Dynamic modeling and robust control method for a slant-axis telescope

Abstract

The invention discloses a dynamic modeling and robust control method for a slant-axis telescope, including: identifying the structural parameters of the slant-axis telescope from finite element software; obtaining the state space expression of the telescope drive system; constructing a disturbance observer in combination with the model parameter error, the unmodeled dynamics and the wind disturbance effect on the telescope when it is actually working, and estimating the size of the disturbance on the slant-axis telescope when it is actually working through the disturbance observer; designing a slant-axis telescope controller, including a feedback controller based on error feedback and a feedforward controller based on disturbance estimation compensation; combining the disturbance observer and the slant-axis telescope controller, obtaining the angular displacement and angular velocity of the azimuth axis and the slant axis in real time, taking the angle expectation value and the corresponding measured value as the input of the disturbance observer and the slant-axis telescope controller, and continuously adjusting the position and velocity of the azimuth axis and the slant axis of the telescope. The invention can greatly improve the robustness of the system.

Description

Technical Field

[0001] The present invention relates to the field of astronomical technology, and in particular to a dynamic modeling and robust control method for a slant-axis telescope. Background Art

[0002] In recent decades, mankind has made great progress in the field of astronomy. In order to obtain better astronomical observation data, the technical requirements for astronomical instruments and equipment have become increasingly stringent, prompting engineers in the field of astronomical technology to explore new types of telescopes. Against this background, the slant-axis telescope came into being. Its special structure, which is different from the equatorial and horizontal telescopes, gives it better characteristics and is suitable for long-term stable operation in harsh environments such as the polar regions. Figure 1 As shown, the dual axes of the slant-axis telescope are non-orthogonal. Compared with the horizontal telescope and equatorial telescope with orthogonal axis design, its dynamic characteristics are more complex, which puts higher requirements on its controller design. Currently, there is little research in this field internationally.

[0003] In the field of mechanical analysis, the Euler-Lagrange method is a powerful analytical tool. This method selects appropriate generalized coordinates of the system, writes the generalized velocity of each particle in the system, and then lists the total energy expression of the system. Using the calculus of variations, a set of differential equations that can fully describe the dynamic characteristics of the system can be obtained. Compared with the traditional Newtonian mechanics method, this method does not need to consider the constraints between particles, does not require tedious force analysis, and is suitable for mechanical analysis of complex systems.

[0004] In the field of telescope control strategies, common algorithms include PID control and LQG control. PID control strategy is a classic control strategy. Its algorithm is simple to implement. In most cases, the effect can meet the requirements. The parameter setting method is perfect and is favored by many engineers. However, this method often has poor control effect on high-order systems and it is difficult to achieve high-precision control. LQG control is a linear system control strategy based on optimization theory. It can effectively suppress sensor Gaussian noise and has a good control effect on the internal modes of high-order systems. However, theory and experiments have shown that this method has poor robustness and is not suitable for nonlinear systems. Summary of the invention

[0005] In view of the deficiencies in the prior art, the present invention provides a dynamic modeling and robust control method for a slant-axis telescope. By reasonably designing a disturbance observer, the external disturbance to the system is estimated, thereby performing feedforward compensation, thereby greatly improving the robustness of the system.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for dynamic modeling and robust control of a slant-axis telescope, the method comprising the following steps:

[0008] S1, identifying the structural parameters of the slant-axis telescope from the finite element software, the structural parameters of the slant-axis telescope include the mass of the block structure, the moment of inertia matrix and the position of the center of mass offset from the rotation axis;

[0009] S2, select generalized coordinates, generate generalized velocity, generalized force and total energy expressions of the telescope drive system, use the variational method to obtain the Euler-Lagrange equation, perform coordinate transformation on the total energy expression of the telescope drive system, and obtain the state space expression of the telescope drive system;

[0010] S3, combining the model parameter errors, the unmodeled dynamics and the wind disturbances experienced by the telescope during actual operation, constructing a disturbance observer, and using the disturbance observer to estimate the magnitude of the disturbances experienced by the slant-axis telescope during actual operation;

[0011] S4, designing a slant-axis telescope controller, wherein the slant-axis telescope controller includes a feedback controller based on error feedback and a feedforward controller based on disturbance estimation compensation;

[0012] S5, in the actual control process, combines the interference observer and the slant-axis telescope controller to obtain the angular displacement and angular velocity of the azimuth axis and the slant axis in real time, takes the expected angle value and the corresponding measured value as the input of the interference observer and the slant-axis telescope controller, calculates the input of the telescope drive system, and continuously adjusts the position and speed of the azimuth axis and the slant axis of the telescope to achieve robust and high-precision control of the telescope pointing.

[0013] To optimize the above technical solutions, the specific measures taken also include:

[0014] Furthermore, in step S1, the structural parameters of the slant-axis telescope include the moment of inertia matrix I of the azimuth axis structural block a ∈R 3×3 , the moment of inertia of the inclined axis block I s ∈R 3×3 , mass of oblique axis structural block m s , the distance d that the center of mass of the inclined axis structure block deviates from the inclined axis, and the distance l from the circular trajectory of the center of mass of the inclined axis to the center of the bottom of the inclined axis.

[0015] Furthermore, in step S2, the process of obtaining the state space expression of the telescope driving system includes the following steps:

[0016] S21, select generalized coordinates, the selected generalized coordinates are the scalar angles θ of the azimuth axis a , the scalar angle θ of the oblique axis a 、Azimuth axis angular velocity ω a , oblique axis angular velocity ωs and the oblique axis velocity v s , yielding an expression for the total energy of the telescope drive system:

[0017]

[0018] The generalized force of the telescope drive system is:

[0019]

[0020] Among them, τ a is the azimuth axis driving torque, τ s is the oblique axis moment, is the sum of the azimuth axis disturbances, is the sum of oblique axis disturbances, g is the gravitational acceleration;

[0021] The Euler-Lagrange equation is obtained by using the variational method. The obtained Lagrange equation is:

[0022]

[0023] In the formula, t is time, θ is angle, is the first derivative of the angle;

[0024] By transforming the total energy expression of the telescope drive system, the state space expression of the telescope drive system is obtained as follows:

[0025]

[0026] Where d is the disturbance term, A. B u , B d , C is the corresponding parameter matrix.

[0027] Furthermore, in step S3, the description equation of the interference observer is:

[0028]

[0029] Among them, ξ is an intermediate variable, are the estimated values ​​of their corresponding variables.

[0030] Further, in step S4, the control amount of the feedback controller is The control quantity of the feedforward controller is The total control quantity is u=u f +u d , where e = x d -x,x d is the expected value of the state variable x, K p , K d are adjustable controller parameters.

[0031] The beneficial effects of the present invention are:

[0032] First, the dynamic modeling and robust control method of the slant-axis telescope of the present invention models the dynamic model of the slant-axis telescope, which reflects the dual-axis non-orthogonal characteristics of the slant-axis telescope and can describe the nonlinear dynamic characteristics of the slant-axis telescope. The present invention also converts the model into a state space model to facilitate controller design.

[0033] Second, the dynamic modeling and robust control method of the slant-axis telescope of the present invention designs a disturbance observer for disturbance factors such as external wind disturbance, unmodeled dynamics and model parameter errors to which the slant-axis telescope is subjected. The disturbance observer can estimate disturbances with arbitrary-order dynamic characteristics.

[0034] Third, the dynamic modeling and robust control method of the slant-axis telescope of the present invention designs a composite robust controller, which uses disturbance observation values ​​to design a feedforward compensation controller and uses error feedback to design a feedback controller. The combination of the two realizes the robust control of the slant-axis telescope system. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a schematic structural diagram of a slant-axis telescope according to an embodiment of the present invention.

[0036] Figure 2 It is a flow chart of the dynamic modeling and robust control method of the slant-axis telescope according to an embodiment of the present invention.

[0037] Figure 3 Schematic diagram of the coordinate system of the slant-axis telescope according to an embodiment of the present invention.

[0038] Figure 4 It is a structural block diagram of a closed-loop robust control system for a slant-axis telescope according to an embodiment of the present invention. DETAILED DESCRIPTION

[0039] The present invention will now be described in further detail with reference to the accompanying drawings.

[0040] It should be noted that the terms such as "upper", "lower", "left", "right", "front", "back", etc. cited in the invention are only for the convenience of description and are not used to limit the scope of implementation of the present invention. Changes or adjustments in their relative relationships should be regarded as the scope of implementation of the present invention without substantially changing the technical content.

[0041] See also Figure 2 The embodiment of the present invention proposes a dynamic modeling and robust control method for a slant-axis telescope, and the specific steps are as follows:

[0042] Step 1: Identify the structural parameters of the slant-axis telescope from the finite element software, including the mass of the block structure, the moment of inertia matrix, and the position of the center of mass away from the rotation axis.

[0043] Step 2: Select appropriate generalized coordinates, give expressions for generalized velocity, generalized force and total energy of the system, use the calculus of variations to obtain the Euler-Lagrange equations, and then perform appropriate coordinate transformation to obtain the state space expression of the system.

[0044] Step 3: Considering the effects of model parameter errors, unmodeled dynamics, and wind disturbances experienced by the telescope during actual operation, a disturbance observer is constructed to estimate the magnitude of the disturbance.

[0045] Step 4: Design a slant-axis telescope controller, which includes a feedback control based on error feedback and a feedforward controller based on disturbance estimate compensation.

[0046] Step 5: In actual control, sensors are used to obtain the angular displacement and angular velocity of the azimuth axis and slant axis in real time. Combined with the given trajectory signal, the controller in step 4 is used to continuously adjust the position and speed of the azimuth axis and slant axis of the telescope to achieve robust and high-precision control of the telescope pointing.

[0047] Specifically, in step 1, the parameters that need to be obtained in the finite element software are: the moment of inertia matrix I of the azimuth axis structural block a ∈R 3×3 , the moment of inertia of the inclined axis block I s ∈R 3×3 , mass of the oblique axis structural block m s , the distance d from the mass center of the slant axis structure block to the slant axis, and the distance l from the circumferential trajectory of the slant axis mass center to the center of the bottom of the slant axis. In the Ansys software, the azimuth axis part and the slant axis part of the slant axis telescope are modally analyzed respectively, and the software will output the above information.

[0048] Figure 3 Schematic diagram of the coordinate system of the oblique-axis telescope according to an embodiment of the present invention. In step 2, the selected generalized coordinates are: the scalar angle θ of the azimuth axis a The scalar angle θ with the oblique axis a ; The angular velocity of the azimuth axis is obtained as The formula for the oblique axis angular velocity is After simplification, we can get The position coordinate expression of the center of mass of the oblique axis structural block is: Its speed expression can be expressed as Where R x (·),R y (·),R z(·) represents the rotation matrix with the x-axis, y-axis and z-axis as the rotation axes, and T(·,·,·) represents the translation matrix.

[0049] In step 2, the total energy of the system includes the kinetic energy of the azimuth axis structure block and the kinetic energy of the oblique axis structure block. The kinetic energy of the azimuth axis structure block only includes translational kinetic energy, while the kinetic energy of the oblique axis structure block includes translational kinetic energy and rotational kinetic energy. The expression of the total energy is:

[0050]

[0051] The generalized forces of the system include the torque acting on the azimuth axis and the torque acting on the slant axis. For a slant-axis telescope, the external torque on the azimuth axis includes the driving torque and the external disturbance torque, and the external forces on the slant axis include the driving torque, the gravity torque and the external disturbance torque. The disturbance torque here includes real external disturbances such as wind load, as well as equivalent disturbances caused by unmodeled dynamics and parameter errors. The generalized forces of the system can be expressed as:

[0052]

[0053] where τ a is the azimuth axis driving torque, τ s is the oblique axis moment, is the sum of the azimuth axis disturbances, is the sum of oblique axis disturbances, g is the acceleration of gravity. Let q = [θ a θ s ] T , the resulting Euler-Lagrange equation is:

[0054]

[0055] The solution of this equation is relatively complex, and its rearranged form is given here. and Indicates I a and I s The elements of , i,j∈1,2,3, have:

[0056]

[0057] Where M(q) is the mass matrix, which is related to the moment of inertia and mass of the telescope structure block and the rotation angle of the telescope. The specific expression is:

[0058]

[0059] in,

[0060]

[0061]

[0062] is the cross-term matrix, which represents the coupling relationship between the two axes and is related to the Coriolis force and the centrifugal force. The specific expression is

[0063]

[0064] in

[0065]

[0066]

[0067] G(q) is the gravity matrix, which is related to the mass of the oblique axis structural block and the oblique axis angle. Its specific expression is:

[0068]

[0069] τ=[τ a ,τ s ] T , is the input torque vector, is the disturbance torque vector. In order to design the controller more conveniently, the above equation is written in the standard state space form as follows:

[0070]

[0071] in, is the state variable, is the disturbance term, u=[τ a ,τ s ] T For input, are output items, A and B u , B d , C is the corresponding parameter matrix, and its expressions are C=I 4×4 .

[0072] In step 3, it is necessary to build a disturbance observer to estimate the disturbance received by the system in preparation for subsequent disturbance compensation. First, build a state observer, which is used to obtain the predicted value of the state and then the predicted value of the output. When building the state observer, we assume that the estimated value of the disturbance has been obtained. Based on the state space expression obtained in step 2, we can construct the following state observer:

[0073]

[0074] Where L xis the observer parameter. Different parameters can obtain different parameter estimation convergence effects. are the estimated values ​​of their corresponding variables respectively. After obtaining the predicted value of the output, the disturbance observer can be further designed. For this purpose, an intermediate variable ξ describing the predicted value of the disturbance is introduced, and the following observer is constructed:

[0075]

[0076] The parameters W and V are used to describe the intrinsic dynamics of the disturbance variable. The setting of the parameters can be based on a priori assumptions, such as the bandwidth of the disturbance. The overall disturbance observation equation is as follows:

[0077]

[0078] In step 4, the feedback controller and feedforward controller are designed according to the dynamic characteristics of the system and the disturbance observation value. The control quantity of the feedback controller is The control quantity of feedforward control is The total control quantity is u=u f +u d , where e = x d -x,x d is the expected value of the state variable x, K p and K d are adjustable controller parameters.

[0079] In step 5, if Figure 4 As shown in FIG. 1 , the specific process of feedback control is as follows: using angle sensors such as encoders to measure the angular displacement and angular velocity of the azimuth axis and the tilt axis of the telescope, comparing the measured value with the expected value, and updating the output value of the controller and the observer. The observer predicts the system state based on the dynamic model obtained in step 1 and step 2, and estimates the disturbance of the system by comparing the predicted value with the actual measured value. The controller performs feedforward compensation based on the estimated value of the disturbance, and performs feedback control based on the error between the expected value and the measured value to ensure the convergence of the variables.

[0080] The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A dynamic modeling and robust control method for a slant-axis telescope, characterized in that: The method comprises the following steps: S1, identifying the structural parameters of the slant-axis telescope from finite element software, the structural parameters of the slant-axis telescope including the mass of the block structure, the moment of inertia matrix and the position of the center of mass offset from the axis of rotation; the structural parameters of the slant-axis telescope include the moment of inertia matrix I of the azimuth axis structure block a ∈R 3×3 , the moment of inertia of the inclined axis block I s ∈R 3×3 , mass of oblique axis structural block m s , the distance d from the center of mass of the oblique axis structure block to the oblique axis and the distance l from the circular trajectory of the center of mass of the oblique axis to the center of the bottom of the oblique axis; S2, selecting generalized coordinates, generating expressions of generalized velocity, generalized force and total energy of the telescope drive system, applying the variational method to obtain the Euler-Lagrange equation, performing coordinate transformation on the total energy expression of the telescope drive system, and obtaining the state space expression of the telescope drive system; comprising the following steps: S21, select generalized coordinates, the selected generalized coordinates are the scalar angles θ of the azimuth axis a , the scalar angle θ of the oblique axis a 、Azimuth axis angular velocity ω a , oblique axis angular velocity ω s and the oblique axis velocity v s , yielding an expression for the total energy of the telescope drive system: The generalized force of the telescope drive system is: Among them, τ a is the azimuth axis driving torque, τ s is the moment of the oblique axis, is the sum of the azimuth axis disturbances, is the sum of oblique axis disturbances, g is the gravitational acceleration; The Euler-Lagrange equation is obtained by using the variational method. The obtained Lagrange equation is: In the formula, t is time, θ is angle, is the first derivative of the angle; By transforming the total energy expression of the telescope drive system, the state space expression of the telescope drive system is obtained as follows: Where d is the disturbance term, A. B u , B d , C is the corresponding parameter matrix; S3, combining the model parameter errors, the unmodeled dynamics and the wind disturbances experienced by the telescope during actual operation, constructing a disturbance observer, and using the disturbance observer to estimate the magnitude of the disturbances experienced by the slant-axis telescope during actual operation; The description equation of the disturbance observer is: Among them, ξ is an intermediate variable, are the estimated values ​​of their corresponding variables respectively; S4, designing a slant-axis telescope controller, wherein the slant-axis telescope controller includes a feedback controller based on error feedback and a feedforward controller based on disturbance estimation compensation; The control quantity of the feedback controller is The control quantity of the feedforward controller is The total control quantity is u=u f +u d , where e = x d -x,x d is the expected value of the state variable x, K p , K d is the adjustable controller parameter; S5, in the actual control process, combines the interference observer and the slant-axis telescope controller to obtain the angular displacement and angular velocity of the azimuth axis and the slant axis in real time, takes the expected angle value and the corresponding measured value as the input of the interference observer and the slant-axis telescope controller, calculates the input of the telescope drive system, and continuously adjusts the position and speed of the azimuth axis and the slant axis of the telescope to achieve robust and high-precision control of the telescope pointing.

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