining the position and velocity equations and the internal model of the electric servo motor mathematical model, we obtain an augmented system of the following form:

[0032]

[0033] in for The derivative;

[0034] The internal model-based state feedback controller is designed as follows:

[0035]

[0036]

[0037] Where K is the constant matrix that needs to be designed.

[0038] Furthermore, in step S3, i q The current loop equation can be written in the following form:

[0039]

[0040] in

[0041] Furthermore, in step S3, the extended state observer takes the following form:

[0042]

[0043]

[0044] Where γ1 and γ2 are respectively i q ,a q The estimated value of (t), γ1 and γ2 are the derivatives, respectively, and p0 is a positive constant.

[0045] Further, in step S3, i q The current loop controller is designed as follows:

[0046]

[0047] Where k1 is a positive constant.

[0048] Furthermore, the i d The current loop uses a PI controller, and is designed as follows:

[0049]

[0050] Where k p1 With k i1 These are the proportional gain and integral gain, respectively.

[0051] Furthermore, the design method for the constant matrix K is to configure the poles so that A a +B a All eigenvalues ​​of K lie in the negative real part.

[0052] Furthermore, the minimal polynomial of the external system matrix A1 is solved using |λE-A1|=0, where E is the identity matrix.

[0053] The present invention also provides a rocket servo system that uses the above-mentioned rocket servo system control method based on internal model and expansion state observer.

[0054] Compared with existing technologies, this invention provides a rocket servo system control method based on internal model and extended state observer. The proposed internal model control method is a global control method that does not require assumptions about the magnitude of control signals and disturbance signals. This method enhances the steady-state performance of the position loop and velocity loop and improves the robustness of the servo system. At the same time, an extended state observer is designed for the current loop to observe the total disturbance of the current loop. This method enhances the disturbance rejection capability of the current loop and improves the dynamic performance of the servo system.

[0055] In summary, this invention not only improves the position and velocity loops to give the servo system high-precision steady-state tracking performance, but also improves the current loop to give the servo system good dynamic response performance, thus solving the problem of load torque interference and parameter perturbation affecting the servo position tracking performance during actual rocket operation. Attached Figure Description

[0056] Figure 1 This is a block diagram of the permanent magnet synchronous electric servo motor control system of the present invention;

[0057] Figure 2 The figure shows the rudder feedback response curve obtained from simulation in an embodiment of the present invention.

[0058] Figure 3 The figure shows the rudder feedback tracking error curve obtained from simulation in an embodiment of the present invention.

[0059] Figure 4 The electromagnetic torque curve obtained from simulation in an embodiment of the present invention is shown. Detailed Implementation

[0060] The present invention will now be further described with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of the present invention, and not all embodiments.

[0061] The present invention discloses a rocket servo system control method based on an internal model and an extended state observer, the method comprising the following steps:

[0062] S1. Using a permanent magnet synchronous motor as the drive motor of the rocket servo system, establish a mathematical model of the permanent magnet synchronous electric servo motor in a two-phase rotating (dq) coordinate system.

[0063] S2. Design a state feedback controller based on internal model for the position loop and velocity loop of an electric servo motor;

[0064] S3. Design an extended state observer for the current loop of the electric servo motor to observe unknown dynamics and obtain the final controller.

[0065] Step S1 is as follows:

[0066] A permanent magnet synchronous motor is selected as the drive motor for the rocket's servo system. Mathematical modeling is performed in a two-phase rotating (dq) coordinate system, and its form is as follows:

[0067]

[0068]

[0069]

[0070]

[0071] Where θ r The servo rotor position, also known as the servo feedback signal, ω r For servo motor speed, u d For the d-axis voltage, u q Let i be the q-axis voltage. d For d-axis current, i q Let L be the q-axis current, L be the stator inductance, and T be the q-axis current. L R is the load torque. s Where J is the stator resistance, B is the moment of inertia, and Φ is the coefficient of viscous friction. v The permanent magnet flux linkage is p, the number of pole pairs of the motor is p, and the electromagnetic torque is T. e =1.5pΦ v .

[0072] Step S2 is as follows:

[0073] S21, Assuming the steering signal θ d It is a sinusoidal signal with frequency w, and the load torque interference T L These are constant signals, and they can all be generated by the following external systems:

[0074]

[0075] Where v = [v1 v2 v3] T Let A1 be the external system variable and A1 be the external system matrix. The derivative of v;

[0076] It can be derived from formula (2) The derivative of v2;

[0077] S22, Let x1 = θ r x2=ω r , Stator current i q It can be used as a reference signal for the q-axis current loop. Since it is also the control input for both the position loop and the velocity loop, the position and velocity equations of the electric servo motor mathematical model can be written in the following form:

[0078]

[0079] in for The derivative;

[0080] S23. Solve for the minimal polynomial of the external system matrix A1 as λ. 3 +w 2 If λ, then an internal model of the following form can be constructed:

[0081]

[0082] Where η is the internal model variable. The derivative of η e = θ r -v1 represents the servo position tracking error;

[0083] S24, Let x a =col(x,η) By combining system (3) and internal module (4), we can obtain an augmented system, which has the following form:

[0084]

[0085] in For x a The derivative;

[0086] S25. Design a state feedback controller based on internal model in the following form:

[0087]

[0088] Where K is the constant matrix to be designed, and by configuring the poles, A can be made... a +B a All eigenvalues ​​of K lie in the negative real part.

[0089] Step 3 specifically involves:

[0090] S31, i q The current loop equation can be written in the following form:

[0091]

[0092] in For i q The second derivative of .

[0093] S32. Design an extended state observer to observe unknown dynamics, in the following form:

[0094]

[0095]

[0096] Where γ1 and γ2 are respectively i q ,a q The estimated value of (t), γ1 and γ2 are the derivatives, respectively, and p0 is a positive constant;

[0097] S33, Design i qCurrent loop controller and i d Current loop controller;

[0098] i q The current loop controller is designed as follows:

[0099]

[0100] Where k1 is a positive constant;

[0101] i d The current loop uses a PI controller, as follows:

[0102]

[0103] Where k p1 With k i1 These are proportional gain and integral gain, respectively.

[0104] Combining (6), (8), (9), and (10), we obtain the final controller, which takes the following form:

[0105]

[0106] To verify the effectiveness of the proposed method, an embodiment of the present invention is provided:

[0107] The nominal value of the selected permanent magnet synchronous electric servo motor is:

[0108] p = 2, Considering the parameter perturbation phenomenon of the electric servo motor during rocket operation, the uncertain motor parameters are selected as follows:

[0109] rudder control signal θ d =30°sin(3t), load torque disturbance T L =1N.m Controller parameters are selected as follows:

[0110] K=[-252-1-5.5-5.4-1.8],k1=20,p0=200,k p1 =3,k i1 =1

[0111] Using the above-mentioned series of parameters, the method of this invention is applied to control the servo system of the permanent magnet synchronous electric servo motor. The control block diagram of the permanent magnet synchronous electric servo motor is as follows. Figure 1 As shown, the system was simulated and verified using the MATLAB platform, and the results are as follows. Figure 2-4 The simulation results are shown. Figure 2 rudder feedback θ r Response curve Figure 3 Position feedback tracking error curve Figure 4Electromagnetic torque T e The simulation results show that the control method has accurate steady-state tracking performance under parameter perturbation and external disturbance conditions, verifying the practical feasibility of the invention.

[0112] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for controlling a rocket rudder system based on an internal model and an extended state observer, characterized in that, Comprising the following steps: S1, using permanent magnet synchronous motor as the driving motor of rocket rudder system, establishing the mathematical model of permanent magnet synchronous motor in two-phase rotating (dq) coordinate system; S2, designing state feedback controller based on internal model for position loop and speed loop of electric rudder: S21, assuming that the rudder control signal and the interference signal are generated by an external system; S22, writing the position and speed equations of the mathematical model of the electric rudder S23, solving the minimum polynomial of the external system matrix to construct the internal model; S24, combining the position and speed equations of the mathematical model of the electric rudder and the internal model to obtain the augmented system; S25, designing state feedback controller based on internal model; S3, designing extended state observer for current loop of electric rudder and obtaining the final controller: S31, writing the current loop equation; S32, designing extended state observer to observe unknown dynamics; S33, design i q Current loop controller and i d Current loop controller; In the step S2, it is assumed that the rudder control signal θ d is a sinusoidal signal with a frequency w, and the load torque disturbance T L is a constant signal, which can be generated by an external system as follows: v = [v1 v2 v3] T , θ d = v1, T L = v3 where v = [v1 v2 v3] T is an external system variable, A1 is an external system matrix, is the derivative of v. Let x1 = θ r ,x2 = ω r , Stator current i q can be used as the reference signal of q-axis current loop It is also the control input of position loop and speed loop, so the position and speed equations of the mathematical model of the electric actuator can be written as follows: where x = (xl x2) T , derivative of x; The minimal polynomial for solving the external system matrix A1 is λ 3 +w 2 λ, then the internal mode of the following form is constructed: where η is the inner model variable, is the derivative of η, e = θ r - v1 is the rudder position tracking error; Let x a = col(x, η), the augmented system is obtained as follows by combining the position and velocity equations of the mathematical model of the electric actuator with the internal model. wherein is the derivative of x a is the derivative of x The state feedback controller based on internal model is as follows: Wherein K is a constant matrix to be designed; where θ r is the rudder rotor position, ω r is the rudder rotation speed, T L is the load torque, J is the moment of inertia, B is the viscous friction coefficient, Φ v is the permanent magnet flux, and p is the number of pole pairs of the motor. In the step S3, i q The current loop equation is written as follows: where γ1, γ2are i q a q an estimate of (t), are derivatives of γ1, γ2, and p0is a constant. The i q The current loop controller is designed as follows: Wherein k1 is a normal number.

2. The control method of a rocket rudder system based on an internal model and extended state observer according to claim 1, characterized in that, In the step S1, the mathematical modeling of the driving motor in two-phase rotating (dq) coordinate system is as follows: where u d is the d-axis voltage, u q is the q-axis voltage, i d is the d-axis current, i q is the q-axis current, L is the stator inductance, R s is the stator resistance, and the electromagnetic torque T e = 1.5pΦ v .

3. The method according to claim 1, wherein The i d The current loop adopts a PI controller, and the design is as follows: where k p1 and k i1 are proportional and integral gains, respectively.

4. The control method of a rocket rudder system based on an internal model and extended state observer according to claim 1, characterized in that, The design method of the constant matrix K is to configure poles so that A a + B a All eigenvalues of K are located in the negative real part.

5. The method according to claim 1, wherein The minimum polynomial of the external system matrix A1 is solved according to λE-A1=0, wherein E is the unit matrix.

6. A rocket rudder system characterized by, The rocket rudder system control method based on internal model and extended state observer is used.

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