A multi-degree-of-freedom motion platform control method based on model reference self-adaptation

Abstract

This invention discloses a multi-degree-of-freedom motion platform control method based on model reference adaptation, relating to the field of flight simulation systems. The method includes: receiving three-axis overload and flight attitude commands output from the flight simulation terminal; establishing a four-level series axis coordinate transformation matrix system from the base to the pilot's end; and completing the initial parameter configuration of the control model. Inverse dynamics is performed along the four-level series axis system to obtain the target rotation angle and target angular velocity commands corresponding to the principal axis, heading axis, roll axis, and pitch axis. This invention directly maps flight overload and attitude commands through inverse dynamics of the four-level series axis system, avoiding the cumulative deviation of step-by-step approximation transformations. It uses weighted tracking error to drive an adaptive law to adjust the gain online, compensating for load fluctuations and friction effects. Simultaneously, wind resistance and coupling torque are superimposed as compensation terms to reduce aerodynamic disturbances. The bottom-level PID cascade loop and the upper-level adaptive loop are smoothly connected, effectively improving the tracking fidelity of the platform under complex operating conditions.

Description

Technical Field

[0001] This invention relates to the field of flight simulation system technology, specifically to a multi-degree-of-freedom motion platform control method based on model reference adaptation. Background Technology

[0002] Multi-degree-of-freedom motion platforms for flight simulators can reproduce the flight attitude and overload sensation of aircraft in ground training environments. The quality of the platform's simulation effect depends on the control performance of the multi-axis linkage control system. Existing motion platforms of the same type generally adopt a PID velocity-position dual closed-loop control architecture, construct a dynamic model based on the Newton-Euler equations, convert flight overload parameters into target motion commands for each motion axis, and use fixed control parameters obtained through offline tuning to achieve motion closed-loop control.

[0003] The invention patent application with application number 202010207104.5 discloses an anti-interference electric six-degree-of-freedom parallel mechanism control method. This application adopts an inner and outer loop dual PID structure with a disturbance observer to suppress the load fluctuation of a single branch of the mechanism and improve the stability of single-axis position tracking under normal working conditions.

[0004] Conventional PID upper-level control is difficult to compensate online for model deviations caused by multibody dynamics coupling and aerodynamic drag disturbances. Under high-speed maneuvering simulation conditions of aircraft, each axis is prone to tracking lag and oscillation. Existing technologies have not yet formed a mature upper-level control strategy and cannot simultaneously take into account the simulation accuracy under all conditions and the robustness of system operation. Summary of the Invention

[0005] In view of the above-mentioned shortcomings of the existing technology, the present invention provides a multi-degree-of-freedom motion platform control method based on model reference adaptation, which can effectively solve the problems of the existing technology.

[0006] To achieve the above objectives, the present invention is implemented through the following technical solutions;

[0007] This invention discloses a multi-degree-of-freedom motion platform control method based on model reference adaptation, comprising:

[0008] The system receives three-axis overload and flight attitude commands from the flight simulation terminal, establishes a four-level series axis coordinate transformation matrix system from the base to the pilot's end, and completes the initial parameter configuration of the control model. It performs inverse dynamics calculations along the four-level series axis system to obtain the target rotation angle and target angular velocity commands corresponding to the principal axis, heading axis, roll axis, and pitch axis. It constructs a reference model for the model reference adaptive controller, using the target rotation angle and target angular velocity of each axis as input to generate the desired dynamic response state variables of the system. It collects real-time rotation angle and real-time angular velocity feedback data for each motion axis, subtracts them from the desired state variables output by the reference model, and generates a system tracking error vector. It performs online adaptive law calculations using the tracking error vector, adjusts the controller's feedback and feedforward gain parameters in real time, and outputs the control adjustment quantities for each axis. It sends the control adjustment quantities of each axis to the corresponding servo drivers, which execute PID-based low-level speed-position closed-loop control, synchronously transmitting back real-time operating status data for each axis.

[0009] Furthermore, the four-level series axis coordinate transformation matrix system established from the base to the pilot's end obeys:

[0010] Along the series power transmission path of the principal axis, yaw axis, roll axis, and pitch axis, five levels of nodal coordinate systems are constructed sequentially: base coordinate system, yaw nodal coordinate system, roll nodal coordinate system, pitch nodal coordinate system, and pilot coordinate system. The homogeneous transformation matrix between adjacent coordinate systems is constructed as follows:

[0011] ;

[0012] In the formula: Let be the homogeneous transformation matrix of the i-th level coordinate system relative to the (i-1)-th level coordinate system, where i takes the values ​​1, 2, 3, and 4, corresponding to the transformation nodes of the principal axis, yaw axis, roll axis, and pitch axis, respectively. This is the rotation matrix for the corresponding axis system; The position vector between the origins of adjacent coordinate systems;

[0013] The total transformation matrix of the four-level series axis system is obtained by multiplying the transformation matrices of each level in the order of motion transmission, i.e. .

[0014] Furthermore, the inverse dynamics calculation along the four-level series axis system is performed to obtain the operational compliance of the target rotation angle and target angular velocity commands corresponding to each axis:

[0015] Pilot-side three-way overload commands output from the flight simulation terminal As input, the target rotation angles for each axis are inversely solved based on the attitude mapping relationship of the total transformation matrix, where the target rotation angle of the roll axis is... Target rotation angle relative to pitch axis Solve analytically using the following formula:

[0016] ;

[0017] In the formula: intermediate variables , , ; These are the trigonometric function values ​​for the corresponding axis rotation angle; The triaxial equivalent overload in the base coordinate system is obtained by combining the principal axial acceleration, tangential acceleration and gravitational acceleration; Always takes -1;

[0018] The target rotation angles of the main axis and the heading axis are obtained by simultaneously solving the relationship between the tangential component of the overload and the transformation of the base coordinate system, and the target angular velocity is generated by differentiating the target rotation angle with respect to time.

[0019] Furthermore, during the inverse dynamics inverse solution process, the wind resistance equivalent disturbance torque of the shaft system motion is calculated simultaneously and superimposed on the target torque command:

[0020] ;

[0021] In the formula: This is the wind resistance equivalent disturbance torque corresponding to single-axis motion; The air density under the current environment; is the air resistance coefficient of the corresponding shaft moving parts; S is the equivalent frontal area of ​​the part; The equivalent force arm for component rotation; This represents the real-time rotational angular velocity of the corresponding axis;

[0022] The calculated wind resistance torque is superimposed as a disturbance compensation term into the target torque output by the inverse dynamics.

[0023] Furthermore, a reference model for the model-reference adaptive controller is constructed, generating the desired dynamic response state variables of the system. For each motion axis, a decoupled second-order linear reference model is constructed, taking the target rotation angle command for that axis as input and outputting the desired state variables composed of the desired rotation angle and desired angular velocity. The state-space expression of the reference model is:

[0024] ;

[0025] In the formula: The state column vector of the reference model; For the desired turning angle; The desired angular velocity; This is the system state matrix; The natural angular frequency of the reference model; The damping ratio is used as a reference model, and both are preset desired dynamic performance parameters. The input matrix is ​​r; r is the target rotation angle command for the corresponding axis. This is the output matrix; The expected rotation angle state quantity output by the reference model.

[0026] Furthermore, when generating the system tracking error vector, the real-time state quantities acquired along each motion axis are subtracted from the expected state quantities output by the reference model, and a diagonal state weighting matrix is ​​introduced to construct an extended tracking error vector:

[0027] ;

[0028] In the formula: This is a column vector of single-axis tracking errors; This refers to the corner tracking error. This refers to the angular velocity tracking error. This is the real-time state column vector of the controlled object; This refers to the real-time rotation angle obtained from the data collection. The real-time angular velocity obtained from the data acquisition; It is a diagonal state weighting matrix; This is the weighting coefficient for the cornering error; This is the angular velocity error weighting coefficient.

[0029] Furthermore, by tracking the error vector and performing online adaptive law calculations to adjust the controller's feedback and feedforward gain parameters in real time, a parameter update law is constructed based on Lyapunov stability theory. This law is used to iteratively adjust the state feedback gain vector and feedforward gain coefficients online, where the update formula for the state feedback gain is:

[0030] ;

[0031] The formula for updating the feedforward gain is:

[0032]

[0033] In the formula: State feedback gain vector The rate of change over time after transpose The row vector of state feedback gain; For corner feedback gain; Angular velocity feedback gain; For the feedback gain adaptive learning rate diagonal matrix, All are positive real number learning rate parameters; The feedforward gain is the adaptive learning rate; P is the Lyapunov equation. The symmetric positive definite solution matrix, Q is a pre-defined second-order symmetric positive definite weighting matrix; , These are the time rates of change of the feedback gain and the feedforward gain, respectively. After numerical integration, the real-time gain parameters for the current period are obtained.

[0034] The time change rates of the two types of gains are numerically integrated to obtain the real-time gain parameters for the current period.

[0035] Furthermore, during the real-time adjustment of the controller's feedback and feedforward gain parameters, feasible region projection constraint calculations are performed on the gain parameters, which follow the following rules:

[0036] ;

[0037] In the formula: Let be the row vector of state feedback gain obtained by adaptive law solution at time t;

[0038] Projection operator The operation logic is as follows: when the gain element exceeds the corresponding upper limit... The upper limit is taken when the value exceeds the corresponding lower limit. Take the lower limit value at that time; and These are the lower and upper bound matrices of the feedback gain, respectively, determined by the physical rated parameters of the shaft servo system;

[0039] Feedforward gain coefficient Execute amplitude constraints with the same rules synchronously.

[0040] Furthermore, the control adjustment amount of each output axis is generated by combining three parts: a feedforward control term, a state feedback control term, and a dynamic compensation term.

[0041] ;

[0042] Where: u is the single-axis control adjustment amount output to the servo driver; For feedforward control terms; This is a state feedback control item; This is a dynamic compensation term.

[0043] Furthermore, when executing the underlying speed-position closed-loop control based on PID, the underlying speed-position closed-loop control uses a cascaded architecture of position loop and speed loop. The position loop generates target angular velocity commands with the target rotation angle of each axis as input.

[0044] After receiving the control adjustment from the upper layer, the servo driver adds it as an adaptive feedforward correction factor to the target angular velocity command output by the position loop, and then performs the calculation using PID control logic in the velocity loop.

[0045] ;

[0046] In the formula: This is the final torque control value output by the speed loop; These are the proportional, integral, and differential gain coefficients corresponding to the velocity loop; The target angular velocity command output by the position loop; The real-time angular velocity feedback value obtained from the acquisition;

[0047] The control adjustment quantity u output by the upper-level model reference adaptive controller is superimposed on the speed loop setpoint.

[0048] Compared with the known prior art, the technical solution provided by this invention has the following beneficial effects:

[0049] This invention constructs a four-level cascaded axis coordinate transformation matrix system and performs inverse dynamics along this chain. The multi-degree-of-freedom motion platform can directly map the overload and attitude commands output from the flight simulation terminal into target motion parameters for each axis, thereby avoiding the cumulative deviation caused by traditional step-by-step approximation transformation. On this basis, a second-order linear reference model is independently configured for each motion axis, and the adaptive law is driven by the weighted tracking error of rotation angle and angular velocity to adjust the feedback and feedforward gain online. This allows the simulation platform to maintain the desired dynamic response when the load changes or friction characteristics fluctuate. At the same time, Lyapunov stability constraints and gain projection limiting are introduced to ensure that the parameter adjustment process is safe and controllable. The wind resistance equivalent disturbance torque and nonlinear coupling torque obtained from the inverse dynamics solution are superimposed on the control quantity as compensation terms to reduce the negative impact of aerodynamic drag and inter-axis coupling on position accuracy under high-speed motion. In addition, the smooth connection between the bottom-level PID speed-position cascade loop and the upper-level adaptive output takes into account the requirements of fast following and steady-state zero steady-state error, ultimately improving the tracking fidelity and operational stability of the platform under complex overload conditions. Attached Figure Description

[0050] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0051] Figure 1 This is a flowchart illustrating a multi-degree-of-freedom motion platform control method based on model reference adaptation.

[0052] Figure 2 This is a schematic diagram of the four-level series axis system and the five-level node coordinate system in this invention;

[0053] Figure 3 This is a schematic diagram of the model reference adaptive control principle in this invention;

[0054] Figure 4 This is a comparison curve of the tracking error between the method in this invention and the traditional fixed-gain PID scheme. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0056] The present invention will be further described below with reference to embodiments.

[0057] Example:

[0058] This embodiment presents a model reference adaptive multi-degree-of-freedom motion platform control method, such as... Figure 1 As shown, it includes:

[0059] Receive the three-axis overload and flight attitude commands output from the flight simulation terminal, establish a four-level serial axis coordinate transformation matrix system from the base to the pilot terminal, and complete the initial parameter configuration of the control model;

[0060] It should be noted that:

[0061] Flight attitude commands include three types of attitude angle commands: pitch angle, roll angle, and yaw angle, which are used to correct the attitude of the shaft rotation angles obtained by the inverse kinematics of overload.

[0062] After obtaining the initial target rotation angles for each axis through inverse dynamics, the attitude increments corresponding to the flight attitude commands are mapped to each motion axis through coordinate transformation, and then superimposed on the initial target rotation angles to obtain the final target rotation angle commands for each axis. This approach balances motion perception simulation with accurate reproduction of attitude angles. The superposition weight of the attitude commands can be adjusted according to the simulation scenario; a weight of 1.0 is used in high-fidelity scenarios, while a weight of 0.3 to 0.7 is used in motion perception-first scenarios.

[0063] The initial parameter configuration includes the initialization of three types of parameters: the first type is structural parameters, which involves entering the structural dimensions, moment of inertia, reduction ratio, and other inherent hardware parameters of each shaft system; the second type is control parameters, which involves setting the reference model's natural frequency and damping ratio, error weighting coefficient, adaptive learning rate, gain upper and lower limits, PID parameters, and other control algorithm parameters; the third type is operating parameters, which involves configuring the control sampling period, communication period, sensor range, and calibration parameters.

[0064] After all parameters are configured, the system stability must be verified by an unloaded step test. Only after confirming that there are no abnormalities can the system be put into formal operation.

[0065] The four-level cascaded axis coordinate transformation matrix system from the base to the pilot's end follows:

[0066] Along the series power transmission path of the principal axis, yaw axis, roll axis, and pitch axis, five levels of nodal coordinate systems are constructed sequentially: base coordinate system, yaw nodal coordinate system, roll nodal coordinate system, pitch nodal coordinate system, and pilot coordinate system. The homogeneous transformation matrix between adjacent coordinate systems is constructed as follows:

[0067] ;

[0068] In the formula: Let be the homogeneous transformation matrix of the i-th level coordinate system relative to the (i-1)-th level coordinate system, where i takes the values ​​1, 2, 3, and 4, corresponding to the transformation nodes of the principal axis, yaw axis, roll axis, and pitch axis, respectively. The rotation matrix for the corresponding axis system is given by the rotation angles of each axis. Generated through trigonometric function operations; The position vector between the origins of adjacent coordinate systems is determined by two structural constants: the effective length of the cantilever and the width of the U-shaped frame.

[0069] At the implementation level:

[0070] The origin of the base coordinate system is set at the center of the upper surface of the platform base. The Z-axis points vertically upward, the X-axis points directly in front of the platform, and the Y-axis points directly to the left of the platform. The principal axis is a slewing bearing axis that rotates about the Z-axis of the base, with a corresponding transformation node i=1. Its rotation matrix is ​​the rotation about the Z-axis. The orthogonal matrix is ​​denoted by ; the heading axis is a swing axis mounted on the main spindle rotary table, rotating about its own Y-axis, corresponding to transformation node i=2, and its rotation matrix is ​​the rotation about the Y-axis. The standard orthogonal matrix; the roll axis is a rotation axis installed at the end of the yaw axis swing arm, rotating about its own X-axis, with corresponding transformation node i=3, and its rotation matrix is ​​a rotation about the X-axis. The standard orthogonal matrix; the pitch axis is the cockpit yaw axis mounted between the roll axis U-frames and rotating about its own Y-axis, corresponding to transformation node i=4, and its rotation matrix is ​​the rotation about the Y-axis. The orthogonal matrix;

[0071] The position vectors at each level are directly assigned values ​​by the structural dimensions such as the cantilever installation length and support installation spacing of the corresponding axis system, and become fixed constants after the platform is assembled.

[0072] The above matrix is ​​based on the power transmission sequence from the base to the pilot in a four-level series axis system, which is then divided into five levels of node coordinate systems. Spatial rotation and position translation are decoupled and encapsulated into a unified matrix structure. The rotation matrix is ​​calculated only by single-axis rotation angle trigonometric functions, and the position vector is directly assigned by the fixed structural dimensions of the equipment. By multiplying them level by level, the spatial mapping relationship of the entire axis system can be completely restored. This is different from the limitation of traditional single-level coordinate transformation, which can only handle two coordinate system transformations. It builds a complete coordinate mapping system that is compatible with multi-axis linkage in one go, providing a unified mathematical carrier for subsequent inverse calculations from overload to rotation angle.

[0073] The total transformation matrix of the four-level series axis system is obtained by multiplying the transformation matrices of each level in the order of motion transmission, i.e. ;

[0074] The specific forms of the rotation matrices corresponding to each level of transformation matrix are as follows: i=1 corresponds to the principal axis, rotating around the Z-axis, and the rotation matrix is ​​[[ ,- ,0],[ , [0,0,1]; i=2 corresponds to the heading axis, rotating around the Y-axis, with the rotation matrix being [[ ,0, ],[0,1,0],[- ,0, i=3 corresponds to the roll axis, rotating around the X-axis, with the rotation matrix being [[1,0,0],[0, ,- ],[0, , i=4 corresponds to the pitch axis, rotating around the Y-axis, with the rotation matrix being [[ ,0, ],[0,1,0],[- ,0, ]];

[0075] Each position vector is a 3×1 column vector, and the element values ​​are directly determined by the structural installation dimensions of the corresponding shaft system.

[0076] Inverse dynamics calculations are performed along the four-level tandem axis system to obtain the target rotation angle and target angular velocity commands corresponding to the main axis, heading axis, roll axis and pitch axis;

[0077] Inverse dynamics calculations are performed along the four-stage tandem axis system to obtain the operational compliance of the target rotation angle and target angular velocity commands for each axis:

[0078] Pilot-side three-way overload commands output from the flight simulation terminal As input, the three-dimensional overload command output by the flight simulation terminal is the specific force overload in the pilot's cockpit body coordinate system. The X-axis points forward along the cockpit longitudinal axis, the Y-axis points to the left along the cockpit transverse axis, and the Z-axis points upward along the cockpit vertical axis. The positive overload direction is consistent with the positive direction of the coordinate axes. This coordinate system completely coincides with the pilot's coordinate system and serves as the target input reference for inverse dynamics. Based on the attitude mapping relationship of the total transformation matrix, the target rotation angles of each axis are solved, including the roll axis target rotation angle. Target rotation angle relative to pitch axis Solve analytically using the following formula:

[0079] ;

[0080] In the formula: intermediate variables , , ; These are the trigonometric function values ​​for the corresponding axis rotation angle; The triaxial equivalent overload in the base coordinate system is obtained by combining the principal axial acceleration, tangential acceleration and gravitational acceleration; Since we always take -1, the above equation has already been simplified.

[0081] The three-dimensional equivalent overload in the base coordinate system is synthesized as follows: Let the spindle rotation radius be R, and the real-time spindle rotation angle be... Real-time angular velocity is Real-time angular acceleration is The magnitude of the centripetal acceleration generated by the principal axis motion is The direction is radially outward along the principal axis; the magnitude of the tangential acceleration is... The direction is tangentially forward along the principal axis. Projecting the centripetal acceleration and tangential acceleration onto the X and Y axes of the base coordinate system, respectively, and combining them with the component of gravitational acceleration on the Z axis, then normalizing to units of gravitational acceleration g, yields the equivalent overload component of the base:

[0082] ;

[0083] The vertical downward component of gravitational acceleration;

[0084] The above formula uses the end-point three-axis overload output from flight simulation as input, and combines the base equivalent overload and intermediate variables of trigonometric functions of each axis system to build an arctangent analytical expression, directly outputting accurate axis rotation angle values. It abandons the calculation delay and iteration convergence deviation caused by traditional numerical iterative inverse solution, and at the same time, it simplifies the gravity constant overload component in advance and integrates it into the intermediate variables to complete the pre-calculation, effectively reducing the amount of calculation in the real-time control cycle. It can meet the high real-time rotation command output requirements of the motion platform and accurately match the nonlinear geometric constraints of overload attitude mapping.

[0085] The four-axis target rotation angle is solved using a step-by-step elimination process:

[0086] First, calculate the spindle azimuth angle based on the horizontal component of the overload at the pilot's end. ;

[0087] by Substituting the known quantities into the base equivalent overload formula yields... ;

[0088] First, solve for the roll axis angle using algebraic elimination. ;

[0089] Will , Substitute the values ​​to solve for the heading axis rotation angle. ;

[0090] Substitute the first three factors into the solution for the pitch axis rotation. ;

[0091] If a negative value is encountered during the solution process, take the square root of its absolute value and adjust the corner sign accordingly to ensure the physical rationality of the overload mapping. The accuracy requirement can be met by completing one solution within a single control cycle.

[0092] During the angle calculation process, the range of solution values ​​is limited according to the mechanical angle range of each axis, and solutions that exceed the range are discarded. If there are multiple valid solutions within the range, the solution with the smaller difference from the target angle of the previous cycle is selected to ensure the continuity of the shaft system motion and avoid jumps. If all solutions exceed the mechanical limit under boundary conditions, the corresponding limit value is taken as the target angle.

[0093] The target rotation angles of the main axis and the heading axis are obtained by simultaneously solving the relationship between the tangential component of the overload and the transformation of the base coordinate system; the target angular velocity is generated by differentiating the target rotation angle with respect to time.

[0094] Among them, the target rotation angle of the main axis Target rotation angle relative to the heading axis Simultaneous calculation using the following formula:

[0095] ;

[0096] ;

[0097] In the formula: , The X and Y direction overload commands output by the flight simulation terminal to the pilot. Roll axis rotation angle The sine value;

[0098] The calculation first involves determining the principal axis azimuth angle using the horizontal component of the overload at the pilot's end. Then, by combining the attitude coupling relationship between the pitch axis and roll axis, the yaw axis yaw angle can be solved. The target angular velocity is obtained by taking the first-order difference of time with respect to the corresponding rotation angle, and the difference step size is consistent with the system control sampling period.

[0099] During the inverse dynamics inverse solution calculation, the wind resistance equivalent disturbance torque of the shaft system motion is calculated simultaneously and superimposed on the target torque command:

[0100] ;

[0101] In the formula: This is the wind resistance equivalent disturbance torque corresponding to single-axis motion; The air density under the current environment; is the air resistance coefficient of the corresponding shaft moving parts; S is the equivalent frontal area of ​​the part; The equivalent force arm for component rotation; This represents the real-time rotational angular velocity of the corresponding axis;

[0102] During the implementation phase, the above parameters are determined as follows:

[0103] The air density ρ is taken as 1.225 kg / m³ at room temperature under standard atmospheric pressure. In actual use, it can be corrected according to the ambient temperature and air pressure.

[0104] air drag coefficient The effective frontal area S is selected based on the shape characteristics of the moving parts. For flat components, the value is 1.0~1.2, and for cylindrical components, it is 0.8~1.0. In high-precision scenarios, it can be calibrated through wind tunnel testing. The equivalent frontal area S is the projected area of ​​the moving part in the direction perpendicular to the rotational linear velocity, calculated based on the component's dimensions. The rotational equivalent force arm... The vertical distance from the center of mass of the moving part to the corresponding axis of rotation is determined by the simulation results of the center of mass of the platform's three-dimensional model or the actual weighing test results.

[0105] The above formula combines the classical calculation logic of fluid low-speed flow resistance, transforms the aerodynamic drag generated by shaft rotation into an equivalent disturbance force rectangle, and incorporates air density, component shape, rotation radius, and real-time angular velocity into a unified formula. It directly quantifies the nonlinear disturbance amplitude caused by wind resistance during motion, and can be synchronously superimposed on the inverse dynamic target torque for feedforward compensation. This makes up for the shortcomings of most similar multi-degree-of-freedom platform control schemes that ignore aerodynamic interference and only consider mechanical inertial coupling, thereby effectively reducing the negative impact of wind resistance on shaft tracking accuracy during high-speed motion.

[0106] The calculated wind resistance torque is superimposed as a disturbance compensation term into the target torque output by the inverse dynamics to offset the impact of aerodynamic disturbances on control accuracy.

[0107] The drag torque compensation is divided into two parts: feedforward and feedback. In the inverse dynamics stage, the target angular velocity is used to calculate the drag feedforward compensation amount to predict the impact of aerodynamic drag in advance. In the real-time control stage, the real-time angular velocity of the previous cycle is used to calculate the drag feedback correction amount to correct the deviation of the feedforward compensation.

[0108] The two compensation amounts are superimposed and incorporated into the dynamic compensation term, taking into account both the real-time performance and accuracy of the compensation.

[0109] The wind resistance torque is uniformly incorporated into the dynamic compensation term, and together with the inertial torque and Coriolis torque, it constitutes a complete nonlinear compensation quantity;

[0110] The calculation first solves for the inertial torque, Coriolis torque and wind resistance torque of a single axis, and then adds the three algebraically to obtain the total compensation torque. After dimensional conversion, it is converted into an equivalent quantity of angular velocity and then substituted into the control adjustment quantity synthesis formula as a compensation term.

[0111] The sign of the drag torque is opposite to the sign of the real-time angular velocity of the corresponding axis to ensure that it counteracts the aerodynamic drag effect during motion.

[0112] A reference model for the adaptive controller is constructed, using the target rotation angle and target angular velocity of each axis as inputs to generate the desired dynamic response state variables of the system.

[0113] A reference model for the adaptive controller is constructed, generating the desired dynamic response state variables of the system. For each motion axis, a decoupled second-order linear reference model is constructed. Taking the target rotation angle command for that axis as input, the output is the desired state variable composed of the desired rotation angle and desired angular velocity. The reference model uses the target rotation angle command as the main input, and simultaneously adds the target angular velocity command as a feedforward compensation term to the state update of the reference model. Specifically, the target angular velocity is directly used as the feedforward component of the desired angular velocity of the reference model, and added to the desired angular velocity obtained from solving the state equations to form the final desired angular velocity state variable. This accelerates the response speed of the reference model to commands and reduces its own dynamic lag. The state-space expression of the reference model is:

[0114] ;

[0115] In the formula: The state column vector of the reference model; For the desired turning angle; The desired angular velocity; This is the system state matrix; The natural angular frequency of the reference model; The damping ratio is used as a reference model, and both are preset desired dynamic performance parameters.

[0116] Among them, the natural angular frequency of the reference model The damping ratio is determined based on the platform's mechanical resonant frequency and the servo response bandwidth, and is taken as 1 / 3 to 1 / 2 of the servo system's closed-loop speed loop bandwidth; in this embodiment, it is taken as 15 rad / s. We set the value to 0.707 to ensure that the system has the optimal second-order dynamic response characteristics, taking into account both response speed and overshoot suppression.

[0117] During actual debugging, the damping ratio can be adjusted within the range of 0.5 to 1.0 according to the platform stability requirements, and the natural angular frequency can be adjusted within the range of 10 to 30 rad / s according to the response speed requirements.

[0118] The input matrix is ​​r; r is the target rotation angle command for the corresponding axis. This is the output matrix; The desired rotation angle state quantity output by the reference model;

[0119] The above formula independently builds a second-order decoupled linear dynamic model for each motion axis, and describes the desired motion process by splitting the dual state variables of rotation angle and angular velocity. The ideal dynamic response characteristics of the platform can be freely set by natural frequency and damping ratio. The reference models of each axis are not coupled to each other, and there is no need for complex decoupling matrix preprocessing input instructions. Compared with multi-axis coupled reference models, it greatly reduces the complexity of online solution, and provides a standardized expected state output benchmark for subsequent calculation of dual tracking errors of rotation angle and angular velocity, which is compatible with the single-axis independent adaptive parameter adjustment architecture.

[0120] The nominal model of a single-axis controlled object adopts a second-order linear time-varying structure, and its state-space expression is as follows: ,in The state vector of the controlled object. The state matrix, The input matrix; These are time-varying parameters related to the moment of inertia and damping coefficient of the shaft system. The gain parameter is related to the servo torque coefficient. Both of them change with load and speed fluctuations and are model uncertainties that need to be compensated for in adaptive control.

[0121] The controller is designed assuming that the relative order of the controlled object is consistent with the reference model and that the high-frequency gain is positive, thus satisfying the standard applicability conditions of model reference adaptive control.

[0122] Collect real-time rotation angle and real-time angular velocity feedback data of each motion axis, and subtract them from the expected state variables output by the reference model to generate the system tracking error vector;

[0123] The real-time rotation angle and real-time angular velocity are both acquired by the photoelectric encoder at the servo motor end. The encoder resolution is no less than 17 bits, and the sampling frequency is consistent with the control cycle. The acquired rotation angle and angular velocity at the motor end need to be divided by the reduction ratio of the reducer and converted into the actual rotation angle and angular velocity at the load end before being used for tracking error calculation and adaptive law solution.

[0124] The encoder's original signal is processed by a first-order low-pass filter before use. The filter cutoff frequency is set to 1 / 10 of the control sampling frequency to suppress high-frequency measurement noise.

[0125] When generating the system tracking error vector, the difference between the real-time state variables acquired from each motion axis and the expected state variables output by the reference model is calculated, and a diagonal state weighting matrix is ​​introduced to construct an extended tracking error vector:

[0126] ;

[0127] In the formula: This is a column vector of single-axis tracking errors; This refers to the corner tracking error. This refers to the angular velocity tracking error. This is the real-time state column vector of the controlled object; This refers to the real-time rotation angle obtained from the data collection. The real-time angular velocity obtained from the data acquisition; It is a diagonal state weighting matrix; This is the weighting coefficient for the cornering error; These are the angular velocity error weighting coefficients, and both are preset positive real constants;

[0128] The weighting coefficients for rotation angle error and angular velocity error are quantified and determined according to the following rules: Using the maximum allowable steady-state rotation angle error and maximum allowable steady-state angular velocity error corresponding to the single-axis motion of the flight simulation platform as the quantification benchmark, the weighting coefficients are proportional to the reciprocal of the corresponding maximum allowable error, i.e., satisfying... , To ensure a uniform scaling factor, a positive real constant is chosen to adjust the overall rate of error convergence. The preset maximum allowable steady-state rotation angle error for a single axis. The maximum allowable steady-state angular velocity error for a single axis is preset, and both are given in advance according to the motion accuracy level index of the platform.

[0129] By tracking the error vector, the adaptive law is solved online, and the feedback and feedforward gain parameters of the controller are adjusted in real time to output the control adjustment amount of each axis.

[0130] By tracking the error vector and performing online adaptive law calculations to adjust the controller's feedback and feedforward gain parameters in real time, a parameter update law is constructed based on Lyapunov stability theory. This law is used to iteratively adjust the state feedback gain vector and feedforward gain coefficients online. The update formula for the state feedback gain is as follows:

[0131] ;

[0132] The formula for updating the feedforward gain is:

[0133]

[0134] In the formula: State feedback gain vector The rate of change over time after transpose The row vector of state feedback gain; For corner feedback gain; Angular velocity feedback gain; For the feedback gain adaptive learning rate diagonal matrix, All are positive real number learning rate parameters; The feedforward gain is the adaptive learning rate; P is the Lyapunov equation. The symmetric positive definite solution matrix, Q is a pre-defined second-order symmetric positive definite weighting matrix;

[0135] The weighting matrix Q is a second-order diagonal positive definite matrix, in the form of: ,in , The value of is positively correlated with the system's expected error convergence speed. In this embodiment... Take 1.0, Take 0.5, which can be adjusted within the range of 0.1 to 10 according to the actual dynamic performance requirements of the platform;

[0136] When solving the P matrix, the state matrix of the reference model is used. Substituting the weighted matrix Q, the symmetric positive definite solution is directly obtained using matrix algebra operations. This solution is a fixed matrix and can be calculated offline and stored in the control program without the need for online real-time solution.

[0137] , These are the time rates of change of the feedback gain and the feedforward gain, respectively. After numerical integration, the real-time gain parameters for the current period are obtained.

[0138] The above formula derives the feedback and feedforward gain iteration formulas based on the Lyapunov global asymptotic stability condition. It splits the independent adaptive learning rate matrices of the rotation angle and angular velocity channels and uses them in conjunction with the positive definite solution matrix of the Lyapunov equation to transmit error correction signals. The learning rate is quantitatively calibrated based on the control sampling period and the expected convergence time. It eliminates the need for manual trial and error to adjust the gain rate. It can continuously correct the controller parameters online while ensuring the stability of the closed-loop system. It adapts to the time-varying nonlinear disturbances caused by shaft inertia and aerodynamic drag, and solves the shortcoming of fixed-gain PID that cannot adapt to dynamic parameter changes.

[0139] The time change rates of the two types of gains are numerically integrated to obtain the real-time gain parameters for the current period.

[0140] Specifically, numerical integration is performed using the first-order forward Euler method, with the integration step size corresponding to the system control sampling period. Equal, the gain parameter is updated once per control cycle, with the iterative form being: , , where k is the current control cycle number and k-1 is the previous cycle number;

[0141] The initial values ​​of the feedback gain and feedforward gain are obtained using conventional PID tuning results. The initial angle feedback gain is taken as 1.2 times the position loop proportional gain, the initial angular velocity feedback gain is taken as 0.8 times the velocity loop proportional gain, and the initial value of the feedforward gain is taken as 1.0, which can ensure the stability of the system in the initial operation phase.

[0142] The parameter update law is constructed by selecting an extended quadratic Lyapunov function composed of the quadratic terms of tracking error and parameter error, and setting the time derivative of this function along the trajectory of the closed-loop system to be negative definite. This is used as a global asymptotic stability constraint. The above gain update formula is derived by substituting it into the state equations of the reference model and the state equations of the controlled object. The solution matrix P of the Lyapunov equation is the intermediate operation matrix of this construction process, and the weighting matrix Q is preset according to the expected convergence speed of the system.

[0143] The following rules apply to quantification: Using the system control sampling period and the expected convergence time constant of the corresponding gain channel as a benchmark, and combining this with the calibration values ​​of the corresponding channel elements of the Lyapunov weighting matrix, the following conditions must be met. ;

[0144] In the formula: The sampling duration is controlled by the system in a single cycle. These are the expected convergence time constants corresponding to the rotation feedback gain and the angular velocity feedback gain, respectively. These are the elements of the first and second rows on the main diagonal of the weighting matrix Q, respectively. All baseline parameters are pre-defined based on the platform's dynamic performance requirements; feedforward gain adaptive learning rate. Using the same rules, independent quantization is performed in conjunction with the feedforward channel calibration coefficients;

[0145] During the real-time adjustment of the controller's feedback and feedforward gain parameters, feasible region projection constraint calculations are performed on the gain parameters, which satisfy the following:

[0146] ;

[0147] In the formula: Let t be the state feedback gain row vector obtained by adaptive law solution at time t, corresponding to the feedback gain parameter of the aforementioned real-time adjusted output;

[0148] The above formula defines the upper and lower limit range of gain based on the rated output range of the servo driver hardware. The gain after adaptive iteration is limited by a piecewise projection operator. The feedforward gain is synchronously applied with the same constraint logic to avoid the continuous drift of gain exceeding the hardware's tolerance range during long-term iteration of the adaptive law. This eliminates servo oscillation and torque saturation problems caused by gain exceeding the limit. While retaining the advantages of adaptive parameter adjustment, it matches the physical execution boundary of the servo system and improves the stability of long-term continuous simulation operation.

[0149] Projection operator The operation logic is as follows: when the gain element exceeds the corresponding upper limit... The upper limit is taken when the value exceeds the corresponding lower limit. Take the lower limit value at that time; and These are the lower and upper bound matrices of the feedback gain, respectively, determined by the physical rated parameters of the shaft servo system;

[0150] The gain upper and lower limits are calculated based on the rated output torque of the servo system. Let the rated output torque of the servo motor be... The reducer has a reduction ratio of i, and the motor torque coefficient is... The upper limit of the corresponding corner feedback gain lower limit value Upper limit of angular velocity feedback gain lower limit value ,in This represents the maximum permissible angle deviation per single cycle. The maximum permissible angular velocity deviation per single cycle is set according to the platform motion accuracy index;

[0151] The upper and lower limits of the feedforward gain are set to 1.5 and 0.5 respectively to ensure that the feedforward amount will not be over-compensated or under-compensated.

[0152] Feedforward gain coefficient The same amplitude constraints are applied synchronously to suppress gain drift and parameter overshoot.

[0153] The output control adjustment quantities for each axis are generated by combining three parts: feedforward control term, state feedback control term, and dynamic compensation term.

[0154] ;

[0155] Where: u is the single-axis control adjustment amount output to the servo driver; This is a feedforward control term used to perform feedforward tracking compensation on the target turning angle command; This is a state feedback control term used for closed-loop correction of real-time state deviations; As a dynamic compensation term, it is a combination of the equivalent inertial moment and Coriolis moment of the shaft system obtained by solving the inverse dynamic model, used to counteract the nonlinear coupling disturbance during the shaft system motion process;

[0156] It should be noted that:

[0157] Both the inertia matrix and the Coriolis matrix are 4×4 in dimension, corresponding to the coupling relationship of the four motion axes. Based on the Newton-Euler dynamics method of the aforementioned four-level series axis system, the following is obtained by step-by-step recursion: First, write the Newtonian translation equation of the center of mass and the Euler rotation equation about the center of mass for each link in turn. Eliminate the internal forces through the force and torque transmission relationship between adjacent links. Then, we obtain the total dynamic equation of the axis system with the rotation angle, angular velocity, and angular acceleration of each axis as variables. The coefficients of the equation constitute the elements of the inertia matrix and the Coriolis matrix. The dynamic compensation term is solved by axis. The compensation amount of the i-th axis corresponds to the calculation result of the i-th row in the total dynamic equation, which includes the inertia term of the axis itself and the coupling torque term generated by the motion of the other three axes on the axis. Thus, the multi-axis coupling effect is uniformly incorporated into the feedforward compensation of each axis.

[0158] The dynamic compensation term is derived from the Newton-Euler dynamic equations of a four-order series axis system, and its specific form is as follows: ,in The moment of inertia matrix of the shaft system is a 4×4 symmetric positive definite matrix. Its elements are calculated by the mass, moment of inertia and real-time rotation angle q of each shaft component through the recursive formula of the link inertia. The matrix of Coriolis force and centrifugal force is a 4×4 matrix. Its elements are calculated from the real-time rotation angle and real-time angular velocity of each axis. When calculating, the rotation angle, angular velocity and angular acceleration of each axis in the current period are substituted into the above formula to obtain the dynamic compensation torque of the corresponding axis, which is used to counteract the inertia and coupling disturbance of the axis system motion.

[0159] The dynamic compensation term is obtained by inverse dynamics calculation based on the aforementioned four-level series axis system, and adopts the same Newton-Euler dynamics modeling basis and the same coordinate transformation matrix system as the target rotation angle calculation of each axis.

[0160] Each component of the control adjustment quantity u is converted to the dimension of angular velocity before being synthesized, where the feedforward gain... The dimensionless value is 1 / s, used to convert the rotation angle command into an angular velocity feedforward; state feedback gain. In the middle, the angle feedback gain Dimensionless 1 / s, angular velocity feedback gain These are dimensionless coefficients. The dynamic compensation term needs to be converted from the force rectangular formula to an equivalent angular velocity. The conversion formula is as follows: ,in For dynamic compensation torque, is the motor torque coefficient, i is the reducer reduction ratio. After the conversion, it is added to the feedforward term and the feedback term to obtain the final control adjustment amount.

[0161] This formula integrates three types of control components: feedforward command tracking, real-time state feedback correction, and inverse dynamics nonlinear compensation. The feedforward component quickly follows the target rotation angle command, the feedback component eliminates the state tracking deviation in real time, and the compensation component uniformly cancels the coupling disturbances of shaft inertia and Coriolis force. The three types of components are calculated based on the same four-level series shaft dynamics model. The physical meaning of each control signal is clear and does not conflict with each other. Compared with a single feedback control scheme, it can simultaneously improve the command response speed and multi-axis coupling suppression capability, and achieve multiple control objectives of tracking, correction, and disturbance compensation in a layered manner.

[0162] The control adjustment values ​​of each axis are sent to the corresponding servo driver, which then performs low-level speed-position closed-loop control based on PID, and synchronously transmits back the real-time operating status data of each axis.

[0163] When executing PID-based low-level speed-position closed-loop control, the low-level speed-position closed-loop control uses a cascaded architecture of position loop and speed loop. The position loop generates target angular velocity commands with the target rotation angle of each axis as input.

[0164] The position loop uses a proportional control law, and the formula for calculating the output target angular velocity command is as follows: ,in This is the target rotation angle command for the corresponding axis. To provide real-time feedback on corner turns, This is the position loop proportional gain;

[0165] The position loop gain is set using the following formula: ,in The desired closed-loop bandwidth of the location loop. To calculate the equivalent moment of inertia at the motor end, This is the motor torque coefficient; when setting the position loop bandwidth, take 1 / 5 to 1 / 3 of the speed loop closed-loop bandwidth to ensure the stability and response speed of the cascade system are matched.

[0166] After receiving the control adjustment from the upper layer, the servo driver adds it as an adaptive feedforward correction factor to the target angular velocity command output by the position loop, and then performs the calculation using PID control logic in the velocity loop.

[0167] ;

[0168] In the formula: This is the final torque control value output by the speed loop; These are the proportional, integral, and differential gain coefficients corresponding to the velocity loop; The target angular velocity command output by the position loop; The real-time angular velocity feedback value obtained from the acquisition;

[0169] The above formula uses a position-velocity cascaded servo closed-loop architecture to superimpose the output adjustment of the upper-level adaptive controller onto the speed loop setpoint, seamlessly connecting the upper-level adaptive correction signal with the lower-level PID control. At the same time, it relies on the servo equivalent rotational inertia and the desired dynamic index to quantitatively tune the three PID gains, avoiding the inefficient process of traditional manual parameter testing. The integral term eliminates steady-state speed deviation, and the derivative term suppresses speed fluctuations. The hierarchical control architecture takes into account both the upper-level multi-axis adaptive global optimization and the lower-level servo torque for rapid and stable output.

[0170] The control adjustment quantity u output by the upper-level model reference adaptive controller is superimposed on the speed loop setpoint to achieve a smooth connection between the upper-level adaptive control and the lower-level closed-loop control.

[0171] The position loop, as the underlying closed loop, is responsible for ensuring basic position tracking accuracy and steady-state performance. Its gain is tuned according to conventional servo system methods. The state feedback term of the upper-level adaptive controller is used to compensate for tracking errors caused by model parameter fluctuations and external disturbances. Its initial gain is set to be less than 1 / 3 of the position loop gain to ensure that the underlying closed loop plays a dominant role in the initial stage.

[0172] The adaptive gain is gradually adjusted during operation, always maintaining a reasonable ratio with the position loop gain. Together, they form a hierarchical architecture of "basic closed loop + adaptive correction", thereby avoiding the problem of excessive superposition of control effects.

[0173] in, Determined quantitatively using model tuning methods:

[0174] The equivalent moment of inertia J of the single-axis servo system is obtained in advance, and the desired closed-loop angular frequency of the velocity loop is set. With expected damping ratio ;

[0175] Then proportional gain coefficient Integral gain coefficient Differential gain coefficient Based on the system damping compensation requirements, the equivalent moment of inertia J is taken as 0.05 to 0.2 times;

[0176] The equivalent moment of inertia J is obtained through an unloaded step response experiment. The desired closed-loop angular frequency and the desired damping ratio are preset according to the response speed and stability margin of the servo system.

[0177] In this embodiment, when the method is executed, the three-axis overload and flight attitude commands output by the flight simulation terminal are used as inputs, and the initial parameter configuration of the control model is completed along the four-level series axis system from the base to the pilot's end.

[0178] The typical parameters used in this embodiment are as follows:

[0179] In terms of structural parameters, the spindle rotation radius is 1.2m, the yaw axis cantilever length is 0.8m, the roll axis equivalent moment of inertia is 25kg·m², and the pitch axis equivalent moment of inertia is 18kg·m². In terms of hardware parameters, the servo motor rated torque is 20N·m, the reducer reduction ratio is 100, and the motor torque coefficient is 0.8N·m / A. In terms of control parameters, the control sampling period is 1ms, the reference model natural angular frequency is 15rad / s, the damping ratio is 0.707, the angular error weight is 100, the angular velocity error weight is 10, the initial value of the angular feedback gain is 50rad / (s·rad), the initial value of the angular velocity feedback gain is 0.8, the initial value of the feedforward gain is 1.0, and the adaptive learning rate is... , Take values ​​of 0.02, 0.005, and 0.01;

[0180] First, a five-level nodal coordinate system is established along the power transmission path of the principal axis, yaw axis, roll axis, and pitch axis. The total transformation matrix is ​​obtained by multiplying the homogeneous transformation matrices between adjacent coordinate systems. This matrix serves as the basis for inverse dynamics inverse solution calculation. During the inverse dynamics inverse solution process, the three-axis overload command from the pilot's end is used as input. The target rotation angles of the roll axis and pitch axis are analytically solved using the attitude mapping relationship of the total transformation matrix. The target rotation angles of the principal axis and yaw axis are solved synchronously by the overload tangential component and the base coordinate system transformation. The target angular velocity is generated by differentiating the rotation angle.

[0181] Simultaneously, in order to improve control accuracy, this stage also calculates the wind resistance equivalent disturbance torque of each axis moving component and adds it to the target torque command to counteract the aerodynamic disturbance effect;

[0182] After obtaining the target rotation angle and angular velocity commands for each axis, the model reference adaptive controller constructs a decoupled second-order linear reference model for each motion axis. Taking the target rotation angle command of that axis as input, it outputs the desired state quantity composed of the desired rotation angle and desired angular velocity, thereby defining the ideal dynamic response characteristics that the system should exhibit. At the same time, it collects real-time rotation angle and angular velocity feedback data from the servo motors of each motion axis, and calculates the difference between these and the desired state quantity output by the reference model to generate a system tracking error vector. To further improve the control quality, a diagonal state weighting matrix is ​​introduced when constructing this error vector. The weight coefficients of rotation angle and angular velocity are quantified and determined according to the maximum steady-state error allowed by the platform in a reciprocal proportional relationship, realizing differentiated consideration of different state deviations.

[0183] Subsequently, the adaptive law is solved online based on the tracking error vector. Specifically, an extended quadratic function containing tracking error and parameter error is constructed according to Lyapunov stability theory. With the global asymptotic stability of the closed-loop system as a constraint, the parameter update formulas for the state feedback gain and feedforward gain are derived. The time change rates of the two types of gains are numerically integrated to obtain the real-time gain parameters for the current control cycle. At the same time, in order to prevent gain drift or over-limit, feasible region projection constraint operation is also required on the gain to ensure that it is always within the reasonable range defined by the physical rated parameters of the servo system. This adaptive adjustment mechanism enables the controller to dynamically optimize the control parameters according to the actual motion state of the platform, which has stronger adaptability to operating conditions compared with fixed gain control.

[0184] Ultimately, the control adjustment of each axis is generated by a combination of three parts: feedforward control, state feedback control, and dynamic compensation. The feedforward term is used to track and compensate for the target rotation angle command, the feedback term is responsible for closed-loop correction of real-time state deviation, and the dynamic compensation term relies on the inverse dynamic model of the four-stage series axis system to solve for inertial torque and Coriolis torque to offset nonlinear coupling disturbances. After the control adjustment is sent to the servo drive, it is superimposed on the target angular velocity command output of the position loop as an adaptive feedforward correction factor. In the velocity loop, the PID logic executes the final torque output, thereby achieving a smooth connection between the upper-level model reference adaptive control and the lower-level PID cascade closed-loop control. This ensures both the platform's fast response and stability, and enhances its robustness to external disturbances and model uncertainties through parameter self-adjustment.

[0185] See Figure 2As shown in the figure, the platform has a four-level serial axis and a five-level node coordinate system. The power path along the main axis, yaw axis, roll axis, and pitch axis is divided into coordinate systems 0 to 4. 0 is the base reference, and 1 to 4 correspond to the yaw, roll, and pitch nodes and the pilot's cockpit coordinate system, respectively. The rotation axis of each axis is marked. Adjacent coordinate systems construct homogeneous transformation matrices, and the total transformation matrix is ​​obtained by multiplying them one by one. This is the geometric basis for inverse dynamics analytical solution and supports the accurate mapping and transformation of flight overload and attitude commands to the target rotation angle and angular velocity of each axis.

[0186] See Figure 3 As shown in the figure, this is a single-axis decoupled model reference adaptive control architecture. The command is input in two ways: one way is sent to the second-order reference model to output the ideal desired state; the other way drives the controlled object to output the actual motion state through an adjustable mechanism. The difference between the two states generates a weighted tracking error e, which is input to the adaptive mechanism. Based on Lyapunov stability theory, the feedforward and feedback gains are updated in real time, and the closed-loop control quantity is corrected to compensate for model deviations caused by inter-axis coupling, wind resistance, and load fluctuations online.

[0187] See Figure 4 As shown in the figure, this figure is a comparison curve of the tracking error between the control method in this embodiment and the traditional fixed-gain PID scheme. The horizontal axis is the simulation running time, and the vertical axis is the axis tracking error. The load sudden disturbance condition is set at 4s. The traditional PID curve has a large fluctuation amplitude and a steady-state error of about 0.8°. The adaptive scheme of this method has a smaller disturbance impact, faster oscillation decay, and a steady-state error of only about 0.08°. This intuitively shows that this method can effectively suppress load disturbance, greatly reduce steady-state tracking deviation, and improve the fidelity of platform motion tracking.

[0188] In summary, the method described in the above embodiments constructs a four-level cascaded axis coordinate transformation matrix system and performs inverse dynamics along this chain. This allows the multi-degree-of-freedom motion platform to directly map the overload and attitude commands output from the flight simulation terminal into target motion parameters for each axis, thereby avoiding the cumulative deviation caused by traditional step-by-step approximation transformations. Based on this, a second-order linear reference model is independently configured for each motion axis, and the adaptive law is driven by the weighted tracking error of rotation angle and angular velocity to adjust the feedback and feedforward gain online. This ensures that the simulation platform can maintain the desired dynamic response when the load changes or friction characteristics fluctuate. At the same time, Lyapunov stability constraints and gain projection limits are introduced to ensure that the parameter adjustment process is safe and controllable. The wind resistance equivalent disturbance torque and nonlinear coupling torque obtained from the inverse dynamics solution are superimposed on the control quantity as compensation terms to weaken the negative impact of aerodynamic drag and inter-axis coupling on position accuracy under high-speed motion. In addition, the smooth connection between the bottom-level PID speed-position cascade loop and the upper-level adaptive output takes into account both the requirements of fast following and steady-state zero steady-state error, ultimately improving the tracking fidelity and operational stability of the platform under complex overload conditions.

[0189] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions will not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A control method for a multi-degree-of-freedom motion platform based on model reference adaptation, characterized in that, include: Receive the three-axis overload and flight attitude commands output from the flight simulation terminal, establish a four-level serial axis coordinate transformation matrix system from the base to the pilot terminal, and complete the initial parameter configuration of the control model; Inverse dynamics calculations are performed along the four-level tandem axis system to obtain the target rotation angle and target angular velocity commands corresponding to the main axis, heading axis, roll axis and pitch axis; A reference model for the adaptive controller is constructed, using the target rotation angle and target angular velocity of each axis as inputs to generate the desired dynamic response state variables of the system. Collect real-time rotation angle and real-time angular velocity feedback data of each motion axis, and subtract them from the expected state variables output by the reference model to generate the system tracking error vector; By tracking the error vector, the adaptive law is solved online, and the feedback and feedforward gain parameters of the controller are adjusted in real time to output the control adjustment amount of each axis. The control adjustment values ​​of each axis are sent to the corresponding servo driver, which then performs low-level speed-position closed-loop control based on PID, and synchronously transmits back the real-time operating status data of each axis.

2. The multi-degree-of-freedom motion platform control method based on model reference adaptation according to claim 1, characterized in that, The four-level series axis coordinate transformation matrix system established from the base to the pilot's end obeys: Along the series power transmission path of the principal axis, yaw axis, roll axis, and pitch axis, five levels of nodal coordinate systems are constructed sequentially: base coordinate system, yaw nodal coordinate system, roll nodal coordinate system, pitch nodal coordinate system, and pilot coordinate system. The homogeneous transformation matrix between adjacent coordinate systems is constructed as follows: ； In the formula: Let be the homogeneous transformation matrix of the i-th level coordinate system relative to the (i-1)-th level coordinate system, where i takes the values ​​1, 2, 3, and 4, corresponding to the transformation nodes of the principal axis, yaw axis, roll axis, and pitch axis, respectively. This is the rotation matrix for the corresponding axis system; The position vector between the origins of adjacent coordinate systems; The total transformation matrix of the four-level series axis system is obtained by multiplying the transformation matrices of each level in the order of motion transmission, i.e. .

3. The multi-degree-of-freedom motion platform control method based on model reference adaptation according to claim 2, characterized in that, The inverse dynamics inverse solution operation is performed along the four-level series axis system to obtain the operational compliance of the target rotation angle and target angular velocity commands corresponding to each axis: Pilot-side three-way overload commands output from the flight simulation terminal As input, the target rotation angles for each axis are inversely solved based on the attitude mapping relationship of the total transformation matrix, where the target rotation angle of the roll axis is... Target rotation angle relative to pitch axis Solve analytically using the following formula: ； In the formula: intermediate variables , , ; These are the trigonometric function values ​​for the corresponding axis rotation angle; The triaxial equivalent overload in the base coordinate system is obtained by combining the principal axial acceleration, tangential acceleration and gravitational acceleration; Always takes -1; The target rotation angles of the main axis and the heading axis are obtained by simultaneously solving the relationship between the tangential component of the overload and the transformation of the base coordinate system, and the target angular velocity is generated by differentiating the target rotation angle with respect to time.

4. The multi-degree-of-freedom motion platform control method based on model reference adaptation according to claim 3, characterized in that, During the inverse dynamics inverse solution process, the wind resistance equivalent disturbance torque of the shaft system motion is calculated simultaneously and superimposed on the target torque command: ； In the formula: This is the wind resistance equivalent disturbance torque corresponding to single-axis motion; The air density under the current environment; is the air resistance coefficient of the corresponding shaft moving parts; S is the equivalent frontal area of ​​the part; The equivalent force arm for component rotation; This represents the real-time rotational angular velocity of the corresponding axis; The calculated wind resistance torque is superimposed as a disturbance compensation term into the target torque output by the inverse dynamics.

5. The multi-degree-of-freedom motion platform control method based on model reference adaptation according to claim 1, characterized in that, A reference model for the adaptive controller is constructed, generating the desired dynamic response state variables of the system. For each motion axis, a decoupled second-order linear reference model is constructed, taking the target rotation angle command for that axis as input and outputting the desired state variables composed of the desired rotation angle and desired angular velocity. The state-space expression of the reference model is as follows: ； In the formula: The state column vector of the reference model; For the desired turning angle; The desired angular velocity; This is the system state matrix; The natural angular frequency of the reference model; The damping ratio is used as a reference model, and both are preset desired dynamic performance parameters. The input matrix is ​​r; r is the target rotation angle command for the corresponding axis. This is the output matrix; The expected rotation angle state quantity output by the reference model.

6. The multi-degree-of-freedom motion platform control method based on model reference adaptation according to claim 5, characterized in that, When generating the system tracking error vector, the difference between the real-time state quantities acquired by each motion axis and the expected state quantities output by the reference model is calculated, and a diagonal state weighting matrix is ​​introduced to construct an extended tracking error vector: ； In the formula: This is a column vector of single-axis tracking errors; This refers to the corner tracking error. This refers to the angular velocity tracking error. This is the real-time state column vector of the controlled object; This refers to the real-time rotation angle obtained from the data collection. The real-time angular velocity obtained from the data acquisition; It is a diagonal state weighting matrix; This is the weighting coefficient for the cornering error; This is the angular velocity error weighting coefficient.

7. The multi-degree-of-freedom motion platform control method based on model reference adaptation according to claim 6, characterized in that, By tracking the error vector and performing online adaptive law calculations to adjust the controller's feedback and feedforward gain parameters in real time, a parameter update law is constructed based on Lyapunov stability theory. This law is used to iteratively adjust the state feedback gain vector and feedforward gain coefficients online. The update formula for the state feedback gain is as follows: ； The formula for updating the feedforward gain is: In the formula: State feedback gain vector The rate of change over time after transpose The row vector of state feedback gain; For corner feedback gain; Angular velocity feedback gain; For the feedback gain adaptive learning rate diagonal matrix, All are positive real number learning rate parameters; The feedforward gain is the adaptive learning rate; P is the Lyapunov equation. The symmetric positive definite solution matrix, Q is a pre-defined second-order symmetric positive definite weighting matrix; , These are the time rates of change of the feedback gain and the feedforward gain, respectively. After numerical integration, the real-time gain parameters for the current period are obtained. The time change rates of the two types of gains are numerically integrated to obtain the real-time gain parameters for the current period.

8. The multi-degree-of-freedom motion platform control method based on model reference adaptation according to claim 7, characterized in that, During the real-time adjustment of the controller's feedback and feedforward gain parameters, feasible region projection constraint calculations are performed on the gain parameters, which satisfy the following: ； In the formula: Let be the row vector of state feedback gain obtained by adaptive law solution at time t; Projection operator The operation logic is as follows: when the gain element exceeds the corresponding upper limit... The upper limit is taken when the value exceeds the corresponding lower limit. Take the lower limit value at that time; and These are the lower and upper bound matrices of the feedback gain, respectively, determined by the physical rated parameters of the shaft servo system; Feedforward gain coefficient Execute amplitude constraints with the same rules synchronously.

9. A multi-degree-of-freedom motion platform control method based on model reference adaptation according to claim 8, characterized in that, The control adjustment amount of each output axis is generated by the single-axis control adjustment amount, which is composed of three parts: feedforward control term, state feedback control term, and dynamic compensation term. ； Where: u is the single-axis control adjustment amount output to the servo driver; For feedforward control terms; This is a state feedback control item; This is a dynamic compensation term.

10. A multi-degree-of-freedom motion platform control method based on model reference adaptation according to claim 9, characterized in that, When executing PID-based low-level speed-position closed-loop control, the low-level speed-position closed-loop control uses a cascaded architecture of position loop and speed loop. The position loop generates target angular velocity commands with the target rotation angle of each axis as input. After receiving the control adjustment from the upper layer, the servo driver adds it as an adaptive feedforward correction factor to the target angular velocity command output by the position loop, and then performs the calculation using PID control logic in the velocity loop. ； In the formula: This is the final torque control value output by the speed loop; These are the proportional, integral, and differential gain coefficients corresponding to the velocity loop; The target angular velocity command output by the position loop; The real-time angular velocity feedback value obtained from the acquisition; The control adjustment quantity u output by the upper-level model reference adaptive controller is superimposed on the speed loop setpoint.

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