An anti-wind interference control method for an astronomical telescope based on active disturbance rejection

Abstract

The application discloses an astronomical telescope wind interference control method based on self-disturbance rejection, introduces ADRC into the control of a three-closed-loop servo system of a permanent magnet synchronous motor, realizes compound control of position and speed by using a second-order ADRC, and changes the traditional three-loop cascade control of position, speed and current into double-loop control of position-speed and current. According to the Davenport spectrum and the average wind speed of a site where the telescope is located, a numerical simulation wind load disturbance method is provided, which can be used for the research on the wind load disturbance resistance of the telescope. In the application, the self-disturbance rejection control technology is used in the three-closed-loop control of the traditional permanent magnet synchronous motor to optimize the position loop and the speed loop into a single position-speed loop, the accuracy requirement of the mathematical model of the control system is not high, meanwhile, the disturbance of the system can be observed in real time and feedback compensation can be carried out during the operation to eliminate the influence of the disturbance on the control system.

Description

Technical Field

[0001] This invention relates to a method for controlling wind disturbance in astronomical telescopes, and particularly to a method for controlling wind disturbance in astronomical telescopes based on self-disturbance rejection. Background Technology

[0002] As humanity continues to explore the universe, scientists are increasingly focusing on more distant and fainter celestial bodies. This necessitates astronomical telescopes with stronger light-gathering capabilities and higher resolution, leading to a continuous increase in telescope aperture and ever-increasing demands on pointing and trajectory tracking accuracy. The transmission method for large-aperture telescopes has evolved from early worm gear drives to today's direct-drive motors, which offer advantages such as high rigidity and ease of installation and debugging. Direct-drive technology is now widely used in astronomical telescopes, such as the 8.2m aperture Subaru developed by Japan, the 10.4m aperture GTC developed by Spain, the 8.2m aperture VLT developed by the European Southern Observatory, and the 1.6m aperture multi-channel sky survey telescope developed by the Nanjing Institute of Astronomical Optics and Electronics.

[0003] Astronomical telescopes have extremely demanding environmental requirements, demanding excellent seeing. They are typically installed in remote, high-altitude mountainous areas or even in Antarctica. Wind disturbance is one of the main interferences affecting the normal operation of astronomical telescopes. During operation, wind disturbance directly affects the telescope frame, severely impacting the telescope's servo control system. Initially, designs such as domes and wind shields were used to mitigate the effects of wind disturbance. With the development and construction of numerous large-aperture astronomical telescopes, to overcome the influence of dome and mirror seeing, observations often involve appropriate ventilation of the dome environment and telescope system, or even open observation with the dome extended. This can cause unpredictable harm to the normal tracking of the astronomical telescope.

[0004] Currently, most telescope control systems employ a traditional three-loop structure from the inside out: a current loop, a velocity loop, and a position loop. Each loop uses a separate PID controller. The current and velocity loops are the inner loop controllers, primarily ensuring system stability; the position loop is the outer loop controller, primarily ensuring tracking accuracy. In practical applications, the system is subject to external disturbances such as wind loads, as well as internal disturbances, which degrade the pointing and tracking accuracy of the telescope control system. Under disturbance conditions, the traditional three-loop control system cannot guarantee the high-precision performance indicators such as speed, accuracy, and stability of the telescope control system.

[0005] Active Disturbance Rejection Control (ADRC) is a nonlinear control method proposed by Professor Han Jingqing of my country. It is widely used because it does not require high accuracy of the mathematical model of the controlled object and exhibits strong robustness to system uncertainties. A typical ADRC consists of three parts: a nonlinear tracking differentiator, an extended state observer, and a nonlinear feedback control law. ADRC uses the extended state observer to estimate the total disturbance of the system in real time, including modeled and unmodeled dynamics and external disturbances; then, it uses a nonlinear feedback control law for compensation feedback to improve the system's control performance. Summary of the Invention

[0006] The purpose of this invention is to design a wind disturbance resistance control method for astronomical telescopes based on active disturbance rejection (ADRROC). This method addresses the problem of weak wind disturbance resistance in existing telescope control systems using a three-loop closed-loop permanent magnet synchronous motor, which fails to maintain high tracking accuracy under external interference. The aim is to improve the high-precision position control, rapid response capability, and anti-interference capability of the telescope control system.

[0007] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0008] A wind disturbance mitigation control method for astronomical telescopes based on active disturbance rejection (ADRC) is proposed. ADRC is introduced into the control of a three-loop servo system of a permanent magnet synchronous motor (PMSM). Second-order ADRC is used to achieve composite control of position and velocity. In terms of control structure, the traditional three-loop cascade control of position, velocity, and current is transformed into a two-loop control of position-velocity and current. The second-order ADRC provides a given position signal θ. ref The differential tracker achieves a smooth transition process, and the differential tracker outputs the extracted position signal value θ. * and the differential value of the position signal The extended state observer outputs the observed position z1 and the observed rotational speed z2 to the feedback control law. The extended state observer estimates the total disturbance z3 acting on the system in real time and applies it to the feedback control law to generate a current loop compensation setpoint u0, outputting the compensated current loop setpoint u, thus achieving active disturbance rejection in structure. The method includes:

[0009] Step 1: Establish a mathematical model of the permanent magnet synchronous motor of the astronomical telescope control system in the dq axis synchronous coordinate system. The mathematical model includes the voltage equation, electromagnetic torque equation, and mechanical motion equation of the permanent magnet synchronous motor.

[0010] Step 2: Use PI control for the current loop to obtain the open-loop transfer function of the current loop;

[0011] Step 3: Based on the mechanical motion equations of the permanent magnet synchronous motor in Step 1, obtain the simultaneous equations to get the control quantity of the active disturbance rejection controller;

[0012] Step 4: Establish a wind load disturbance model using numerical simulation; analyze the characteristics of wind using Davenport spectrum, and obtain pulsating wind by passing white noise with a mean of 0 through a Davenport filter.

[0013] Furthermore, the mathematical model in step 1 includes:

[0014] Voltage equation:

[0015]

[0016] Electromagnetic torque equation:

[0017]

[0018] Electromagnetic torque equation:

[0019]

[0020] Equations of motion for machines:

[0021]

[0022] In the dq axis synchronous coordinate system

[0023] ω e =P n *ω m #(5)

[0024] In the formula, u q u d These are the q-axis and d-axis voltages, respectively; i q i d These are the q-axis and d-axis currents, respectively; R is the phase resistance of the motor; L q L d Inductances along the q and d axes, respectively; ψ f For permanent magnet flux linkage; ω e T is the electric angular velocity of the rotor. e P represents the electromagnetic torque of the motor. n T is the number of pole pairs of the motor; J is the moment of inertia of the motor and the load; T L ω is the load torque. m θ is the mechanical angular velocity of the rotor; B is the coefficient of viscous friction; θ m This refers to the mechanical angle of the motor.

[0025] Furthermore, in step 2, the open-loop transfer function of the current loop is:

[0026]

[0027] Configure it as a typical Type I system and use the zero-pole cancellation method to obtain:

[0028]

[0029] Furthermore, in step 3, the simultaneous equations are:

[0030]

[0031] Furthermore, output Choose state variable x1 = θ m , x3 = f, Equation 8 is transformed into an extended state equation:

[0032]

[0033] Furthermore, based on the extended state equation obtained in step 3, the extended state observer (ESO) is designed, with the following design form:

[0034]

[0035] In the formula, z1 is the estimated value of the position signal x1; e is the position estimation error of LESO; z2 is the estimated value of the velocity signal x2; z3 is the estimated value of the disturbance f; u is the system control quantity; l1, l2, and l3 are the extended state observer gains, which are determined by the system state.

[0036] Furthermore, the position-velocity loop employs a tracking differentiator to manage the transition process, with the following design:

[0037]

[0038] The steepest synthesis function fst(x1, x2, r, h) has the following specific form:

[0039]

[0040] In the formula, θ m is the input signal at the position being followed; r is the tracking acceleration factor, which determines the speed at which the given signal is tracked; h is the filtering factor, which is generally taken as an integer multiple of the integration step size; sign() is the sign function.

[0041] Furthermore, based on the design of the extended state observer and the transient process, the error feedback control law is designed in the following form:

[0042]

[0043] In the formula, v1 and v2 are the output position and velocity signals during the transient process, respectively; z1 and z2 are the position and velocity of the telescope control system estimated by the extended state observer, respectively; e1 and e2 are the position error and velocity error, respectively; β1 and β2 are the gain of the error feedback control law; fal is a nonlinear function with the following form:

[0044]

[0045] In the formula, δ is the error threshold; sign() is the sign function; and a is a constant between 0 and 1.

[0046] The control input of the active disturbance rejection controller is further obtained as follows:

[0047]

[0048] Furthermore, in step 4, the Davenport spectrum takes the following form:

[0049]

[0050]

[0051] In the formula, v m Here, k is the average wind speed, n is the surface drag coefficient, and n is the frequency.

[0052] Furthermore, the wind speed signal is converted into a wind force signal using the following formula:

[0053]

[0054] In the formula, ρ is the local air density at the telescope site, and C is the density of the local air density at the telescope site. d Let A be the drag coefficient, A be the windward area of ​​the structure, and v be the wind speed.

[0055] Overall, the technical solution proposed in this invention has the following advantages compared with the prior art:

[0056] (1) For telescope drive control systems, wind load disturbance is one of the main sources of disturbance affecting its control effect and trajectory tracking accuracy. This invention proposes a method for numerically simulating wind load disturbance based on the Davenport spectrum and the average wind speed at the telescope site, which can be used for research on the resistance of telescopes to wind load disturbance.

[0057] (2) In this invention, the three-loop control of a traditional permanent magnet synchronous motor utilizes active disturbance rejection (ADRR) technology to optimize the position and velocity loops into a single position-velocity loop. ADRR is less demanding on the accuracy of the mathematical model of the control system and performs real-time observation and feedback compensation of disturbances during operation to eliminate their impact on the control system. In contrast, traditional control methods such as PID control are highly sensitive to control parameters, resulting in poor control performance and robustness when the control system is subjected to disturbances. Attached Figure Description

[0058] Figure 1 This is the overall block diagram of the PMSM vector control system;

[0059] Figure 2 It is a PMSM three-closed-loop control PI model;

[0060] Figure 3 It is the PMSM dual closed-loop control ADRC model. Detailed Implementation

[0061] The present invention will now be described in further detail with reference to the accompanying drawings.

[0062] A wind disturbance control method for a permanent magnet synchronous motor in an astronomical telescope based on self-disturbance rejection. Its structural block diagram is attached. Figure 1 The dashed line in the block diagram represents the second-order ADRC. ADRC is introduced into the control of a three-loop servo system for a permanent magnet synchronous motor, using the second-order ADRC to achieve composite control of position and speed. In terms of control structure, the traditional three-loop cascade control of position, speed, and current is transformed into a two-loop control of position-speed and current. In the second-order ADRC, the given position signal θ... ref A smooth transition process is achieved under the action of the differential tracker, θ * The value extracted is the location signal. Z1 is the differential value of the position signal. The extended state observer estimates the total disturbance z3 (including modeled, unmodeled dynamics and external disturbances) acting on the system in real time, z1 is the observed value of position, z2 is the observed value of rotational speed, and applies it to the feedback control law to generate the current loop compensation setpoint u0, where u is the current loop setpoint after compensation, thus achieving "active" disturbance rejection in structure.

[0063] Specific implementation steps:

[0064] Step 1: Astronomical telescope control systems generally employ surface-mounted permanent magnet synchronous motors. Based on this, a mathematical model of the permanent magnet synchronous motor in the dq-axis synchronous coordinate system is established:

[0065] Voltage equation:

[0066]

[0067] Electromagnetic torque equation:

[0068]

[0069] Because a surface-mounted permanent magnet synchronous motor L is used d =L q Then the electromagnetic torque equation is:

[0070]

[0071] Equations of motion for machines:

[0072]

[0073] In the dq axis synchronous coordinate system

[0074] ω e =P n *ω m #(5)

[0075] In the formula u q u d These are the q-axis and d-axis voltages, respectively; i q i d These are the q-axis and d-axis currents, respectively; R is the phase resistance of the motor; L q L d Inductances along the q and d axes, respectively; ψ f For permanent magnet flux linkage; ω e T is the electric angular velocity of the rotor. e P represents the electromagnetic torque of the motor. n T is the number of pole pairs of the motor; J is the moment of inertia of the motor and the load; T L ω is the load torque. m θ is the mechanical angular velocity of the rotor; B is the coefficient of viscous friction; θ m This refers to the mechanical angle of the motor.

[0076] Step Two: The telescope control system is for low-speed applications. Traditional control methods employ three closed-loop controls: current, speed, and position. The current loop has a much higher bandwidth than the speed and position loops; therefore, PI control is used for the current loop in this invention. The open-loop transfer function of the current loop is as follows:

[0077]

[0078] Configure it as a typical Type I system and use the zero-pole cancellation method to obtain:

[0079]

[0080] Step 3: Based on the mechanical motion equations of the permanent magnet synchronous motor in Step 1, we can simultaneously obtain:

[0081]

[0082] Furthermore, output i q =u, Choose state variable x1 = θ m , x3 = f, Equation 8 is transformed into an extended state equation:

[0083]

[0084] Furthermore, based on the extended state equation obtained in step three, the extended state observer (ESO) is designed, with the following design form:

[0085]

[0086] In the formula, z1 is the estimated value of the position signal x1; e is the position estimation error of LESO; z2 is the estimated value of the velocity signal x2; z3 is the estimated value of the disturbance f; u is the system control quantity; l1, l2, and l3 are the extended state observer gains, which are determined by the system state.

[0087] Furthermore, the position-velocity loop employs a tracking differentiator to manage the transition process, with the following design:

[0088]

[0089] The steepest synthesis function fst(x1, x2, r, h) has the following specific form:

[0090]

[0091] In the formula, θ m is the input signal at the position being followed; r is the tracking acceleration factor, which determines the speed at which the given signal is tracked; h is the filtering factor, which is generally taken as an integer multiple of the integration step size; sign() is the sign function.

[0092] Furthermore, based on the design of the extended state observer and the transient process, the error feedback control law is designed in the following form:

[0093]

[0094] In the formula, v1 and v2 are the output position and velocity signals during the transient process, respectively; z1 and z2 are the position and velocity of the telescope control system estimated by the extended state observer, respectively; e1 and e2 are the position and velocity errors, respectively; β1 and β2 are the gain of the error feedback control law; fal is a nonlinear function with the following form:

[0095]

[0096] In the formula, δ is the error threshold; sign() is the sign function; and a is a constant between 0 and 1.

[0097] Furthermore, the control quantity of the active disturbance rejection controller can be obtained:

[0098]

[0099] Step 4: Mathematical Modeling of Wind Load Disturbance

[0100] This invention uses numerical simulation to establish a wind load disturbance model. Wind can generally be considered as consisting of two parts: mean wind and fluctuating wind. Mean wind is the average wind speed over a given observation period; its effect can be equivalent to a constant torque applied to the telescope rig. Fluctuating wind is a dynamic wind load, whose intensity and direction change constantly, equivalent to a time-varying torque acting on the telescope rig. Dynamic wind load can be viewed as a linear combination of different static wind loads at different stages. This invention uses the Davenport spectrum to analyze wind characteristics; fluctuating wind is obtained by passing zero-mean white noise through a Davenport filter. The Davenport spectrum is as follows:

[0101]

[0102]

[0103] In the formula, v m Here, k is the average wind speed, n is the surface drag coefficient, and n is the frequency.

[0104] Furthermore, the wind speed signal is converted into a wind force signal using Formula 18.

[0105]

[0106] In the formula, ρ is the local air density at the telescope site, and C is the density of the local air density at the telescope site. d Let A be the drag coefficient, A be the windward area of ​​the structure, and v be the wind speed.

[0107] In summary, in the two-axis drive control system of a telescope, the traditional control strategy is three-loop control, with each loop using a separate PID controller. This invention, however, integrates the velocity and position loops into a single loop using active disturbance rejection control (ADRC), thereby better ensuring trajectory tracking stability and reducing tracking errors. The inner current loop is retained to ensure the control system's rapid response capability. Based on the Davenport spectrum and the average wind speed at the telescope site, this invention proposes a method for numerically simulating wind load disturbances. Different wind load models can be performed according to the geographical location of the telescope site and the actual local wind speed, which is used for research on the telescope's resistance to wind load disturbances.

[0108] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for controlling wind disturbance in astronomical telescopes based on self-disturbance rejection, characterized in that, ADRC is introduced into the control of a three-loop servo system for a permanent magnet synchronous motor. Second-order ADRC is used to achieve composite control of position and speed. In terms of control structure, the traditional three-loop cascade control of position, speed, and current is transformed into a two-loop control of position-speed and current. The second-order ADRC provides a given position signal. The differential tracker achieves a smooth transition process, and the differential tracker outputs the extracted position signal value. and the differential value of the position signal The observed value of the output position of the extended state observer and observed values ​​of rotational speed The feedback control law allows the extended state observer to estimate the total disturbances acting on the system in real time. And apply it to the feedback control law to generate a current loop to compensate the setpoint. Output current loop setpoint after compensation The method achieves active disturbance rejection in its structure; the method includes: Step 1: Establish a mathematical model of the permanent magnet synchronous motor of the astronomical telescope control system in the dq axis synchronous coordinate system. The mathematical model includes the voltage equation, electromagnetic torque equation, and mechanical motion equation of the permanent magnet synchronous motor. Step 2: Use PI control for the current loop to obtain the open-loop transfer function of the current loop; Step 3: Based on the mechanical motion equations of the permanent magnet synchronous motor in Step 1, obtain the simultaneous equations to get the control quantity of the active disturbance rejection controller; Based on the extended state equation obtained in step 3, the extended state observer (ESO) is designed as follows: ； In the formula It is a position signal The estimated value; e is the position estimation error of LESO; It is a speed signal The estimated value; It is an estimate of the disturbance f; For system control variables; , , The gain of the extended state observer is determined by the system state; The position-velocity loop uses a tracking differentiator to manage the transition process, and the design is as follows: ； Fastest synthesis function The specific format is as follows: ； In the formula, It is the input signal at the position being followed; is the tracking acceleration factor, which determines the speed at which a given signal is tracked; h is the filtering factor, which is generally taken as an integer multiple of the integration step size; sign() is the sign function. Step 4: Establish a wind load disturbance model using numerical simulation; analyze wind characteristics using the Davenport spectrum, with pulsating wind obtained from white noise with a mean of 0 through a Davenport filter; the Davenport spectrum is in the following form: ； ； In the formula, For average wind speed, Where n is the surface drag coefficient and n is the frequency; The wind speed signal is converted into a wind force signal using the following formula: ； In the formula, The local air density at the telescope site, Let A be the drag coefficient, A be the windward area of ​​the structure, and v be the wind speed.

2. The method for controlling wind disturbance in an astronomical telescope based on self-disturbance rejection according to claim 1, characterized in that, The mathematical model in step 1 includes: Voltage equation: ； Electromagnetic torque equation: ； Electromagnetic torque equation: ； Equations of motion for machines: ； In the dq axis synchronous coordinate system ； In the formula, , These are the q-axis and d-axis voltages, respectively. , These are the q-axis and d-axis currents, respectively; R is the phase resistance of the motor. , These are the q-axis and d-axis inductances, respectively. For permanent magnet flux linkage; The electric angular velocity of the rotor; This refers to the electromagnetic torque of the motor. denoted by , where is the number of pole pairs of the motor; J is the moment of inertia of the motor and the load. This is the load torque; ω is the mechanical angular velocity of the rotor; B is the coefficient of viscous friction. This refers to the mechanical angle of the motor.

3. The method for controlling wind disturbance in an astronomical telescope based on self-disturbance rejection as described in claim 1, characterized in that, In step 2, the open-loop transfer function of the current loop is: ； Configure it as a typical Type I system and use the zero-pole cancellation method to obtain: 。 4. The method for controlling wind disturbance in an astronomical telescope based on self-disturbance rejection according to claim 1, characterized in that, In step 3, the simultaneous equations are: 。 5. The method for controlling wind disturbance in an astronomical telescope based on self-disturbance rejection according to claim 4, characterized in that, Output , , Select state variables , , Equation 8 is transformed into an extended state equation: 。 6. The method for controlling wind disturbance in an astronomical telescope based on self-disturbance rejection according to claim 1, characterized in that, Based on the design of the extended state observer and the transient process, the error feedback control law is designed in the following form: ； In the formula, , The outputs are position and velocity signals, respectively, during the transition process. These are the position and velocity of the telescope control system estimated by the extended state observer, respectively. , These are position error and velocity error, respectively. , The gain is the error feedback control law gain; fal is a nonlinear function with the following form: ； In the formula, The error threshold is used; sign() is the sign function. A constant between 0 and 1; The control input of the active disturbance rejection controller is further obtained as follows: 。

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