A time-scale separation based design method for overactuated flight controllers

Abstract

The application discloses a time scale separation-based overload driver design method, which respectively designs a long-period subsystem and a short-period subsystem to process long-period state variables and short-period state variables in a high dynamic flight process, so as to realize fast and accurate tracking of an overload instruction of a super-long-range guided rocket in a high dynamic motion process and guarantee that the super-long-range guided rocket has good stability and robustness.

Description

Technical Field

[0001] The invention belongs to the field of rocket technology, and in particular relates to a method for designing an overload autopilot based on time scale separation. Background Art

[0002] For ultra-long-range guided rockets with a range exceeding 500 km, the flight envelope expands as the range increases, with altitudes extending from the ground to tens of kilometers, and speeds ranging from tens of meters per second to several Mach. Control system parameters fluctuate dramatically, and the harsh flight environment exacerbates the impact of nonlinear perturbations, such as aerodynamic nonlinearity and servo failures, on the rocket's flight process. These adverse factors affecting rocket stability control necessitate the development of robust and adaptive autopilots to ensure accurate and stable tracking of control signals during highly dynamic flight. Summary of the Invention

[0003] In order to overcome the shortcomings of the existing technology, the present invention provides an overload autopilot design method based on time scale separation. By designing a long-period subsystem and a short-period subsystem respectively to process the long-period state variables and short-period state variables in the high-dynamic flight process, the ultra-long-range guided rocket can quickly and accurately track the overload instructions during the high-dynamic movement process, thereby ensuring that the ultra-long-range guided rocket has good stability and robustness.

[0004] The technical solutions adopted by the present invention to solve the technical problems are as follows:

[0005] Step 1: During the high-dynamic flight of the ultra-long-range guided rocket using tail-fin control STT, the servo system is considered as a first-order link, and the pitch channel control model is shown in Equation (1):

[0006]

[0007] Where α is the angle of attack, ω z is the pitch angular velocity, δ z is the rudder deflection angle, δ zc is the steering gear deflection command, M is the rocket Mach number, ω a is the natural frequency of the servo, K α and They are defined as:

[0008] K α =0.7PS / mυ s

[0009]

[0010] Where, P = P0(1-0.0065h / T0) 5.2561is the static aerodynamic pressure, S is the characteristic area of ​​the rocket, m is the mass of the rocket, I y is the pitch moment of inertia, d r is the characteristic diameter, υ s is the speed of sound; aerodynamic coefficient C n (α,δ z ,M) and aerodynamic moment coefficient C m (α,δ z ,M) are defined as follows:

[0011]

[0012] Among them, a n 、b n 、c n d n 、a m 、b m 、c m and d m All are aerodynamic constants, obtained from wind tunnel tests;

[0013] Rocket overload is expressed as:

[0014]

[0015] in, The real-time update model of Mach number is:

[0016]

[0017] Among them, c y is the longitudinal drag coefficient;

[0018] In actual engineering, the calculation process of rocket overload is:

[0019] a y =(0.7)PSC a / m (6)

[0020] Among them, C a is the drag coefficient;

[0021] The height variation model is as follows:

[0022]

[0023] Where g is the acceleration due to gravity, θ m is the ballistic inclination angle;

[0024] Step 2: Design a control structure for the ultra-long-range guided rocket based on time scale separation;

[0025] Step 2-1: Long-period subsystem;

[0026] In the time scale separation structure, the overload change dynamics model is regarded as a long-period subsystem, and Equation (4) is adjusted to:

[0027]

[0028] in,

[0029]

[0030] The last term d in formula (8) η ' represents the external disturbance caused by measurement noise and servo failure;

[0031] definition:

[0032]

[0033] in, and The coefficients are and Initial value;

[0034] At this time, formula (8) is rewritten as:

[0035]

[0036] in, represents the long-period subsystem disturbance.

[0037] At this time, Equation (10) is the dynamic model of the long-period subsystem of the longitudinal channel of the ultra-long-range guided rocket;

[0038] Step 2-2: Short-term subsystem;

[0039] In the time scale separation structure, the dynamic model representing the change of pitch angular velocity is regarded as a short-period subsystem, and the system model is adjusted as follows:

[0040]

[0041] in,

[0042]

[0043] The last term of formula (11) Indicates possible external disturbances;

[0044] Simplifying the system model, equation (11) is adjusted to:

[0045]

[0046] in, and They are and The initial value of is the normalized disturbance of the short-period subsystem, satisfying:

[0047] At this time, Equation (12) is the dynamic model of the short-period subsystem of the longitudinal channel of the ultra-long-range guided rocket;

[0048] Step 3: Design of overload pilot for ultra-long-range guided rocket based on time scale separation;

[0049] Step 3-1: Design an adaptive robust controller for the long-period subsystem;

[0050] The pitch velocity ω z It is regarded as a virtual control of the long-period subsystem (10);

[0051] Design the following first-order sliding surface:

[0052] s1=a y -a y * (13)

[0053] Among them, a y * Indicates the expected or required acceleration;

[0054] By taking the derivative of formula (13), we can get:

[0055]

[0056] Pitch angular velocity command ω zc Expressed as:

[0057]

[0058] Among them, c1>0, γ1>0, k1>0 and k2>0 are all design parameters. is the long-period subsystem disturbance The upper bound of can be obtained by adaptive term estimation, and the update process is:

[0059]

[0060] Step 3-2: Design an adaptive robust controller for the short-period subsystem;

[0061] Control the pitch angular velocity ω zc Tracking desired pitch angular velocity ω z , ignoring the first-order servo system, the rudder deflection command δ is required zc Considered as the real rudder deflection δ z ;

[0062] Design a new sliding surface:

[0063] s2=ω z -ω zc (17)

[0064] Derivative of the sliding surface formula (17):

[0065]

[0066] Rudder deflection δ z Expressed as:

[0067]

[0068] Among them, c2>0, γ2>0, k3>0 and k4>0 are design parameters. is the short-period subsystem disturbance The upper bound of can be obtained by adaptive term estimation, and the update process is:

[0069]

[0070] At this time, the system controller using time scale separation is expressed as:

[0071]

[0072] s2=ω z -ω zc

[0073]

[0074] Step 3-3: Design the tracking differentiator;

[0075] Design a tracking differentiator for the estimation process:

[0076]

[0077] Among them, r0>0 is the control parameter, υ1 and υ2 are the state variables of the tracking differentiator;

[0078] The sign function sign(·) is replaced by the sigmoid function sgmf(·), which is defined as:

[0079]

[0080] Among them, ε represents the boundary layer width of the sigmoid function.

[0081] Preferably, k=180 / π.

[0082] Preferably, the ω z and a y Obtained by angular velocity gyroscope and accelerometer.

[0083] Preferably, the a y * Indicates the expected or required acceleration, which can be preset or calculated by the guidance law.

[0084] The beneficial effects of the present invention are as follows:

[0085] (1) The present invention adopts a time-scale separation autopilot structure, which fundamentally avoids the adverse effects caused by the time-scale incoordination between the overload change dynamics model and the pitch angular velocity change dynamics model during the high-dynamic flight of ultra-long-range guided rockets, and thus enables the rocket overload autopilot to have good control performance;

[0086] (2) Since adaptive terms and sliding mode terms are designed for the long-period subsystem and short-period subsystem of the autopilot respectively, the autopilot has good adaptability and robustness as a whole. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Figure 1 This is a framework diagram of the method of the present invention.

[0088] Figure 2 Comparison curves of the adaptive robust adaptive autopilot using time scale separation, the FSMC overload autopilot, and the FSMC autopilot with ESO under the simulation conditions of the embodiment, (a) acceleration change curve, (b) angle of attack change curve, (c) rudder angle change curve, and (d) adaptive term curve.

[0089] Figure 3 Monte Carlo simulation experimental results of the adaptive robust adaptive autopilot using time scale separation, (a) acceleration change curve, (b) angle of attack change curve, (c) rudder angle change curve, and (d) adaptive term curve. DETAILED DESCRIPTION

[0090] The present invention will be further described below with reference to the accompanying drawings and examples.

[0091] The purpose of the present invention is to provide a time scale separated adaptive sliding mode overload autopilot design method for ultra-long-range guided rockets, which can ensure that the ultra-long-range guided rockets can quickly and accurately track overload instructions during high dynamic motion.

[0092] The method of the present invention respectively designs a long-period subsystem and a short-period subsystem to deal with state variables of different periods in the ultra-long-range guided rocket dynamics model, and designs adaptive terms and sliding mode terms in each subsystem, which is conducive to enabling the ultra-long-range guided rocket to quickly and accurately track overload instructions during high-dynamic motion, and ensure that the ultra-long-range guided rocket has good stability and robustness.

[0093] 1. During the high-dynamic flight of an ultra-long-range guided rocket using tail-fin control (STT), considering the servo system as a first-order link, the pitch channel control model is as follows:

[0094]

[0095] Among them, δ zc is the steering gear deflection command, M is the rocket Mach number, ω a is the natural frequency of the servo, K α and Defined as:

[0096] K α =0.7PS / mυ s

[0097]

[0098] Where, P = P0(1-0.0065h / T0) 5.2561 is the static aerodynamic pressure, d r is the characteristic diameter, υ s is the speed of sound, the aerodynamic coefficient C n (α,δ z ,M) and aerodynamic moment coefficient C m (α,δ z ,M) is defined as follows:

[0099]

[0100] Among them, a n 、b n 、c n d n 、a m 、b m 、c m and d m are aerodynamic constants obtained from wind tunnel tests, k = 180 / π.

[0101] The model of rocket overload change can be expressed as:

[0102]

[0103] in, The real-time update model of Mach number is:

[0104]

[0105] Among them, c y is the longitudinal drag coefficient, and the calculation process of rocket overload is:

[0106] a y =(0.7)PSC a / m (6)

[0107] Among them, C a is the drag coefficient.

[0108] The height variation model is as follows:

[0109]

[0110] Where g is the acceleration due to gravity, θ m is the ballistic inclination angle.

[0111] In the actual flight process, z and a y It can be obtained from angular velocity gyroscopes and accelerometers.

[0112] 2. Design a control structure for ultra-long-range guided rockets based on time scale separation.

[0113] The guidance and control process of ultra-long-range guided rockets is generally considered to be a time-scale separation system, in which the dynamic model representing the overload change is regarded as a long-period state variable, and the dynamic model representing the pitch angular velocity change is regarded as a short-period state variable. In order to eliminate the adverse effects of the time scale inconsistency between the dynamic model of overload change and the dynamic model of pitch angular velocity change during the high-dynamic flight of the rocket, a time-scale separation structure is designed for the longitudinal dynamic model of the ultra-long-range guided rocket by dividing the parts of the system with different period times into two subsystems with long period and short period. The long-period subsystem receives the overload command given by the guidance system and calculates the required pitch angular velocity ω zc , the short-period subsystem is used to process the required pitch angular velocity ω zc Information and generate the required rudder deflection command δ zc , the system structure diagram is attached Figure 1 .

[0114] (1) Long-period subsystem;

[0115] In the time scale separation structure, the overload change dynamics model is regarded as a long-period subsystem, and Equation (4) can be adjusted to

[0116]

[0117] in,

[0118]

[0119] The last term d in formula (8) η ′ represents external disturbances caused by measurement noise, servo failure, etc.

[0120] coefficient and It is not a constant value, and sometimes even varies in a short period, which brings certain difficulties to control system design and parameter selection. For this reason, we define:

[0121]

[0122] in, and The coefficients are and Initial value. At this time, formula (8) can be rewritten as:

[0123]

[0124] in, represents the long-period subsystem disturbance.

[0125] At this time, Equation (10) is the dynamic model of the long-period subsystem of the longitudinal channel of the ultra-long-range guided rocket.

[0126] (2) Short-period subsystem

[0127] In this time scale separation structure, the dynamic model representing the pitch angular velocity change is regarded as a short-period subsystem, and the system model can be adjusted as follows:

[0128]

[0129] in,

[0130]

[0131] The last term of formula (11) Represents the possible external disturbance. Simplifying the system model, equation (11) can also be adjusted to:

[0132]

[0133] in, and They are and The initial value of is the normalized disturbance of the short-period subsystem, satisfying:

[0134] At this time, Equation (12) is the dynamic model of the short-period subsystem of the longitudinal channel of the ultra-long-range guided rocket.

[0135] 3. Design of overload pilot for ultra-long-range guided rocket based on time scale separation.

[0136] (1) Design of adaptive robust controller for long-period subsystems;

[0137] The pitch velocity ωz Considered as a virtual control of the long-period subsystem (10), the goal of this step is to construct the pitch angular velocity command ω zc Tracking pitch angular velocity ω z .

[0138] Design the following first-order sliding surface:

[0139] s1=a y -a y * (13)

[0140] Among them, a y * represents the expected or required acceleration, which can be preset or calculated by the guidance law. Taking the derivative of equation (13) we get:

[0141]

[0142] Pitch angular velocity command ω zc It can be expressed as:

[0143]

[0144] Among them, c1>0, γ1>0, k1>0 and k2>0 are all design parameters. is the long-period subsystem disturbance The upper bound of can be obtained by adaptive term estimation, and the update process is:

[0145]

[0146] (2) Design of adaptive robust controller for short-period subsystem;

[0147] To design the required rudder deflection command δ zc , controls the pitch angular velocity ω zc Tracking desired pitch angular velocity ω z , ignoring the first-order servo system, the rudder deflection command δ is required zc It can be regarded as the real rudder deflection δ z . Design a new sliding surface:

[0148] s2=ω z -ω zc (17)

[0149] Derivative of the sliding surface formula (17):

[0150]

[0151] Rudder deflection δ z It can be expressed as:

[0152]

[0153] Among them, c2>0, γ2>0, k3>0 and k4>0 are design parameters. is the short-period subsystem disturbance The upper bound of can be obtained by adaptive term estimation, and the update process is:

[0154]

[0155] At this time, the system controller using time scale separation can be expressed as:

[0156]

[0157] s2=ω z -ω zc

[0158]

[0159] The formula (1), (4) and (21) is shown in the following figure. Figure 1 The adaptive robust autopilot system shown has a four-loop control structure. The two inner loops form the short-period subsystem, while the two outer loops form the long-period subsystem. The short-period and long-period subsystems are clearly separated. Two adaptive terms are used to estimate the upper bounds of the normalized perturbations for their respective subsystems. Different control parameters are selected for different frequencies of different state variables. For example, larger control parameters are selected for the short-period subsystem, and vice versa.

[0160] Items used to form the sliding surface is a continuous function, which can effectively weaken the sliding mode chattering. In addition, when |s i |>1, k1=k3, k2=k4, the linear term k i s i The nonlinear term will dominate Speed ​​up the asymptotic convergence. When |s i When |≤1, the nonlinear term The dominant linear term k i s i , which speeds up the finite time convergence process, and when γ i =1, which means gradual convergence.

[0161] (3) Design tracking differentiator;

[0162] In order to obtain the time derivative of the pitch angular velocity, the following tracking differentiator is designed for the estimation process:

[0163]

[0164] Among them, r0>0 is the control parameter, υ1 and υ2 are the state variables of the tracking differentiator. Choosing a suitable r0 will make υ1 and υ2 converge to ω respectively. zc and

[0165] In order to track the normalized perturbation upper bound in real time, the parameter c representing the approximation speed is used in the adaptive process. i Cannot be too small. However, when c i When it is large, it will cause chattering of the servo signal. To solve this problem, the sigmoid function sgmf(·) is used instead of the sign function sign(·). sgmf(·) is defined as:

[0166]

[0167] Among them, ε represents the boundary layer width of the sigmoid function.

[0168] In order to switch the gain, the traditional sliding mode controller needs to know the boundary information of the normalized disturbance in advance. The controller designed in this chapter does not require disturbance boundary information and does not require an observer for estimation.

[0169] Example:

[0170] The method of the present invention can effectively avoid the adverse effects caused by the time scale inconsistency between the overload change dynamics model and the pitch angular velocity change dynamics model of an ultra-long-range guided rocket during high-dynamic flight, so that the rocket overload autopilot has good control performance. At the same time, corresponding adaptive terms and sliding mode terms are designed in the long-period subsystem and the short-period subsystem, so that the autopilot has good adaptability and robustness as a whole.

[0171] Through simulation, the control performance of a certain ultra-long-range guided rocket using a time-scale separated adaptive robust adaptive autopilot is analyzed under the simulation conditions shown in Table 1 below: the rocket's initial altitude h = 6090 m, and the Mach number M = 2.25.

[0172] Table 1

[0173]

[0174] C m and C n The parameter perturbations in are Gaussian distributed with a standard deviation of 40%.

[0175] The expected acceleration change process is shown in Table 2:

[0176] Table 2

[0177] Time(s) Expected acceleration t>4 <![CDATA[a y * =80m / s 2 ]]> 4≤t<6 <![CDATA[a y * =-80m / s 2 ]]> t≥6 <![CDATA[a y * =80m / s 2 ]]>

[0178] Two robust overload pilots, the Fast Sliding Mode Control (FSMC) overload pilot and the FSMC autopilot with Extended State Observer (ESO), were selected as the control group.

[0179] Control group 1: FSMC autopilot is:

[0180]

[0181] Among them, τ1, τ2, τ3 and τ4 are positive constants.

[0182] The TSMC algorithm is highly resistant to unknown disturbances and, when properly parameterized, can be effectively applied to autopilot design. Typically, the parameters of a sliding mode controller are larger than the upper bound of the normalized disturbance. However, in practice, disturbances are often unknown and uncertain. Therefore, the parameters are often larger when selected. However, excessively large parameters can cause control signal chatter. Compared to the autopilot designed in this paper, the TSMC autopilot ignores the adaptive term, serving as a control group for simultaneous comparative analysis of the performance of both the adaptive term and the robust controller.

[0183] The FSMC autopilot with ESO is:

[0184]

[0185] Among them, Z2 and Z4 are a η0 (α)η and a q0 The observed value of (α) can be obtained by ESO estimation, and χ1, χ2, χ3 and χ4 are positive constants.

[0186] The ESOs are:

[0187]

[0188] Where β1>0, β2>0, ε>0 and 0<γ<1. The symbolic function fal(e,γ,ε) is defined as:

[0189]

[0190] The present invention analyzes three different autopilot control performances. Figure 2 (a) It shows that all three autopilots can accurately track the G command within 3 seconds. Figure 2 (b) shows that the angle of attack change curves of the three autopilots are similar, and all of them can ensure that the angle of attack is within a reasonable range. Figure 2Figure (c) shows that the FSMC autopilot servo change curve clearly exceeds the actual allowable range when the expected acceleration changes from 2s to 4s, indicating that the FSMC autopilot cannot be directly applied to actual engineering processes. The other two autopilots can track the expected overload command within the allowable range of the rudder deflection angle.

[0191] The embodiment of the present invention analyzes three different autopilot control performances, combined with the attached Figure 2 (a) and Figure 2 The simulation results of (c) show that the rudder angle signal can be kept within a reasonable range while the autopilot proposed in the present invention tracks the overload command. Figure 2 (d) The adaptive term curve separating the long-period subsystem and the short-period subsystem of the autopilot for the time scale designed in this chapter. The adaptive term is bounded during the simulation process, indicating that the system is stable.

[0192] The embodiment of the present invention analyzes the adaptive robust adaptive autopilot using time scale separation when the number of samples is 300 and the aerodynamic parameters C m and C n The parameter perturbation in the Monte Carlo experiment is Gaussian distributed with a standard deviation of 40%. The simulation results are shown in the attached Figure 3 As shown, attached Figure 3 (a) shows that the autopilot can track the expected g-load command during the Monte Carlo test. Figure 3 (b) shows that the autopilot can ensure that the angle of attack is within a reasonable range while effectively tracking the expected overload command. Figure 3 (c) It is shown that the rudder angle changes are within the acceptable range while effectively tracking the desired G-load command. Figure 3 (b) shows that the adaptive terms of the long-period subsystem and the short-period subsystem are both bounded, and the systems are both stable.

Claims

1. A method for designing an overload autopilot based on time scale separation, characterized in that: The steps include: Step 1: During the high-dynamic flight of the ultra-long-range guided rocket using tail-fin control STT, the servo system is considered as a first-order link, and the pitch channel control model is shown in Equation (1): Where α is the angle of attack, ω z is the pitch angular velocity, δ z is the rudder deflection angle, δ zc is the steering gear deflection command, M is the rocket Mach number, ω a is the natural frequency of the servo, K α and They are defined as: K α =0.7PS / mυ s Where, P = P0(1-0.0065h / T0) 5.2561 is the static aerodynamic pressure, S is the characteristic area of ​​the rocket, m is the mass of the rocket, I y is the pitch moment of inertia, d r is the characteristic diameter, υ s is the speed of sound; aerodynamic coefficient C n (α,δ z ,M) and aerodynamic moment coefficient C m (α,δ z ,M) are defined as follows: Among them, a n 、b n 、c n d n 、a m 、b m 、c m and d m All are aerodynamic constants, obtained from wind tunnel tests; Rocket overload is expressed as: in, The real-time update model of Mach number is: Among them, c y is the longitudinal drag coefficient; In actual engineering, the calculation process of rocket overload is: to y =(0.7)PSC a / m (6) Among them, C a is the drag coefficient; The height variation model is as follows: Where g is the acceleration due to gravity, θ m is the ballistic inclination angle; Step 2: Design a control structure for the ultra-long-range guided rocket based on time scale separation; Step 2-1: Long-period subsystem; In the time scale separation structure, the overload change dynamics model is regarded as a long-period subsystem, and Equation (4) is adjusted to: in, The last term d in formula (8) η ' represents the external disturbance caused by measurement noise and servo failure; definition: in, and The coefficients are and Initial value; At this time, formula (8) is rewritten as: in, represents the long-period subsystem disturbance; At this time, Equation (10) is the dynamic model of the long-period subsystem of the longitudinal channel of the ultra-long-range guided rocket; Step 2-2: Short-term subsystem; In the time scale separation structure, the dynamic model representing the change of pitch angular velocity is regarded as a short-period subsystem, and the system model is adjusted as follows: in, The last term of formula (11) Indicates possible external disturbances; Simplifying the system model, equation (11) is adjusted to: in, and They are and The initial value of is the normalized disturbance of the short-period subsystem, satisfying: At this time, Equation (12) is the dynamic model of the short-period subsystem of the longitudinal channel of the ultra-long-range guided rocket; Step 3: Design of overload pilot for ultra-long-range guided rocket based on time scale separation; Step 3-1: Design an adaptive robust controller for the long-period subsystem; The pitch velocity ω z It is regarded as a virtual control of the long-period subsystem (10); Design the following first-order sliding surface: s1=a y -a y * (13) Among them, a y * Indicates the expected or required acceleration; By taking the derivative of formula (13), we can get: Pitch angular velocity command ω zc Expressed as: Among them, c1>0, γ1>0, k1>0 and k2>0 are all design parameters. is the long-period subsystem disturbance The upper bound of can be obtained by adaptive term estimation, and the update process is: Step 3-2: Design an adaptive robust controller for the short-period subsystem; Control the pitch angular velocity ω zc Tracking desired pitch angular velocity ω z , ignoring the first-order servo system, the rudder deflection command δ is required zc Considered as the real rudder deflection δ z ; Design a new sliding surface: s2=ω z -oh zc (17) Derivative of the sliding surface formula (17): Rudder deflection δ z Expressed as: Among them, c2>0, γ2>0, k3>0 and k4>0 are design parameters. is the short-period subsystem disturbance The upper bound of can be obtained by adaptive term estimation, and the update process is: At this time, the system controller using time scale separation is expressed as: s1=a y -a y * s2=ω z -oh zc Step 3-3: Design the tracking differentiator; Design a tracking differentiator for the estimation process: Among them, r0>0 is the control parameter, υ1 and υ2 are the state variables of the tracking differentiator; The sign function sign(·) is replaced by the sigmoid function sgmf(·), which is defined as: Among them, ε represents the boundary layer width of the sigmoid function.

2. The method for designing an overload autopilot based on time scale separation according to claim 1, characterized in that: The k=180 / π.

3. The method for designing an overload autopilot based on time scale separation according to claim 1, characterized in that: The ω z and a y Obtained by angular velocity gyroscope and accelerometer.

4. The method for designing an overload autopilot based on time scale separation according to claim 1, characterized in that: The a y * Indicates the expected or required acceleration, which can be preset or calculated by the guidance law.

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