A Rotor Propulsion Air-Float Motion Control Method Based on Modified Cascade Fuzzy PID

Abstract

This invention discloses a method for controlling the motion of a rotor propulsion air-bearing platform based on a modified cascade fuzzy PID controller, relating to the field of spacecraft ground-based semi-physical testing technology. It improves the PID control scheme to enhance the adjustment accuracy of the rotor propulsion air-bearing platform's motion control. The invention includes: using a propeller-type rotor as the air-bearing platform's motion control actuator; establishing a thrust characteristic mathematical model, wherein the air-bearing platform adopts a three-axis decoupled thruster configuration; constructing an air-bearing platform motion control feedback system; and using the thrust characteristic mathematical model to establish a cascade fuzzy PID control model for the air-bearing platform's motion control feedback system; and adjusting the cascade three-axis PID parameters in real time by using correction coefficients to adjust the correction amount transmitted from the outer loop to the inner loop of the air-bearing platform's motion control feedback system.

Description

Technical Field

[0001] This invention relates to the field of spacecraft ground-based semi-physical testing technology, and in particular to a method for controlling the motion of a rotor propulsion air-bearing platform based on a modified cascade fuzzy PID controller. Background Technology

[0002] Spacecraft are expensive to build and difficult to maintain after entering orbit. Planar three-axis air-bearing platforms, as important ground-based semi-physical simulation devices for spacecraft, can verify key technologies and conduct feasibility studies for on-orbit missions in advance. Rotary thrusters are widely used in fields such as UAVs, consuming electrical energy and utilizing linear control laws for continuous output, characterized by long-term, accurate, and stable output. Traditional air-bearing platform propulsion devices mostly use cold-gas propulsion systems. Due to the limited gas capacity of high-pressure cylinders, the endurance of ground-based air-bearing platforms is short; the pressure drop in cylinders during experiments causes jet thrust output to vary over time; and the fluid effects in the air result in thrust output accuracy and attitude control accuracy lower than in the on-orbit vacuum environment. To further improve the usable experimental time and attitude control accuracy of ground-based experimental platforms, this paper proposes using a propeller-type rotor thruster as the motion control actuator for the air-bearing platform. The rotor motor drives the blades to rotate at high speed, generating continuous small thrust, which has higher accuracy than the intermittent output of jet propulsion controlled by relays. Furthermore, the motor speed does not change with battery power, achieving long-term, stable, and high-precision thrust output.

[0003] Currently, the mainstream algorithm for the actual motion control of air-bearing platforms is still the PID control algorithm. Considering the continuous low-thrust operating characteristics of differential rotor thrusters and the actual experimental conditions of ground-based air-bearing platforms, including: the small-angle tilt of the guide surface platform causing lateral force disturbances to the air-bearing platform, and the existence of flatness deviations that are difficult to accurately measure and model; and the presence of air resistance, friction, lateral forces, and unknown time-varying disturbance terms in the kinematic equations, the system is required to maintain tracking accuracy while ensuring speed and stability under sensitive small disturbances. In this regard, the PID parameters are constant values ​​at all stages of trajectory tracking, making it difficult to simultaneously meet the speed requirements when the initial error is large under continuous low rotor thrust output and the high precision requirements in the final adjustment stage.

[0004] Therefore, how to improve the adjustment accuracy of the rotor propulsion air-bearing platform motion control by improving the PID control scheme has become a problem that needs to be studied.

[0005] Clearly, this control method is difficult to solve problems such as coupling of the air-bearing platform, rotor, and environmental model, as well as time-varying interference. It is also difficult to adapt to different environmental characteristics and achieve fast, high-precision, and stable motion control of the air-bearing platform. Summary of the Invention

[0006] The embodiments of the present invention provide a method for controlling the motion of a rotor propulsion air-bearing platform based on a modified cascade fuzzy PID controller, which improves the PID control scheme and thus enhances the adjustment accuracy of the rotor propulsion air-bearing platform motion control.

[0007] To achieve the above objectives, the embodiments of the present invention adopt the following technical solutions:

[0008] A method for controlling the motion of a rotor propulsion air-bearing platform based on modified cascade fuzzy PID control includes:

[0009] S1. Using a bladed rotor as the motion control actuator for the air-floating platform, a mathematical model of thrust characteristics is established, wherein the air-floating platform adopts a three-axis decoupled thruster configuration.

[0010] S2. Build a motion control feedback system for the air-bearing platform, and use the thrust characteristic mathematical model to establish a cascade fuzzy PID control model for the motion control feedback system of the air-bearing platform.

[0011] Among them, a motion control feedback system for an air-bearing platform was built. The planar three-axis air-bearing platform was used as the controlled object. The preset posture information and the measured posture information of the air-bearing platform were acquired in real time. Based on the deviation and deviation rate between the measured feedback value and the preset value, membership functions and fuzzy rules were designed respectively. The cascaded three-axis PID parameters were adjusted in real time. On this basis, a correction coefficient Kc was added to adjust the proportion of correction amount transmitted from the outer loop to the inner loop in real time, so as to complete the controllable, high-precision and speed-stable motion control of the air-bearing platform during a large-range maneuver.

[0012] S3. During the adjustment of the cascaded three-axis PID parameters, the correction amount transmitted from the outer loop to the inner loop of the air-bearing platform motion control feedback system is adjusted in real time by the correction coefficient.

[0013] Specifically, in S1, the mathematical model of thrust characteristics includes: C T =2λ 2 Where λ represents the rotor blade inflow ratio, C represents the normalized blade radius. T The thrust coefficient is represented by α, the angle of attack of the incoming flow is represented by θ, the installation pitch angle is represented by σ, and the solidity of the rectangular blade is represented by σ. The rotor blades have N blades, and the rectangular blades have a width of c and a radius of R.

[0014] In practical applications, when the rotor blades operate in a steady flow field, based on the rotor disk theory, the flow field around the rotor has axisymmetry. First, assuming the induced velocity is uniformly distributed on the rotor disk surface, we obtain the thrust coefficient expression. Then, using the blade element method, we dissect the blade and extract a micro-element segment for analysis to obtain the thrust coefficient C. T .

[0015] Therefore, a flow field model near the propeller disk can be established first: the number of rotor blades is N, the width of the rectangular blade is c, the radius is R, the rotational speed around the central axis is w, and the solidity of the rectangular blade is defined as That is, the sum of the areas of all blades is dimensionless by the propeller disk area. The action disk is located at section 1, and the upstream far section 0 and the downstream far section ∞ are defined as the model boundaries. At section 0, V0 is the moving speed of the air floating platform perpendicular to the propeller disk. After acceleration, the air flow speed increases to V1 and V at section 1 and section ∞ ∞ , and the increments v1 and v ∞ are the induced velocities at that location. The power thrust P and thrust coefficient T of a single rotor can be expressed as:

[0016]

[0017] T = 2ρv1V1S1 = 2ρπR 2 (V0 + v1)v1

[0018] The dimensionless representation of T is C T = T / (ρπω 2 R 4 );

[0019] It can be obtained that

[0020] When V0 << v1, the dimensionless induced velocity of the propeller disk is:

[0021] After that, a microscopic model on the microelement is established using the blade element method: the propeller disk is regarded as an infinite number of concentric circular ring belt microelement segments dA = 2πrdr by cutting at the blade radius r using the blade element method. The thrust microelement and thrust coefficient microelement are: dT = 2ρ(V0 + v1)v1dA, As shown in the appendix Figure 3 , the oncoming flow velocity of each microelement is decomposed into the tangential u T , the radial u R and the vertical u P . Ignoring the drift velocity component u R , there is a combined velocity u T = ωr. The inflow ratio λ of the rotor blade is defined as the ratio of the projection of the relative oncoming flow velocity V1 of the rotor in the vertical direction of the propeller disk to the tip rotational linear velocity wR, and can be decomposed into λ c and λ i , that is Exactly The expression of the oncoming flow angle of attack is: θ is the constant installed pitch angle, is the combined velocity angle of the oncoming flow of the microelement The oncoming flow angle λ and the inflow ratio The relationship between them is

[0022] Finally, we can define The expression for the thrust coefficient of a single rotor is:

[0023]

[0024] In the preferred embodiment, the triaxial decoupled thruster configuration includes: a thruster layout covering six channels (positive and negative) across three axes; specifically, eight thrust output ports, four of which are responsible for the positive, negative, clockwise, and counterclockwise rotations of the x-axis, and the other four for the positive, negative, clockwise, and counterclockwise rotations of the y-axis. Specifically, constrained by the three degrees of freedom of translation and rotation of the air-bearing platform on the marble platform, this can be considered as the planar motion of the air-bearing platform's center of mass and the rotation of other particles on the air-bearing platform around a vertically upward axis around the center of mass. Therefore, the thruster layout should cover six channels (positive and negative) across three axes, as shown in the attached diagram. Figure 4 and Figure 5 The diagram shows the thruster layout. To improve the thrust output accuracy and thus control accuracy, eight thrust output ports are designed to handle the positive and negative x and y axes, as well as clockwise and counterclockwise rotation, respectively, thus completely decoupling the outputs of the six channels.

[0025] The triaxial decoupled thruster configuration includes: [the system x] b The angle between the axis and the x-axis of the inertial frame is θ. The coordinate transformation matrix from the local frame to the inertial frame is: right Inverse transformation yields the coordinate transformation matrix from the inertial frame to the home frame. in: [F in inertial frame] x F y T z ] T Rotate the coordinate matrix Transformed to this system [f x f y τ] T F x F y T z f represents the control force and torque along the x and y axes of the three channels in an inertial frame. x f y τ and τ represent the control forces and torques of the three channels along the x and y axes of this system, calculated by the main control computer.

[0026] Optionally, in the three-axis decoupled thruster configuration, a rotor thruster is used; the thrust difference generated by controlling a group of opposing rotor thrusters to simultaneously output is equal to a preset value f, wherein the operating reference speed w of the rotor thruster is set. base To fix the offset; specifically, to address the dead zone problem in rotor thrust, a differential rotor thrust distribution scheme is proposed; the motion controller calculates [F] in the inertial frame of the planar air-bearing platform. x F y T z Triaxial forces and moments, using coordinate transformation matrices We can obtain [f] under this system. x f y [τ]. Rotary thrusters can achieve linear control and continuously varying output, but in the low-thrust, low-speed range (F≤0.02N, w≤20rad / s), the model exhibits high nonlinearity. In practical applications, they also face the problem of ESC identifying the dead zone of low-duty-cycle PWM waves. The rotor operating reference speed w is set. base To maintain a fixed bias, controlling the thrust difference generated by a set of opposing rotors simultaneously outputting thrust equal to a preset value f effectively avoids chattering issues caused by PWM dead zones and poor linearity in the speed-thrust model. The thrust distribution scheme based on the rotor thruster includes:

[0027]

[0028]

[0029]

[0030] Where: f x f y τ and f1 represent the three-axis control forces and torques calculated by the main control computer, respectively; the forces decomposed into positive and negative channels on the x-axis are f1 and f5, respectively; the forces decomposed into positive and negative channels on the y-axis are f3 and f7, respectively; clockwise output torque utilizes channels f2 and f6; counterclockwise output torque utilizes channels f4 and f8, f1, f2, f3, f4, f5, f6, f7, f8, f9 ... base This represents the reference thrust output by the rotor. The corresponding thrust, f, is obtained by inverse solving the rotor dynamics model. 1～8 motor speed w 1～8 Then, based on the relationship between the ESC-identified PWM duty cycle and the output speed, t is obtained by inverse solving. 1～8 The two are roughly linearly related. In the microcontroller board hardware programming, the PWM waveform signal can be manually pulled up or down to adjust the rotor speed in real time and change the thrust to achieve the control effect.

[0031] In this embodiment, a motion control feedback system for an air-bearing platform is constructed, using a three-axis air-bearing platform as the controlled object. The system acquires the preset and measured pose information of the air-bearing platform in real time. Based on the deviation *e* and deviation rate *ec* between the measured feedback position (angle) and velocity (angular velocity) values ​​and the preset values ​​of the trajectory planning, membership functions and fuzzy rules are designed to adjust the cascaded three-axis PID parameters in real time. Furthermore, a correction coefficient *Kc* is added to adjust the proportion of correction transmitted from the outer loop to the inner loop in real time, achieving controllable, high-precision, and stable motion control of the air-bearing platform over a wide range of maneuvers. Firstly, the input to the fuzzy controller acting on the PID parameter adjustment of the inner loop (velocity loop) can be designed as the velocity error *e* and the velocity error rate *ec*. Through fuzzification, fuzzy inference, and defuzzification, the final output is ΔK. P ,ΔK I ,ΔK D Real-time adjustment of PID parameters balances response time and adjustment accuracy. The fuzzy logic is: proportional coefficient |K P To determine response speed, for the unit step signal tracking process, the proportional coefficient should be increased as much as possible in the initial adjustment stage when the speed error e and error rate ec are large to improve system speed. As e and ec gradually converge, the proportional coefficient should be decreased accordingly to avoid overshoot. In the final fine-tuning stage, the proportional coefficient should be slightly increased to improve control accuracy. Integral coefficient |K I The function of | is to eliminate the steady-state error of the system. When e and ec are large, a smaller integral coefficient should be chosen to avoid oscillation and divergence, and the proportional coefficient should be increased during the later error convergence process to reduce the error. Differential coefficient |K D |Determines the dynamic performance of the system; appropriately selecting the derivative coefficients can avoid overshoot and reduce settling time. Amplify |K when e and ec are relatively large initially. D | and as it converges, |K P Slowly reduce the degree of the differential disk.

[0032] Specifically, in S2, the fuzzy output of the cascaded fuzzy PID control model is ΔK. P ,ΔK I ,ΔK D ΔK represents the real-time adjustment amount, based on the proportional, integral, and derivative coefficients obtained from fuzzy inference, according to the initial adjustment benchmark. P ,ΔK I ,ΔK D The membership functions of each fuzzy subset are all triangular membership functions;

[0033] The methods used in the cascaded fuzzy PID control model for real-time tuning of the PID parameters of the triaxial inner loop controller include: Among them, K P K represents the proportionality coefficient. I K represents the integral coefficient. DK represents the differential coefficient. P0 K I0 K D0 These represent the initial adjustment bases for the proportional coefficient, integral coefficient, and derivative coefficient, respectively.

[0034] Specifically, the position and attitude deviations e and their rate of change ec of the air-bearing platform are fuzzified. This involves defining several fuzzy subsets in the universe of discourse and specifying their membership functions, thereby converting the sharp input into fuzzy input. A set of fuzzy control rule tables is defined to describe the fuzzy inputs, i.e., the position deviation e and its rate of change ec of the linear motion guide rail, and the fuzzy output, ΔK. P ΔK I ΔK D A set of "if-then" conditional statements, where ΔK P ΔK I ΔK D These are the proportional, integral, and differential coefficients, respectively. Based on these, the fuzzy subset to which the fuzzy output belongs and its corresponding membership degree are determined. Using a defuzzification method, the specific ΔK is calculated based on the fuzzy subset to which the fuzzy output belongs and its corresponding membership degree. P ΔK I ΔK D and through Real-time tuning of the PID parameters of the three-axis inner loop controller. Specifically, the membership functions of all fuzzy subsets of the fuzzy input quantities e and ec are Gaussian combination membership functions; the fuzzy output quantity ΔK... P ΔK I ΔK D Triangular membership functions are used for all fuzzy subsets.

[0035] The triangular membership functions include:

[0036]

[0037] ξ a ξ b ξ c ξ represents the x-coordinates of each control endpoint of the triangular membership function, used to control the shape of the triangular membership function, and ξ represents the parameter variable. As mentioned above, in the inner loop (velocity loop) fuzzy PID algorithm, the universes of discourse of each fuzzy subset are uniformly distributed, and the x-coordinates of the control points are arranged at equal intervals from smallest to largest.

[0038] In this embodiment, a cascaded fuzzy PID control method with correction can be established by introducing a correction coefficient. Specifically, in S3, this includes: introducing a correction coefficient K. cThe correction amount transferred from outer-loop position tracking to inner-loop velocity tracking is adjusted online to improve the dynamic performance of the air-bearing platform motion control system, ensuring system stability and controllability during rapid convergence of large errors. Its correction coefficient K... c Based on the position (angle) error Δx=x 反馈 -x 预期 And (angular) velocity error Δv=v 反馈 -v 预期 The real-time adjustment of the position loop PID output correction takes precedence over the speed loop input parameters e and ec. This is used to avoid sudden speed changes while ensuring settling time, and the improvement in dynamic performance can be reflected in the smoothing optimization of the speed curve. For example, setting the correction coefficient K... c According to the position error Δx = x 反馈 -x 预期 and angular velocity error Δv=v 反馈 -v 预期 By adjusting the coefficient K c The real-time adjustment of the correction amount of the position loop PID output takes precedence over the speed loop input parameters e and ec, where e represents the position and attitude deviation and ec represents the rate of change of e.

[0039] Wherein, the correction coefficient K c The real-time adjustment of the correction amount of the position loop PID output has the following priority among the speed loop input parameters e and ec: when |Δx| is detected to be greater than the preset value, amplify K. c Increase the proportion of position tracking correction in e and ec; decrease K as |Δx| increases after |Δv| begins to converge. c until |Δx| converges to near 0.

[0040] The present invention provides a rotor propulsion air-bearing platform motion control method based on modified cascade fuzzy PID. Addressing the issues of short time and time-varying output in jet control during simulation experiments of a planar three-axis air-bearing platform, this invention proposes a scheme using propeller-driven rotor thrust as the actuator for air-bearing platform motion control. Considering the significant characteristic differences between propeller-driven rotors and traditional jet thrusters, a mathematical model of rotor thrust characteristics is constructed. A three-axis decoupled thruster configuration is proposed. Furthermore, to address the dead zone problem in rotor thrust, a differential rotor thrust allocation scheme is proposed. To improve the dynamic performance of the system, a fuzzy adaptive cascade PID control is proposed to control the rotor speed. Using a three-axis air-bearing platform as the controlled object, the preset and measured position and attitude information of the air-bearing platform are acquired in real time. Based on the deviation and deviation rate between the measured feedback value and the preset value, a membership function and fuzzy rules are designed to adjust the cascade PID parameters in real time. On this basis, a correction coefficient Kc is added to adjust the proportion of the correction amount transmitted from the outer loop to the inner loop in the inner loop e and ec in real time, so as to achieve controllable, high-precision, and stable motion control of the air-bearing platform during a wide range of maneuvers. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 A block diagram illustrating the principle of a cascaded fuzzy PID control method with correction coefficient Kc, provided as an example of the present invention.

[0043] Figure 2 A schematic diagram of the flow field distribution around the rotor disk surface provided for an example of the present invention;

[0044] Figure 3 A schematic cross-sectional view of a rotor thruster blade provided as an example of the present invention;

[0045] Figure 4 This is a schematic diagram of a possible thruster configuration provided in an embodiment of the present invention;

[0046] Figure 5 This is a schematic diagram of a possible thrust output layout provided by an embodiment of the present invention;

[0047] Figure 6 A schematic diagram of the membership functions of the fuzzy input quantities e and ec acting on the inner loop PID (speed loop) fuzzy controller provided for an example of the present invention;

[0048] Figure 7 A schematic diagram of the membership function of the fuzzy output quantity ΔKp acting on the inner loop PID (speed loop) fuzzy controller provided for an example of the present invention;

[0049] Figure 8 A schematic diagram of the membership function of the fuzzy output quantity ΔKi acting on the inner loop PID (speed loop) fuzzy controller provided for an example of the present invention;

[0050] Figure 9 A schematic diagram of the membership function of the fuzzy output quantity ΔKd acting on the inner loop PID (speed loop) fuzzy controller provided for an example of the present invention;

[0051] Figure 10 The fuzzy input Δζ of the Kc fuzzy regulator provided in this invention example x A diagram illustrating the membership functions;

[0052] Figure 11 The fuzzy input Δζ of the Kc fuzzy regulator provided in this invention example v A diagram illustrating the membership functions;

[0053] Figure 12 A schematic diagram of the position (angle) tracking trajectory curve of the three-axis tracking trajectory under the control method provided in this invention example;

[0054] Figure 13 A schematic diagram of the velocity (angular velocity) curve of the three-axis tracking trajectory under the control method provided in this invention example;

[0055] Figure 14 A schematic diagram of the convergence curve of the position (angle) error of the three-axis tracking trajectory under the control method provided in this invention example. Detailed Implementation

[0056] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Embodiments of the present invention will be described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention. Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in the specification of the present invention means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein can include wireless connections or couplings. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items. It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the meaning consistent with their meaning in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0057] Currently, PID parameters remain constant throughout all stages of trajectory tracking, making it difficult to simultaneously meet the speed requirements during the initial stage of continuous low thrust output by the rotor, which involves large initial errors, and the high precision requirements during the final adjustment stage. Clearly, this control method struggles to address issues such as coupling between the air-bearing platform, rotor, and environmental model, as well as time-varying disturbances, and is ill-suited to different environmental characteristics, failing to achieve rapid, high-precision, and stable motion control for the air-bearing platform. The purpose of this embodiment is to address the problems of existing technologies by providing a rotor propulsion air-bearing platform motion control method based on modified cascade fuzzy PID.

[0058] The general idea of ​​this embodiment is as follows: By establishing a mathematical model of the rotor propulsion system, a three-axis decoupled thruster configuration is proposed, and a differential rotor thrust allocation scheme is proposed to address the dead zone problem in rotor thrust. Specifically, a rotor propulsion air-bearing platform motion control method based on a cascaded fuzzy PID controller with correction coefficients is provided. This method uses a planar three-axis air-bearing platform as the controlled object and the rotor as the thrust device. A correction coefficient Kc is introduced into the cascaded fuzzy PID controller to adjust the correction amount transmitted from position (outer loop) tracking to velocity (inner loop) tracking in real time. It can utilize fuzzy mathematics to simulate human brain thinking, solve problems such as model coupling and time-varying interference, and adapt to changes in environmental characteristics, thereby achieving high-precision and fast control of the air-bearing platform. The control block diagram is attached. Figure 1 As shown.

[0059] Step 1: Establishment of the mathematical model of the rotor thruster, specifically including: when the rotor blades are operating in a steady flow field, based on the disk theory, the flow field around the blades has axisymmetry. First, it is assumed that the induced velocity is uniformly distributed on the disk surface to obtain the thrust coefficient expression. Then, the blade element method is used to cut open the blades and extract the micro-element segments for analysis to obtain the thrust coefficient C. T The rotor blades have N blades, a rectangular blade width of c and radius R, and a rotational speed of w around the central axis. The solidity of the rectangular blades is defined as... This involves using the area of ​​the propeller disk to make the sum of the areas of all propeller blades dimensionless.

[0060] The action disk is located at section 1, and the upstream distant section 0 and the downstream distant section ∞ are defined as the model boundaries. At section 0, V0 is the moving velocity of the air-floating platform perpendicular to the propeller disk. After acceleration, the airflow velocity increases to V1 and V2 when it reaches sections 1 and ∞, respectively. ∞ Increment v1 and v ∞ This represents the induced velocity at that location.

[0061] The change in momentum of the fluid passing through the rotor disk is equal to the force T' exerted by the rotor on the fluid. The expression for the reaction force of the airflow on the blades, i.e., the rotor thrust T, is: in, The mass of fluid flowing through a certain cross-section of the action disk per unit time can be expressed as:

[0062] The blade power can be expressed as: P = TV1 = TV0 + Tv1;

[0063] Where TV0 is the effective rotor power, Tv1 is the induced power, and...

[0064] Rotor power can be expressed as:

[0065] The induced velocity relationship is v ∞ =2v1, the thrust can be expressed as Expanded to: T = 2ρv1V1S1 = 2ρπR 2 (V0+v1)v1,

[0066] Dimensionless T is applied, where C T =T / (ρπω) 2 R 4 ), get: Using the blade element method, the blade is cut at radius r, and the blade disk is considered as infinitesimal segments dA = 2πrdr of countless concentric circular rings. Then:

[0067] dT=2ρ(V0+v1)v1dA

[0068]

[0069] When the air-floating platform moves at low speed on the guide surface, it can be simplified to: The dimensionless induced velocity of the propeller disk during low-speed movement.

[0070] As attached Figure 2 Appendix Figure 3 The diagram shows a schematic of the airflow environment along the rotor blade profile. Analyzing each micro-element, the future flow velocity can be decomposed into the tangential u-axis of the blade element. T radial u R and vertical u P Ignore the rotor blade deflection velocity component u R There is a combined speed The vertical velocity can be decomposed into u P =V0+v1, the tangential velocity u at the infinitesimal element T =ωr. The rotor blade inflow ratio λ is defined as the ratio of the projection of the rotor relative to the incoming flow velocity V1 onto the rotor disk in the vertical direction to the rotor tip rotational linear velocity wR, which can be decomposed into λ... c and λ i ,Right now Just right

[0071] The expression for the angle of attack of the incoming flow is: θ represents the constant installation pitch angle. For the velocity angle of the infinitesimal element's flow convergence During actual rotor blade operation Generally in small quantities, with The relationship between the incoming flow angle and the inflow ratio is:

[0072] Lift coefficient C L and drag coefficient C D These are defined as the ratios of lift and drag to the reference dynamic pressure, respectively.

[0073]

[0074] The coordinate transformation expression between the normal force dz and the axial force dx is:

[0075]

[0076] Thrust and thrust coefficient can be expressed as:

[0077] dT=Ndz=N(dLcosφ-dDsinφ)

[0078]

[0079] Simplify equation (16) when When taking small amounts Also a small amount, the drag coefficient term Negligible; can be approximated as The simplified result is:

[0080] Integrating along the blade root m to the blade tip, the rotor thrust coefficient expression is obtained as follows: Substituting the empirical expression for the lift coefficient without stall effect We can obtain:

[0081] definition We can obtain the equation regarding λ: Solving for: λ in hovering state c =0, the inflow ratio expression can be simplified to: The average inflow ratio of the rotor disk was obtained: The thrust coefficient expression is obtained as: C T =2λ 2 .

[0082] Step 2: A three-axis decoupled thruster configuration is proposed, specifically including: the three degrees of freedom of the air-bearing platform—translation and rotation—on the marble platform can be considered as the planar motion of the air-bearing platform's center of mass and the rotation of other particles on the air-bearing platform around the center of mass perpendicularly upwards. That is, the thruster layout should cover six channels in total, covering positive and negative channels in three axes. To improve the thrust output accuracy and thus control accuracy, eight thrust output ports are designed to handle the positive and negative x and y axes, as well as clockwise and counterclockwise attitude rotation, achieving complete decoupling of the output of the six channels. The thruster configuration and layout are shown in the attached figure. Figure 4 and attached Figure 5 As shown.

[0083] Define this system x b The angle between the axis and the x-axis of the inertial frame is θ, and we obtain... Let be the coordinate transformation matrix from the system to the inertial frame. Inverting this matrix yields the coordinate transformation matrix from the inertial frame to the system. Represented as:

[0084]

[0085]

[0086] Step 3: To address the dead zone problem in rotor thrust, a differential rotor thrust distribution scheme is proposed, specifically including: the motion controller calculates the [F] in the inertial frame of the planar air-bearing platform. x F y T z Triaxial forces and moments, using coordinate transformation matrices We can obtain [f] under this system. x f y τ].

[0087] Rotor thrusters can achieve linear control and continuously changing output, but the model has a high degree of nonlinearity in the low thrust and low speed range with F≤0.02N and w≤20rad / s. In practical applications, they also face the problem of ESC identifying the dead zone of low duty cycle PWM waves.

[0088] By setting the rotor operating reference speed wbase to a fixed offset, and controlling the thrust difference generated by a group of opposing rotors to be equal to a preset f, the chattering problem caused by PWM dead zone and poor linearity of the speed-thrust model can be effectively avoided. The thrust distribution scheme is as follows:

[0089]

[0090]

[0091]

[0092] Where: f x f y τ and τ represent the three-axis control force and torque calculated by the main control computer, respectively; the forces decomposed into positive and negative channels on the x-axis are f1 and f5, respectively; the forces decomposed into positive and negative channels on the y-axis are f3 and f7, respectively; clockwise output torque utilizes channels f2 and f6; counterclockwise output torque utilizes channels f4 and f8.

[0093] Based on the rotor dynamics model, the corresponding f is solved. 1～8 motor speed w 1～8 Then, based on the relationship between the ESC-identified PWM duty cycle and the output speed, t is obtained by inverse solving. 1～8 The two are roughly linearly related. In the microcontroller board hardware programming, the PWM waveform signal can be manually pulled up or down to adjust the rotor speed in real time and change the thrust to achieve the control effect.

[0094] Step 4: Based on the rotor output mathematical model in Step 1, design a cascade fuzzy PID control algorithm. The control flowchart of this algorithm is shown below. Figure 1 As shown, it includes:

[0095] Step 4-1: The outer loop controller tracks the position / angle of the air-floating platform and corrects the input parameters e and ec of the fuzzy adaptive PID controller selected for the inner loop (angular) velocity tracking in real time. The fuzzy adaptive controller is a dual-input, three-output system that performs fuzzification, fuzzy inference, and defuzzification on the velocity deviation e and the rate of change of velocity deviation ec, ultimately outputting ΔK. P ,ΔK I ,ΔK D The PID parameters are adjusted in real time to balance the response time and adjustment accuracy. Taking translational motion as an example, the domains of discourse for the input quantities e and ec are set to [-5, 5] to match the outer-loop PID output and feedback accuracy, and ΔK is set. P ΔK I ΔK D The output universe of discourse is [-700, 700][-0.0005, 0.0005] and [-30000, 30000]; the fuzzy subset is defined as {NB, NM, NS, ZO, PS, PM, PB}, which means negative large, negative medium, negative small, zero, positive small, positive medium, and positive large, respectively. Figures 6 to 9 As shown;

[0096] Step 4-2: Define a set of fuzzy control rule tables, which are used to describe the fuzzy input quantities (e and ec) and the fuzzy output quantity ΔK. P ,ΔK I ,ΔK DThe following is a fuzzy control rule table showing a set of "if-then" conditional statements (using the min-max implication fuzzy inference model in this embodiment):

[0097] Table 1: ΔK P Fuzzy control rule table

[0098]

[0099] Table 2: ΔK I Fuzzy control rule table

[0100]

[0101] Table 3: ΔK D Fuzzy control rule table

[0102]

[0103] Where: fuzzy output quantity ΔK P ,ΔK I ,ΔK D The membership functions of each fuzzy subset are all triangular membership functions, which have the following form:

[0104] ξ a ξ b ξ c The x-coordinates of each control endpoint of the triangular membership function are used to control the shape of the triangular membership function; as mentioned above, in the inner loop (velocity loop) fuzzy PID algorithm, the universes of discourse of each fuzzy subset are uniformly distributed, and the x-coordinates of the control points are arranged at equal intervals from small to large.

[0105] Step 4-3: Using the defuzzification method, calculate the specific ΔK based on the fuzzy subset to which the fuzzy output belongs and its corresponding membership degree. P ΔK I ΔK D Clear quantity, and through: Real-time tuning of the PID parameters of the three-axis inner loop controller (in this embodiment, the centroid defuzzification method is used).

[0106] Step 5: Add a correction coefficient Kc to the cascaded fuzzy PID in Step 4, and calculate Δx = x at each time step. 反馈 -x 预期 and Δv=v 反馈 -v 预期The stage of the air-bearing platform during trajectory tracking is determined, and fuzzy rules are used to real-time correct the priority of the transmission of the outer loop position tracking correction to the inner loop velocity tracking parameters e and ec. This is done to avoid sudden velocity changes while ensuring settling time, and the improvement in dynamic performance can be reflected in the smoothing optimization of the velocity curve. This includes:

[0107] Step 5-1: The fuzzy logic is as follows: Initial adjustment: Position tracking error is large. The air-bearing platform accelerates to Vl in a short time, then its speed changes smoothly around Vl for a short period, smoothing the speed curve and maintaining high-speed operation while avoiding sudden speed spikes. Final adjustment: Position error converges. The speed decreases rapidly from around Vl without overshoot, converging with high precision to near the target value. When |Δx| is large, K is amplified. c Increase the proportion of position tracking correction in e and ec; with rapid convergence of |Δx|, Δv changes significantly, and as |Δv| increases, K... c Decrease; determine if |Δx| converges to near 0, K c Reduce speed changes to achieve high-precision dynamic trajectory tracking.

[0108] Table 4: Kc Fuzzy Control Rule Table

[0109]

[0110] Step 5-2: Let Δx, Δv, K c The linguistic variables are δx, δv, and Kc, respectively. The fuzzy subset is defined as {NB, NM, NS, ZO, PS, PM, PB}. A correction coefficient K is designed to be suitable for trajectory tracking with arbitrary initial states. c Fuzzy controller. Taking planar position tracking as an example, the universe of discourse for the entire process Δx is set to [-1, 1] (m), and the universe of discourse for Δv is set to [-0.025, 0.025] (m / s); the universe of discourse for the correction coefficient Kc is set to [0.8, 1.2]. Where: the fuzzy input Δx = x 反馈 -x 预期 and Δv=v 反馈 -v 预期 The fuzzy subsets all adopt trapezoidal membership functions, such as Figure 10 and Figure 11 As shown, the membership function of each fuzzy subset of the fuzzy output Kc adopts the triangular membership function, and the universe of discourse of the fuzzy subset is uniformly distributed.

[0111] While traditional cascade PID controllers offer advantages such as simplicity, high control accuracy, and the ability to improve system maneuverability to some extent by controlling both position and speed, their effectiveness remains unsatisfactory due to the crucial role of PID parameter selection. If speed limiting of the air-bearing platform's motion is required, simply adding a speed limit to the dynamic model without applying control corrections will lead to long-term deviations between the actual output and the calculated value. This embodiment improves upon the cascade PID controller by introducing fuzzy control into the inner loop (velocity loop). Cascade fuzzy PID control is applied to the air-bearing platform's motion control, and a correction coefficient Kc is added using the fuzzy controller to adjust the proportion of correction transmitted from the outer loop to the inner loop in real time. This effectively addresses the challenge of intelligently determining the air-bearing platform's trajectory tracking state, balancing the need for rapid adjustment when initial errors are large with the need for high precision in the final adjustment phase. Simultaneously, it avoids sudden speed spikes, improving the controllability of large-inertia air-bearing platforms.

[0112] Specifically, in this embodiment, to address the issues of short time and low accuracy in jet control during simulation experiments of a planar three-axis air-bearing platform, this invention proposes a scheme that uses rotor thrust as an alternative to act as the motion control actuator for the air-bearing platform; considering the significant characteristic differences between the rotor and traditional jet thrusters, a mathematical model of rotor output thrust characteristics is constructed; a three-axis decoupled thruster configuration is proposed; and to address the dead zone problem in rotor thrust, a differential rotor thrust allocation scheme is proposed.

[0113] Furthermore, to improve the dynamic performance of the system, a fuzzy adaptive cascaded PID control algorithm is proposed for controlling the rotor speed. Utilizing fuzzy mathematics to simulate human thought, the PID parameters can be tuned and optimized in real time based on the deviation *e* and the deviation rate *ec*. This approach is suitable for addressing problems such as model coupling and time-varying disturbances, adapting to changes in environmental characteristics. Using a three-axis air-bearing platform as the controlled object, the preset and measured pose information of the air-bearing platform are acquired in real time. Based on the deviation and deviation rate between the measured feedback value and the preset value, a membership function and fuzzy rules are designed to adjust the cascaded PID parameters in real time. A correction coefficient *Kc* is added to adjust the proportion of correction transmitted from the outer loop to the inner loop in real time. This balances the need for rapid adjustment when the initial error is large and the need for high precision in the final adjustment stage, avoiding sudden changes and spikes in motion speed. Moreover, this control algorithm improves stability for large-inertia air-bearing platform systems by simultaneously controlling position and velocity, achieving rapid convergence without overshoot. This results in controllable, high-precision, and stable motion control of the air-bearing platform during a wide range of maneuvers.

[0114] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on its differences from other embodiments. In particular, the device embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. The above descriptions are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for motion control of a rotor propulsion air-bearing platform based on modified cascade fuzzy PID, characterized in that, include: S1. Using a bladed rotor as the motion control actuator for the air-floating platform, a mathematical model of thrust characteristics is established, wherein the air-floating platform adopts a three-axis decoupled thruster configuration. S2. Build a motion control feedback system for the air-bearing platform, and use the thrust characteristic mathematical model to establish a cascade fuzzy PID control model for the motion control feedback system of the air-bearing platform. S3. During the adjustment of the cascaded three-axis PID parameters, the correction amount transmitted from the outer loop to the inner loop of the air-bearing platform motion control feedback system is adjusted in real time by the correction coefficient. In S1, the mathematical model of thrust characteristics includes: , and ,in, Indicates the rotor blade inflow ratio. This represents the normalized blade radius. Indicates the thrust coefficient. Indicates the angle of attack of the incoming flow. Indicates the installation pitch angle. Indicates the solidity of a rectangular blade and The number of rotor blades is The width of the rectangular fan blade is radius is ; The triaxial decoupled thruster configuration includes: a thruster layout covering positive and negative channels in three axes, totaling six channels; There are a total of 8 thrust output ports. Four thrust output ports are responsible for the positive, negative, clockwise and counterclockwise rotation of the x-axis, respectively. The other four thrust output ports are responsible for the positive, negative, clockwise and counterclockwise rotation of the y-axis, respectively.

2. The method according to claim 1, characterized in that, The three-axis decoupled thruster configuration includes: This system Axis and Inertial Frame The angle between the axes is The coordinate transformation matrix from this system to the inertial frame is: ,right Inverse transformation yields the coordinate transformation matrix from the inertial frame to the home frame. ,in: , in an inertial frame Rotate the coordinate matrix Transformed to this system , , , This represents the control forces and torques along the x and y axes of the three channels in an inertial frame. , , These are the control forces and torques of the three channels along the x and y axes of this system, calculated by the main control computer.

3. The method according to claim 1, characterized in that, In the aforementioned three-axis decoupled thruster configuration, a rotor thruster is adopted; The thrust difference generated by controlling a group of opposing rotor thrusters to output simultaneously is equal to a preset value. Among them, the operating reference speed of the rotor thruster was set. For a fixed bias; Thrust distribution schemes based on rotor thrusters include: ， ， ,in: , , These are the three-axis control forces and torques calculated by the main control computer; the forces decomposed into the positive and negative channels along the x-axis are respectively... and The forces decomposed into positive and negative channels along the y-axis are respectively and Clockwise output torque utilizes the channel and Counterclockwise output torque utilizes the channel and , This represents the reference thrust output by the rotor.

4. The method according to claim 1, characterized in that, In S2, the fuzzy output of the cascaded fuzzy PID control model is: , respectively, represent the real-time adjustment values ​​of the proportional, integral, and derivative coefficients; The methods used in the cascaded fuzzy PID control model for real-time tuning of the PID parameters of the triaxial inner loop controller include: ,in, Represents the proportionality coefficient. Represents the integral coefficient. Represents the differential coefficient. , , These represent their initial adjustment references.

5. The method according to claim 4, characterized in that, Trigonometric membership functions include: , These are the x-coordinates of the control endpoints of the trigonometric membership function, used to control the shape of the trigonometric membership function. Indicates parameter variables.

6. The method according to claim 1, characterized in that, S3 includes: Set correction factor ; According to position error and angular velocity error By correction coefficient Real-time adjustment of the correction amount of the position loop PID output in the speed loop input parameters and Medium priority level, among which, Indicates position and attitude deviation. express The rate of change.

7. The method according to claim 6, characterized in that, The correction coefficient Real-time adjustment of the correction amount of the position loop PID output in the speed loop input parameters and Medium priority levels include: When detected When the value is greater than the preset value, magnify. Increase position tracking correction amount and The proportion of the middle; Accompanied After it begins to converge, Increase while decreasing until It converges to near 0.

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