Fixed time preset performance adaptive control system of large-aperture space telescope

Abstract

The invention relates to a control system, in particular to a fixed time preset performance self-adaptive control system of a large-aperture space telescope. Comprising a first subtracter, a first error conversion unit, a first fixed time convergence preset performance function device, a sliding mode surface construction unit, a second error conversion unit, a second fixed time convergence preset performance function device, a fixed time controller, an adder, a neural network state observer NNSO and a second subtracter. According to the method, the fixed time convergence preset performance function is adopted, and compared with an existing asymptotic convergence preset performance function, the convergence speed is higher, and the convergence time is irrelevant to the size of an initial value; compared with an existing fixed time convergence performance function, the structure is simpler, and the derivative is continuous; meanwhile, a neural network state observer NNSO is adopted, and the estimation error of the NNSO is smaller than that of the NN.

Description

Technical Field

[0001] The present invention relates to a control system, and more particularly to a fixed-time preset performance adaptive control system for a large-aperture space telescope. Background Art

[0002] With the development of technology and the increasingly fierce competition in the space field, space situation awareness plays an increasingly important role in national security and economic development. As an important part of space situation awareness, space telescopes have the advantages of being unaffected by the atmosphere, operating all-weather, and performing surveillance tasks over a wide area. With the improvement of detection requirements and launch capabilities, it has become possible to improve the resolution by increasing the telescope aperture. Although most of the currently orbiting telescopes have relatively small apertures, over time, large-aperture space telescopes have gradually been applied and will play an increasingly important role in future space technology. High-precision and high-reliability control technology is one of the key technologies for large-aperture space telescopes. Through the movement of the two axes of the telescope's pitch axis and azimuth axis, all-round monitoring of space targets, as well as tasks such as searching and capturing large-range space targets, precise pointing and locking tracking of targets, etc., can be achieved.

[0003] Different from large-aperture ground-based telescopes, due to the limitation of launch capabilities, large-aperture space telescopes need to pursue extreme lightweight design. The system has low stiffness and flexible attachments such as sunshades. The system resonance frequency is low and the flexible attachments at the end are extremely prone to vibration, severely restricting the system control performance and even possibly causing safety problems. And due to structural limitations, only position sensors are installed on the motor side of the large-aperture space telescope, which is a typical partially state-feedback nonlinear high-order system. In addition, there are also the influences of nonlinear friction, model uncertainty, installation unbalanced torque, vacuum and weightlessness environments, and winding torque. These adverse factors not only severely limit the control accuracy and closed-loop bandwidth of large-aperture space telescopes, but may even cause the system to be unstable. The research on closed-loop control technology for current ground-based large-aperture telescopes has been relatively mature, while the research on control technology for large-aperture space telescopes is still less.

[0004] In the design of large-aperture ground-based telescope controllers, the telescope is usually regarded as a dual-inertia system. The difficulty of its control lies in resonance suppression. Common resonance suppression methods include notch filters, dual second-order filters, acceleration feedback, and active disturbance rejection control (ADRC). Since ground-based telescopes are fixed on the ground and generally do not use flexible accessories, the closed-loop control of large-aperture ground-based telescopes does not need to consider the influence of terminal vibration. In addition, ground-based telescopes use liquid lubrication and have a good friction environment. Therefore, the existing control methods for large-aperture ground-based telescopes are not suitable for large-aperture space telescopes with flexible accessories involved in this study. It is necessary to explore control strategies suitable for large-aperture space telescopes based on the existing research on large-aperture ground-based telescope control methods and the latest research results in the field of control. Neural networks (NNs) can approximate continuous functions with arbitrary precision and have obvious advantages in dealing with model uncertainties. Therefore, NNs have broad application prospects in dealing with uncertainties and resonances of large-aperture space telescopes.

[0005] At present, most telescope controls can only obtain the results of asymptotic stability or finite-time stability of the closed-loop system. Although finite-time stability has better control quality than asymptotic stability, the convergence time of the trajectory tracking error of finite-time stability is seriously dependent on the initial conditions of the system. Compared with finite-time stable control, the upper bound of the convergence time of fixed-time stable control of nonlinear systems is independent of the initial conditions of the system and is a priori uniformly bounded. In addition, fixed-time stable control of nonlinear systems also has excellent control qualities such as faster transition process and higher steady-state accuracy. Thanks to the above advantages, fixed-time stability has great potential in improving the closed-loop bandwidth and control accuracy of large-aperture space telescopes.

[0006] On the other hand, the existing telescope control system generally only focuses on the steady-state performance of the system, ignoring the system transient performance such as convergence rate and overshoot, which also affect the quality of motion control. It is well known that increasing the control torque to improve the transient convergence rate of trajectory tracking error is an effective means to improve the closed-loop bandwidth of the telescope, but this will lead to the generation and increase of overshoot. Excessive overshoot is harmful to the system and may even cause irreversible damage to the system structure. In addition, unreasonable convergence rate and overshoot will not only excite the resonance of the flexible attachment and cause vibration at the end of the telescope, but also have an adverse effect on the attitude control of the satellite. These adverse effects will eventually reduce the control accuracy of the telescope and may even threaten the on-orbit safety of the telescope and satellite. Preset performance control is an important method to study the transient and steady-state performance of nonlinear systems. It provides the possibility of improving the response speed of the closed-loop system of large-aperture space telescopes while maintaining small overshoot and reducing terminal vibration.

[0007] In summary, by combining NN, a fixed-time convergence strategy, and a preset performance control method, a control system suitable for large-aperture space telescopes is proposed, which has important value for the on-orbit application of large-aperture space telescopes. Summary of the Invention

[0008] The object of the present invention is to solve the technical problems of existing telescope control systems, which can only obtain the results of asymptotic stability or finite-time stability of the closed-loop system, seriously rely on the initial conditions of the system, and only focus on the steady-state performance of the system, ignoring the convergence rate and overshoot, etc., which also affect the motion control quality and are easy to cause the generation and increase of overshoot, thus exciting the resonance of flexible accessories, causing vibration at the end of the telescope, and then having an adverse impact on the attitude control of the satellite, ultimately reducing the control accuracy of the telescope and even threatening the on-orbit safety of the telescope and the satellite. Therefore, a fixed-time preset performance adaptive control system for a large-aperture space telescope is provided.

[0009] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0010] A fixed-time preset performance adaptive control system for a large-aperture space telescope, characterized in that:

[0011] It includes a first subtractor, a first error conversion unit, a first fixed-time convergence preset performance function generator, a sliding mode surface construction unit, a second error conversion unit, a second fixed-time convergence preset performance function generator, a fixed-time controller, an adder, a neural network state observer NNSO, and a second subtractor;

[0012] The two input ends of the first subtractor are respectively connected to the external reference input r and the output x1 of the controlled object, and the output end outputs the position tracking error e1 to the input end of the first error conversion unit;

[0013] The two output ends of the first fixed-time convergence preset performance function generator are respectively connected to the control end of the first error conversion unit and the first control end of the fixed-time controller;

[0014] The two input ends of the sliding mode surface construction unit are respectively connected to the converted tracking error e output by the first error conversion unit 1r and the position tracking error e2 output by the second subtractor, and the output end outputs the sliding mode surface s to the input end of the second error conversion unit;

[0015] The two output ends of the second fixed-time convergence preset performance function generator are respectively connected to the control end of the second error conversion unit and the second control end of the fixed-time controller;

[0016] The two input ends of the fixed-time controller are respectively connected to the converted sliding mode surface s output by the second error conversion unit rLumped disturbance estimation output by the neural network state observer NNSO The output of the output end outputs the control output u to the adder and the first input end of the neural network state observer NNSO respectively;

[0017] The second input end of the adder is connected to the external disturbance d, and the output end is connected to the control end of the controlled object;

[0018] The second input end of the neural network state observer NNSO and the first input end of the second subtractor are respectively connected to the output x2 of the controlled object;

[0019] The second input end of the second subtractor is connected to the derivative of the reference input

[0020] Furthermore, the state equation of the neural network state observer NNSO is:

[0021]

[0022] In the formula: is the actual network weight; is the transpose matrix of; h(σ) is the Gaussian function; σ is the neural network input; b is the control gain; β i is the observer gain, i = 1 and 2; is the state of NNSO; sign() is the sign function; μ > 1.

[0023] Furthermore, the control law of the fixed-time controller is:

[0024]

[0025] In the formula: u0 and u sm are both auxiliary variables; ω s = s / ρ s ; ρ e and ρ s are the functions in the first fixed-time convergence preset performance functioner and the second fixed-time convergence preset performance functioner respectively; λ1, λ2, α1 and α2 are all constants, and λ1 > 0, λ2 > 0, α1 > 0, 0 < α2 < 1; ω e = e1 / ρ e ; k1, k2 are control parameters; v(ω e ) is the derivative of the function ρ e in the first fixed-time convergence preset performance functioner; δ is a constant, δ > 0.

[0026] Furthermore, satisfies the following update law:

[0027]

[0028] where: Γ is the neural network parameter; ν(ω s ) is the derivative of the function ρ in the second fixed-time convergence preset performance function s .

[0029] Furthermore, the sliding mode surface s of the sliding mode surface creation unit satisfies the following equation:

[0030]

[0031] Furthermore, the function ρ in the first fixed-time convergence preset performance function e and the function ρ in the second fixed-time convergence preset performance function s both satisfy the following equation:

[0032]

[0033] where: ρ0 and ρ ∞ are both pre-selected positive constants and satisfy 0 < ρ ∞ < ρ < ρ0, l1 > 0, l2 > 0; z is an auxiliary variable; is the error between the auxiliary variable z and the positive constant ρ0; is the error between the auxiliary variable z and the positive constant ρ ∞ ; ρ is a preset performance function with respect to time t, which are the functions ρ in the first fixed-time convergence preset performance function e and the function ρ in the second fixed-time convergence preset performance function s respectively.

[0034] Furthermore, both the first error conversion unit and the second error conversion unit satisfy the following equation:

[0035]

[0036] where: is the overshoot exponent, e(0) is the initial error; x is the converted error, corresponding to the position tracking error e1 and the sliding mode surface s respectively; ψ(x) is the error conversion function.

[0037] The beneficial effects of the present invention are:

[0038] 1) The present invention adopts the neural network state observer NNSO, which has a smaller estimation error than the NN;

[0039] 2) The present invention adopts the fixed-time convergence preset performance function. Compared with the existing asymptotically convergent preset performance function, it has a faster convergence speed and the convergence time is independent of the initial value size; compared with the existing fixed-time convergence performance function, its structure is simpler and the derivative is continuous;

[0040] 3) The present invention adopts a fixed-time convergence preset performance control law, which has stronger disturbance rejection ability compared with the existing preset performance control laws.

[0041] 4) For a space telescope with a flexible attachment at the end, the present invention proposes to use preset-time control to suppress the end vibration. This method does not require an accurate model and has stronger robustness. Description of the Drawings

[0042] Figure 1 is a schematic structural diagram of an existing large-aperture space telescope;

[0043] Figure 2 is an equivalent three-inertia system model diagram of an existing large-aperture space telescope;

[0044] Figure 3 is a schematic structural diagram of an embodiment of the present invention;

[0045] Figure 4 is a step response comparison diagram of the motor end angle in an embodiment of the present invention;

[0046] Figure 5 is a step response comparison diagram of the end angle of the sunshade in an embodiment of the present invention. Detailed Embodiment

[0047] To make the objectives, advantages, and features of the present invention clearer, the following further elaborates on a fixed-time preset performance adaptive control system for a large-aperture space telescope proposed by the present invention in conjunction with the accompanying drawings and specific embodiments. According to the following detailed embodiments, the advantages and features of the present invention will be clearer.

[0048] (1) Dynamics Model of Large-Aperture Space Telescope

[0049] According to Figure 1 the structure of the large-aperture space telescope shown, including a sunshade, an optical load, a pitch axis and the corresponding encoder, a U-shaped frame, an azimuth axis and the corresponding encoder, it can be equivalently regarded as a three-inertia system as Figure 2 shown

[0050] Equivalent motor inertia J M is connected to the equivalent load inertia J L through a spring with a stiffness of K L ; the equivalent load inertia J L is connected to the equivalent sunshade inertia J H through a spring with a stiffness of K H . The output torque of the motor is τ, and the viscous damping coefficient of the motor is B M . θ M 、ω Mare the angular position and angular velocity of the motor, respectively, θ L , ω L are the angular position and angular velocity of the load, respectively, θ H , ω H are the angular position and angular velocity of the end of the light shield, respectively.

[0051] According to Figure 2 the following dynamic model can be obtained:

[0052]

[0053] Considering the effects of disturbances and model uncertainties, Equation (1) can be rewritten as:

[0054]

[0055] where: N H , N L , N M represent the model uncertainties on the light shield, load, and motor sides, respectively, and d is the disturbance torque acting on the motor, including frictional force and external disturbances.

[0056] (2) Fixed-time convergence preset performance function and error transformation design

[0057] For any generalized tracking error e(t), the preset performance index is designed as follows:

[0058]

[0059] where: e is the error variable to be constrained, and ρ is the preset performance function with respect to time t. and n are mathematically described as:

[0060]

[0061] where: is the overshoot exponent, and e(0) is the initial error. The fixed-time convergence preset performance function is designed as follows:

[0062]

[0063] where: ρ0 and ρ ∞ are both pre-selected positive constants and satisfy 0 < ρ ∞ < ρ < ρ0, l1 > 0, l2 > 0; z is the auxiliary variable; is the error between the auxiliary variable z and the positive constant ρ0; is the error between the auxiliary variable z and the positive constant ρ ∞ ; p1 and p2 satisfy p1 = 1 + 1 / m and p2 = 1 - 1 / m and m > 1.

[0064] In the preset performance control, generally, an error conversion function is used to convert the error, so as to achieve the equivalent conversion from the constrained space to the unconstrained space. A commonly used error conversion function is:

[0065]

[0066] The derivative of the above formula is:

[0067]

[0068] (3) Design of neural network state observer NNSO

[0069] Step 1: Let and assume that it can be approximated by a neural network, that is:

[0070]

[0071] where: W T is the transpose matrix of the neural network weight, ε is the neural network approximation error, σ is the neural network input, and h(σ) is the Gaussian function:

[0072]

[0073] where: δ > 0 and c j are constants.

[0074] Step 2: For the nonlinear system (2), let x1 = θ M , The state space expression of (2) is:

[0075]

[0076] Use W to represent the ideal network weight, ε is the neural network approximation error, is the control gain, u = τ is the control input, and y is the system output.

[0077] Step 3: Design the NNSO as follows:

[0078]

[0079] where: is the state of the NNSO; β i is the observer gain, i = 1 and 2; μ > 1; is the actual network weight; is the transpose matrix of.

[0080] (4) Fixed-time controller design

[0081] Step 1: Define the following error variables

[0082]

[0083] To suppress the occurrence of end vibration and ensure sufficient control bandwidth and disturbance rejection performance, it is necessary to constrain the output state of the motor. First, constrain the position tracking error e1

[0084] e 1r = ψ(ω e ) (13)

[0085] where ω e = e1 / ρ e , ρ e is defined as in (5). Differentiating the above equation gives the transformed tracking error e 1r as:

[0086]

[0087] Step 2: Define the following sliding surface s:

[0088]

[0089] where λ1 > 0, λ2 > 0, α1 > 1, 0 < α2 < 1 are constants;

[0090]

[0091] where δ > 0 is a constant. Further constrain the sliding surface s, and then there is the transformed sliding surface s r :

[0092] s r = ψ(ω s ) (17)

[0093] where ω s = s / ρ s , ρ s is defined as in (5). Differentiating the above equation gives:

[0094]

[0095] Step 3: The control law of the fixed-time controller is designed as:

[0096]

[0097] where u0 and u sm are auxiliary variables, satisfying the following update law:

[0098]

[0099] where: Γ is the neural network parameter; ν(ω s ) is the derivative of the fixed-time convergence preset performance function ρ s .

[0100] The fixed-time convergence preset performance function (5), error transformation (6), NNSO (11), control law (19), and adaptive update law (20) together constitute a fixed-time preset performance adaptive control system, and its structural block diagram is as Figure 3 shown. This system includes a first subtractor, a first error conversion unit, a first fixed-time convergence preset performance function unit, a sliding mode surface construction unit, a second error conversion unit, a second fixed-time convergence preset performance function unit, a fixed-time controller, an adder, a neural network state observer NNSO, and a second subtractor;

[0101] The two input terminals of the first subtractor are respectively connected to the external reference input r and the output x1 of the controlled object, and the output terminal outputs the position tracking error e1 to the input terminal of the first error conversion unit;

[0102] The two output terminals of the first fixed-time convergence preset performance function unit are respectively connected to the control terminal of the first error conversion unit and the first control terminal of the fixed-time controller;

[0103] The two input terminals of the sliding mode surface construction unit are respectively connected to the transformed tracking error e 1r output by the first error conversion unit and the position tracking error e2 output by the second subtractor, and the output terminal outputs the sliding mode surface s to the input terminal of the second error conversion unit;

[0104] The two output terminals of the second fixed-time convergence preset performance function unit are respectively connected to the control terminal of the second error conversion unit and the second control terminal of the fixed-time controller;

[0105] The two input terminals of the fixed-time controller are respectively connected to the transformed sliding mode surface s r output by the second error conversion unit and the lumped disturbance estimation output by the neural network state observer NNSO. The output terminal outputs the control output u to the adder and the first input terminal of the neural network state observer NNSO respectively;

[0106] The second input terminal of the adder is connected to the external disturbance d, and the output terminal is connected to the control terminal of the controlled object;

[0107] The second input terminal of the neural network state observer NNSO and the first input terminal of the second subtractor are respectively connected to the output x2 of the controlled object;

[0108] The second input terminal of the second subtractor is connected to the reference input after the first-order derivative

[0109] This embodiment illustrates the implementation process of the present invention in combination with the position control problem of a large-aperture space telescope. Since the two axes of the telescope are orthogonally installed, only the single-axis control results are shown here.

[0110] The parameters of the preset performance function for fixed-time convergence are set to ρ e : l1 = l2 = 2.25, ρ0 = 0.2, p1 = 1.5, p2 = 0.5, ρ ∞ = |e1(0)| + 10; ρ s : l1 = l2 = 5, ρ0 = 0.1, p1 = 1.5, p2 = 0.5, ρ ∞ = |s1(0)| + 5.

[0111] The controller parameters are selected as k1 = 6, k2 = 1, λ1 = 1, λ2 = 0.25, β1 = 100, β2 = 10, α1 = 1.5, α2 = 0.75, μ = 4 / 3.

[0112] The parameters of the controlled object are J M = 15 kg·m 2 、J L = 10 kg·m 2 、J H = 1.25 kg·m 2 、B M = 0.056 N·m·s / rad、K L = 131976 N·m / rad、K H = 5,476·m / rad.

[0113] The results of the simulation experiments are as shown in Figure 4 and Figure 5 . It can be seen from Figure 4 and Figure 5 that ADRC fails to effectively suppress resonance and end vibration, resulting in significant oscillations in the step responses at the motor end and the end of the sunshade. However, the proposed new controller better suppresses resonance and vibration, so there is no oscillation phenomenon. Moreover, the new controller has no overshoot.

Claims

1. A fixed time preset performance adaptive control system for a large aperture space telescope, characterized in that: It includes a first subtractor, a first error conversion unit, a first fixed time convergence preset performance function, a sliding surface construction unit, a second error conversion unit, a second fixed time convergence preset performance function, a fixed time controller, an adder, a neural network state observer NNSO and a second subtractor; The two input ends of the first subtractor are respectively connected to the external reference input r and the output x1 of the controlled object, and the output end outputs the position tracking error e1 to the input end of the first error conversion unit; Two output terminals of the first fixed time convergence preset performance function device are respectively connected to the control terminal of the first error conversion unit and the first control terminal of the fixed time controller; The two input ends of the sliding surface construction unit are respectively connected to the conversion tracking error e output by the first error conversion unit 1r The output end outputs the sliding surface s to the input end of the second error conversion unit; Two output terminals of the second fixed time convergence preset performance function device are respectively connected to the control terminal of the second error conversion unit and the second control terminal of the fixed time controller; The two input ends of the fixed time controller are respectively connected to the converted sliding surface s output by the second error conversion unit r and the lumped disturbance estimation of the output of the neural network state observer NNSO The output terminal outputs the control output u to the adder and the first input terminal of the neural network state observer NNSO respectively; The second input terminal of the adder is connected to the external disturbance d, and the output terminal is connected to the control terminal of the controlled object; The second input terminal of the neural network state observer NNSO and the first input terminal of the second subtractor are respectively connected to the output x2 of the controlled object; The second input terminal of the second subtractor is connected to the derivative of the reference input 2. The fixed time preset performance adaptive control system for a large aperture space telescope according to claim 1, characterized in that: The state equation of the neural network state observer NNSO is: Where: is the actual network weight; for The transposed matrix; h(σ) is the Gaussian function; σ is the neural network input; b is the control gain; β i is the observer gain, i = 1 and 2; is the state of NNSO; sign() is the sign function; μ>

1.

3. The fixed time preset performance adaptive control system for a large aperture space telescope according to claim 1 or 2, characterized in that: The control law of the fixed time controller is: Where: u0 and u sm All are auxiliary variables; ω s =s / ρ s ρ e and ρ s are functions in the first fixed time convergence preset performance function device and the second fixed time convergence preset performance function device respectively; λ1, λ2, α1 and α2 are all constants, and λ1>0, λ2>0, α1>0, 0<α2<1; ω e =e1 / ρ e ; k1, k2 are control parameters; v(ω e ) is the function ρ in the first fixed time convergence preset performance function e The derivative of ; δ is a constant, δ>0.

4. The fixed time preset performance adaptive control system for a large aperture space telescope according to claim 3, characterized in that: Said The following update law is satisfied: Where: Γ is the neural network parameter; v(ω s ) is the function ρ in the second fixed time convergence preset performance function s The derivative of .

5. The fixed time preset performance adaptive control system for a large aperture space telescope according to claim 4, characterized in that: The sliding surface s of the sliding surface creation unit satisfies the following equation:

6. The fixed time preset performance adaptive control system for a large aperture space telescope according to claim 5, characterized in that: The first fixed time converges the preset performance function function ρ e and the second fixed time convergence preset performance function function ρ s All satisfy the following equations: Where: ρ0 and ρ ∞ are all pre-selected normal numbers and satisfy 0<ρ ∞ <ρ<ρ0, l1>0, l2>0; z is an auxiliary variable; is the error between the auxiliary variable z and the positive constant ρ0; are auxiliary variables z and positive constant ρ ∞ The error; ρ is the preset performance function about time t, which are the function ρ in the first fixed time convergence preset performance function device e and the function ρ in the second fixed time convergence preset performance function s .

7. The fixed time preset performance adaptive control system for a large aperture space telescope according to claim 6, characterized in that: The first error conversion unit and the second error conversion unit both satisfy the following equation: Where: θ is the overshoot index, e(0) is the initial error; x is the converted error, corresponding to the position tracking error e1 and the sliding surface s respectively; ψ(x) is the error conversion function.

Images