Multi-axis coupling control method for aerial remote sensing stable platform based on model predictive control

Abstract

The present application belongs to the field of general control or regulation system, and relates to a multi-axis coupling control method for an aerial remote sensing stable platform based on model predictive control. The method first establishes a dynamic model containing multi-axis coupling torque and Stribeck friction effect, and then constructs a compound control structure in which a MPC is connected in series with a PID compensator. The MPC calculates optimal control amount by rolling prediction according to real-time state, so as to realize multi-axis coordinated control. The PID compensates for prediction error quickly to improve transient response. Through the combination of prediction optimization and feedback correction, the present application can effectively suppress initial overshoot, reduce steady-state error, and improve pointing accuracy and disturbance suppression ability of the system under complex flight conditions. The method has small calculation burden and is easy to implement in engineering, and is suitable for attitude stabilization control of multi-axis aerial remote sensing stable platforms and various high-precision photoelectric loads.

Description

Technical Field

[0001] This invention belongs to the general field of control or regulation systems, and relates to the control of airborne remote sensing stabilization platforms, specifically to a multi-axis coupled control method for airborne remote sensing stabilization platforms based on model predictive control. Background Technology

[0002] Aerial remote sensing is a comprehensive detection technology that uses manned aircraft, unmanned aerial vehicles (UAVs), hot air balloons, and other platforms, employing technologies such as optics and radar to acquire ground information. It is mainly used in topographic mapping, disaster prediction, and military reconnaissance. As a crucial component of aerial remote sensing systems, aerial cameras are inevitably affected by external disturbances such as vibration during operation, resulting in poor image quality and failing to meet expectations. The image quality of aerial remote sensing cameras directly impacts the development level of remote sensing technology. Therefore, improving the image quality of remote sensing systems is currently a research hotspot in the field. Aerial remote sensing stabilization platforms are core equipment for aerial photography, reconnaissance, and mapping missions. Their main function is to isolate the interference of UAV / aircraft movement and external environmental vibrations (such as air disturbances) on the camera's line of sight, ensuring that the camera can stably and accurately align with the target, thereby acquiring high-resolution, clear images. Stabilization platforms typically employ a three-axis stabilization structure, achieving full-attitude stabilization of the camera's line of sight through coordinated control of the roll, pitch, and yaw axes.

[0003] In recent years, research on the control performance of airborne remote sensing stabilization platforms has deepened, and many scholars have proposed different research strategies. Regarding decoupling and disturbance rejection control, Zhang Ying and Chen Junjiang pointed out that the axes of a three-axis stabilization platform are difficult to keep orthogonal throughout the motion process, resulting in coupling interference. They proposed using hardware circuit compensation to achieve decoupling (based on a gyroscope decoupling method for a three-axis stabilization platform, Microcomputer Information, 2009). Lin Cunhai conducted dynamic analysis on a three-axis, three-frame inertial rotation platform, providing model support for decoupling control, and compensated for coupling torque through negative feedback (Decoupling and Control of a Three-Axis Turntable Based on Improved Repetitive Control, Optoelectronic Technology and Application, 2014). Wei Wei established a coordinate system for the airborne remote sensing stabilization platform, calculated the dynamic model of the three-axis frame, and used Lie derivative decoupling to achieve full-state linearization, improving system stability and accuracy (Research on Linear Stabilization Technology of High-Precision Airborne Optoelectronic Platform, Doctoral Dissertation, Changchun Institute of Optics, Fine Mechanics and Physics, 2015). Regarding mitigating unknown disturbances, Fang Jiancheng designed an unbalanced torque observer and implemented feedforward compensation to achieve real-time suppression of disturbances. Li Zengyan constructed an improved Stribeck friction model and used a genetic algorithm to identify parameters, combining it with feedforward compensation to improve isolation performance (Feedforward Compensation Method for Unbalanced Torque of Three-Axis Inertial Stabilization Platform for Airborne Remote Sensing, Journal of Chinese Inertial Technology, 2010). Tuo Xudong proposed a fuzzy adaptive PID algorithm, whose dynamic response speed is superior to traditional fuzzy and adaptive algorithms (Research on Control Algorithm of Stabilized Platform, Harbin Engineering University, 2017). Zhou Xiangyang introduced confidence allocation and smoothness optimization to improve the cerebellar model joint controller, and combined it with PID to suppress unknown nonlinear disturbances, thereby improving control accuracy and stability. Although the above studies have achieved significant results in decoupling modeling, disturbance compensation, and friction nonlinearity processing, there are still shortcomings in constraint processing of multi-input multi-output systems and prediction-based forward control. Summary of the Invention

[0004] To address the problems existing in the background technology, this invention provides a multi-axis coupled control method for an airborne remote sensing stabilization platform based on model predictive control. This method constructs a complete dynamic model including three-axis coupling terms and the Stribeck friction model. Based on the constructed multi-axis coupled dynamic model, a controller based on model predictive control (MPC) is designed, giving full play to the coordination and optimization capabilities of MPC in multivariable systems, realizing unified modeling and collaborative control of multi-axis systems, and overcoming the problem that traditional single-axis independent control methods are difficult to effectively suppress inter-axis coupling interference.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A multi-axis coupled control method for an airborne remote sensing stabilization platform based on model predictive control, the method comprising the following steps:

[0007] Step S1. Construct a multi-axis coupled dynamic model of the airborne remote sensing stabilization platform;

[0008] Step S101. Taking into account the voltage balance equation, torque equation, torque balance equation of the supporting load, and gear transmission ratio of the brushless DC torque motor, construct the dynamic model of the single-axis brushless DC torque motor of the airborne remote sensing stabilization platform and obtain the torque equation of the single-axis brushless DC torque motor.

[0009] Step S102. Based on the inertial coordinate system of the attitude compensation unit and the rotational relationship of the airborne remote sensing stabilization platform base, roll axis frame, pitch axis frame, and yaw axis frame, determine the angular velocity of each frame relative to the inertial coordinate system and the relative angular velocity of the airborne remote sensing stabilization platform. Based on the torque equation of each frame, obtain the comprehensive torque equation of the attitude compensation unit.

[0010] Step S103. Based on the equations determined in steps S101 and S102, a multi-axis coupled dynamic model is obtained, wherein the multi-axis coupled dynamic model includes multi-axis coupled torque and Stribeck friction effect;

[0011] Step S2. The model predictive control controller makes rolling predictions and calculates the optimal control quantity based on the current state and the reference trajectory;

[0012] Step S3. Introduce a PID compensator on the model predictive control-based controller to correct the prediction error in real time and form the final control signal.

[0013] As a preferred embodiment of the present invention, the expression for the torque equation of the single-axis brushless DC torque motor in step S101 is as follows:

[0014] ;

[0015] in, The moment of inertia between the load and the frame. It is the equivalent load damping. It is the input torque of the load. It is the frictional torque of the platform. The angular acceleration of the platform's axis of rotation. The angular velocity of the platform's axis of rotation. This is the equivalent impedance of the armature inductance in the frequency domain. This represents the gear ratio. The torsional coefficient of a brushless DC torque motor. Armature voltage, For resistance, It is the back electromotive force coefficient. The rotational angular velocity of the brushless DC torque motor. This refers to the frictional torque at the motor end.

[0016] As a preferred embodiment of the present invention, the expression for the comprehensive torque equation of the attitude compensation unit in step S102 is as follows:

[0017] ;

[0018] in, , , The coupling moments between the pitch axis and roll / yaw axis, the roll axis and pitch / yaw axis, and the yaw axis and pitch / roll axis are respectively; the coupling moments between the base and the pitch axis, roll axis, and yaw axis are respectively. , , ; , The projection components of the moment of inertia of the yaw shaft frame relative to the inertial coordinate system on the x and z axes of the inertial coordinate system; , The projection components of the moment of inertia of the pitch pivot frame relative to the inertial coordinate system on the x and y axes of the inertial coordinate system. This is the projection component of the moment of inertia of the roll axis frame relative to the inertial coordinate system onto the y-axis of the inertial coordinate system. Let be the angular acceleration of the pitch axis about the x-axis of the inertial coordinate system. Angular acceleration of the roll axis about the y-axis of the inertial coordinate system. Let be the angular acceleration of the yaw axis about the z-axis of the inertial coordinate system. The equivalent driving torque acting on the pitch axis, The equivalent driving torque acting on the roll shaft, This is the equivalent driving torque acting on the yaw axis.

[0019] As a preferred embodiment of the present invention, the expression for the multi-axis coupled dynamics model in step S103 is as follows:

[0020] ;

[0021] in, The torque constant of the pitch axis motor is... This is the torque constant of the roll axis motor. Let be the torque constant of the yaw axis motor. Let be the back electromotive force constant of the pitch axis motor. Let be the back electromotive force constant of the roll axis motor. Let be the back electromotive force constant of the yaw axis motor. This is the control input voltage for the pitch axis motor. This is the control input voltage for the roll axis motor. This is the control input voltage for the yaw axis motor.

[0022] As a preferred embodiment of the present invention, the frictional torque of the platform at time t The friction is divided into two cases: static friction and dynamic friction. The Stribeck friction torque curve is used as the mathematical model for friction compensation. The specific relationship corresponding to the Stribeck friction torque curve is as follows:

[0023] when At that time, the static friction is:

[0024] ;

[0025] when At that time, the kinetic friction is:

[0026] ;

[0027] in, Let t be the motor output driving torque. For the Coulomb friction of the platform, This is the proportionality coefficient for viscous friction torque. Let be the angular velocity of rotation at time t. For positive integers, For the maximum static friction force, Let be the angular acceleration of the platform's axis at time t.

[0028] In a preferred embodiment of the present invention, the model predictive control-based controller in step S2 includes a predictive model, an optimizer, a discrete integrator, and a controlled object. The predictive model estimates the future output based on the current state and a reference trajectory, and the optimizer solves for the optimal control quantity change sequence under given cost functions and constraints. Then, the discrete integrator selects the first control quantity from the obtained control quantity change sequence. Apply to the controlled object.

[0029] As a preferred embodiment of the present invention, the controlled object is represented by a discrete-time model of the following form:

[0030] ;

[0031] Wherein, the state transition matrix is The input matrix is The output matrix is The state variables are Control input is Controlled output is The reference trajectory is The state variable at the next moment is ;

[0032] At each sampling time, for a given prediction time domain and control time domain, the model predictive control-based controller minimizes a cost function, said cost function The expression is:

[0033] ;

[0034] in, At the current discrete moment, Predict step size, Control the step size, This is the weight matrix. , and They represent the times respectively. Given all measurement information, for time... The predicted values ​​of the output of the controlled object, the trajectory of the output setpoint, and the increment of the control quantity.

[0035] As a preferred embodiment of the present invention, the discrete expression of the PID compensator is:

[0036] ;

[0037] Among them, the current time is Sampling time is , This represents the compensation error at time k. The compensation error at time i is represented by the proportional gain. Integral gain is The differential gain is , Let be the compensation control quantity at time k. This represents the compensation error at time k-1.

[0038] As a preferred embodiment of the present invention, the final control signal is the actual control input. .

[0039] The advantages and beneficial effects of this invention are as follows:

[0040] (1) In view of the multi-axis coupling interference and friction nonlinearity problems existing in the operation of the airborne remote sensing stabilization platform, the present invention constructs a complete dynamic model including a three-axis coupling term and a Stribeck friction model, so that the mathematical description of the system is closer to the actual operating state, thereby reducing the adverse effects of model mismatch on control performance and improving the accuracy and reliability of control design.

[0041] (2) Based on the constructed multi-axis coupled dynamic model, the present invention designs a controller based on model predictive control (MPC), giving full play to the coordination and optimization capabilities of MPC in multivariable systems, realizing unified modeling and coordinated control of multi-axis systems, and overcoming the problem that traditional single-axis independent control methods are difficult to effectively suppress inter-axis coupling interference.

[0042] (3) Based on the use of model predictive control to suppress nonlinear disturbances of the system, this invention proposes an MPC-PID series control structure to address the shortcomings of MPC in the initial response stage, which is prone to error fluctuations and overshoot. While maintaining the global optimization and look-ahead prediction capabilities of MPC, PID compensation is introduced to correct the prediction error in real time.

[0043] (4) Through the synergistic effect of MPC and PID, the present invention can effectively suppress overshoot and oscillation generated during transient processes such as system startup, instruction switching and disturbance change, and improve the stability of the system dynamic response and the control process.

[0044] (5) The present invention exhibits faster dynamic response speed and higher steady-state control accuracy during continuous trajectory tracking, while taking into account the requirements of multi-axis coupling suppression and high-precision tracking, and is suitable for airborne remote sensing imaging tasks with high requirements for pointing stability.

[0045] (6) In the control design, the present invention explicitly considers the system input, output and their rate of change constraints, avoids sudden changes and saturation of control quantities, and improves the smoothness of control signals and the safety of system operation.

[0046] (7) The present invention can still maintain good control stability and tracking performance under complex working conditions such as model uncertainty, external disturbance and load change, and enhance the robustness and environmental adaptability of the airborne remote sensing stabilization platform.

[0047] (8) The MPC-PID series control structure proposed in this invention has a clear hierarchy, relatively independent parameters, and moderate computational complexity of the control algorithm, making it easy to implement in embedded or real-time control systems and having good engineering feasibility.

[0048] (9) The method of the present invention does not depend on a specific platform structure or hardware configuration. It can be integrated and upgraded without changing the mechanical structure of the existing airborne remote sensing stabilization platform. It can also be applied to other multi-degree-of-freedom photoelectric stabilization platforms and precision pointing control systems. It has high application value and promotion prospects. Attached Figure Description

[0049] To further illustrate the embodiments of this application, 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 only embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 This is a schematic diagram of the system structure of the airborne remote sensing stabilization platform of the present invention;

[0051] Figure 2 This is a schematic diagram of the MPC-PID structure after the optimization model predictive control of this invention;

[0052] Figure 3 These are the unoptimized model predictive control roll axis tracking and error curves in the experiments of this invention;

[0053] Figure 4 This is the roll axis tracking and error curve after the optimized model predictive control in the experiment of this invention. Detailed Implementation

[0054] The present invention will now be described in detail with reference to the embodiments shown in the accompanying drawings. However, these embodiments do not limit the present invention, and any structural, methodological, or functional modifications made by those skilled in the art based on these embodiments are included within the scope of protection of the present invention.

[0055] It should be understood that the specific implementation process of the present invention is only applicable to illustrative or explanatory purposes of the principles of the present invention, and does not constitute a limitation of the present invention.

[0056] A multi-axis coupled control method for an airborne remote sensing stabilization platform based on model predictive control, the method comprising the following steps:

[0057] Step S1. Construct a multi-axis coupled dynamic model of the airborne remote sensing stabilization platform;

[0058] Step S101. Single-axis frame dynamic modeling:

[0059] The voltage balance equation for a brushless DC torque motor is as follows:

[0060] (1)

[0061] in, Armature voltage, For current, For resistance, It is the back electromotive force coefficient. For inductance, This refers to the rotational angular velocity of a brushless DC torque motor.

[0062] The torque equation for a brushless DC torque motor is as follows:

[0063] (2)

[0064] in, This represents the moment of inertia of the brushless DC torque motor. Equivalent damping of a brushless DC torque motor Electromagnetic torque, This refers to the load torque on the output side of the brushless DC torque motor. This refers to the frictional torque at the motor end. The torsional coefficient of a brushless DC torque motor. This refers to the angular acceleration of the brushless DC torque motor. For each rotating axis, the torque output of the brushless DC torque motor is insufficient to support the platform; therefore, a gear mechanism is used to withstand a larger load torque, with a gear ratio of [value missing]. .

[0065] The torque balance equation for the load supported by the airborne remote sensing stabilization platform can be expressed as:

[0066] (3)

[0067] in, The moment of inertia between the load and the frame. It is the equivalent load damping. It is the input torque of the load. It is the frictional torque of the platform (load end). The angular acceleration of the platform's axis of rotation. ω represents the angular velocity of the platform's axis of rotation.

[0068] Considering the gear ratio The system satisfies the following relationship due to the influence of:

[0069] (4)

[0070] The dynamic model of the single-axis brushless DC torque motor of the airborne remote sensing stabilization platform is obtained, and the specific relationships are as follows:

[0071] (5)

[0072] (6)

[0073] (7)

[0074] in, The equivalent impedance of the armature inductance in the frequency domain; due to the equivalent damping of the brushless torque motor Therefore, these two items are ignored. The impact on the system is minimal, and the torque equation for the single-axis brushless DC torque motor is finally obtained as follows:

[0075] (8)

[0076] The characteristics of a linear model are reflected in its state-space representation of system matrices, namely the state transition matrix A, the input matrix B, and the output matrix C. These matrices are used to characterize the dynamic properties of the system, and their representation is as follows:

[0077] , , (9)

[0078] Step S102. Platform triaxial coupled dynamics modeling:

[0079] To obtain the mathematical model of the airborne remote sensing stabilization platform, the base coordinates of the airborne remote sensing stabilization platform are assumed to be... The coordinate system of the roll axis frame is The coordinate system of the pitch and rotation frame is The coordinate system of the yaw shaft frame is The axial base of the roll pivot frame The rotation angle of the shaft is The corresponding transformation matrix is The pitch pivot frame's axis around the roll pivot frame. The rotation angle of the shaft is The corresponding transformation matrix is Yaw pivot frame around pitch pivot frame The rotation angle of the shaft is The corresponding transformation matrix Based on the inertial coordinate system of the attitude compensation unit and the rotational relationships of each rotating frame, the specific transformation matrix can be obtained as follows:

[0080]

[0081] (10)

[0082] The rotation angles of the three axes of the airborne remote sensing stabilization platform are set as follows: The relative angular velocities of the three rotating shafts are: The angular velocity of the base is . These represent the projection components of the base angular velocity onto its own coordinate system's x, y, and z axes (velocity components rotating about x, y, and z). Since the base angular velocity of the airborne remote sensing stabilization platform is known, the kinematic formulas for the angular velocities of the three rotating frames are as follows, where the roll axis angular velocity of the airborne remote sensing stabilization platform is:

[0083] (11)

[0084] The pitch axis angular velocity of the airborne remote sensing stabilization platform is:

[0085] (12)

[0086] The yaw axis angular velocity of the airborne remote sensing stabilization platform is:

[0087] (13)

[0088] in,[ , , ], [ , , ], [ , , These are the angular velocity vectors of the roll, pitch, and yaw axis frames relative to the inertial coordinate system, respectively. The subscripts x, y, and z represent the projection components on the x, y, and z axes of the inertial coordinate system. They are respectively The first derivative, combined with the above formulas (11), (12), and (13), shows that the relative angular velocity of the airborne remote sensing stabilization platform is as follows:

[0089]

[0090] (14)

[0091] When constructing the dynamic model of the attitude compensation unit, based on the aforementioned definition of the coordinate system, secondary factors such as machining errors and noise are ignored, and the focus is mainly on the key interference sources of the system. Given that the brushless DC motor is the provider of driving torque, its output torque needs to have sufficient margin to effectively suppress external interference. To simplify the modeling process and reduce nonlinear effects, it is assumed that the frame structure of the attitude compensation unit is completely symmetrical, i.e., the diagonal elements of its inertia matrix are non-zero, while the non-diagonal elements are assumed to be zero. Based on the Newton-Euler rotation equations, the torque on the rotating shaft frame can be expressed as...

[0092] (15)

[0093] In the formula, T The torque on the pivot frame J For the moment of inertia of a rotating rigid body, w For the angular velocity of the rotating rigid body, for w The first derivative.

[0094] Therefore, the torque of the roll axis about the inertial coordinate system is The torque equation for the corresponding roll pivot frame is:

[0095] (16)

[0096] The torque on the pitch axis is The corresponding torque equation for the pitch pivot frame is:

[0097] (17)

[0098] Yaw axis moment is The torque equation for the yaw shaft frame is:

[0099] (18)

[0100] in,[ ],[ ],[ These are the moments of inertia of the roll, pitch, and yaw pivot frames relative to the inertial coordinate system, respectively. The subscripts x, y, and z represent the projection components on the x, y, and z axes of the inertial coordinate system.

[0101] The equation for the total torque (combined torque) of the attitude compensation unit system can be further derived:

[0102] (19)

[0103] The following relation is obtained:

[0104] (20)

[0105] After further processing and refinement, the comprehensive torque equation of the attitude compensation unit can be finally derived:

[0106] (twenty one)

[0107] The coupling terms in the formula can be categorized into two types: one is the coupling torque between each rotating shaft, and the other is the coupling torque between the base and each rotating shaft; among them, the coupling torque between the rotating shaft frames is denoted as... , , These correspond to the coupling torques between the pitch axis and roll / yaw axis, the roll axis and pitch / yaw axis, and the yaw axis and pitch / roll axis, respectively. The coupling torques between the base and each axis are respectively... , , It covers the interaction between the pitch axis, roll axis, yaw axis and the base.

[0108] Coupling torque between the pitch axis and other rotation axes It can be represented as:

[0109] (twenty two)

[0110] Coupling torque of the base This mainly originates from the interaction between the pitch axis and the base, as specifically expressed below:

[0111] (twenty three)

[0112] Coupling torque between the roll axis and other axes The expression is:

[0113] (twenty four)

[0114] Coupling torque of the base It is mainly determined by the interaction between the roll shaft and the base, specifically as follows:

[0115] (25)

[0116] Coupling torque between the yaw axis and other axes Represented as:

[0117] (26)

[0118] Coupling torque of the base The main issue is the coupling between the pitch axis and the base, as detailed below:

[0119] (27)

[0120] Step S103. Combining the comprehensive torque equation of the airborne remote sensing stabilization platform in formula (21) and the dynamic model (mathematical model) of the DC brushless torque motor in formula (7), the following multi-axis coupled dynamic model (mathematical model) of the airborne remote sensing stabilization platform is obtained:

[0121] (28)

[0122] in, , , The coupling moments between the pitch axis and roll / yaw axis, the roll axis and pitch / yaw axis, and the yaw axis and pitch / roll axis are respectively; the coupling moments between the base and the pitch axis, roll axis, and yaw axis are respectively. , , ; , The projection components of the moment of inertia of the yaw shaft frame relative to the inertial coordinate system on the x and z axes of the inertial coordinate system; , The projection components of the moment of inertia of the pitch pivot frame relative to the inertial coordinate system on the x and y axes of the inertial coordinate system. This is the projection component of the moment of inertia of the roll axis frame relative to the inertial coordinate system onto the y-axis of the inertial coordinate system. Let be the angular acceleration of the pitch axis about the x-axis of the inertial coordinate system. Angular acceleration of the roll axis about the y-axis of the inertial coordinate system. Let be the angular acceleration of the yaw axis about the z-axis of the inertial coordinate system. The equivalent driving torque acting on the pitch axis, The equivalent driving torque acting on the roll shaft, The equivalent driving torque acting on the yaw axis, The torque constant of the pitch axis motor is... This is the torque constant of the roll axis motor. Let be the torque constant of the yaw axis motor. Let be the back electromotive force constant of the pitch axis motor. Let be the back electromotive force constant of the roll axis motor. Let be the back electromotive force constant of the yaw axis motor. This is the control input voltage for the pitch axis motor. This is the control input voltage for the roll axis motor. This is the control input voltage for the yaw axis motor.

[0123] Furthermore, this invention primarily employs the Stribeck friction curve as the mathematical model for friction compensation. The specific relationship corresponding to the Stribeck friction torque curve is as follows:

[0124] when At that time, the static friction is:

[0125] (29)

[0126] when At that time, the kinetic friction is:

[0127] (30)

[0128] In the formula, To provide the driving torque for the motor output, For the Coulomb friction of the platform, This is the proportionality coefficient for viscous friction torque. Rotational angular velocity, For positive integers, This represents the maximum static friction force.

[0129] Step S2. Design a controller based on Model Predictive Control (MPC). MPC predicts and calculates the optimal control quantity based on real-time state to achieve multi-axis coordinated control.

[0130] Step S201. Model Predictive Controller Design

[0131] The core of Model Predictive Control (MPC) lies in building and optimizing the feedback controller in real time at every discrete time point. It possesses foresight, capable of adjusting control actions before the system output setpoint changes, thereby enhancing the proactiveness of the system response. The basic structure of a controller based on Model Predictive Control (MPC) includes a predictive model, an optimizer, a discrete integrator, and the controlled object. The controller adjusts its actions based on the current state... and reference trajectory The future output is estimated through a predictive model, and the optimizer solves for the optimal control quantity change sequence under given cost function and constraints. .

[0132] In a model-based predictive control framework, a model is needed to describe the behavior of the controlled object. Typically, it is assumed that the controlled object can be represented by a discrete-time model of the following form:

[0133] (31)

[0134] Its main element is state variables. Control input Controlled output and reference trajectory , , respectively represent the state transition matrix, input matrix, and output matrix of a single-axis brushless DC torque motor.

[0135] Meanwhile, the state transition matrix of the motor under the influence of inter-shaft coupling can be further derived based on formula (28). Input matrix Output matrix .

[0136]

[0137]

[0138] ;

[0139] in, The torque constant of the pitch axis motor is... This is the torque constant of the roll axis motor. Let be the torque constant of the yaw axis motor. Let be the back electromotive force constant of the pitch axis motor. Let be the back electromotive force constant of the roll axis motor. is the back electromotive force constant of the yaw axis motor.

[0140] To build a predictive model, it is necessary to deduce the future. Step output sequence about the current state and future control input sequence The relationship. This is achieved by progressively expanding the system state update formula:

[0141]

[0142]

[0143]

[0144]

[0145] (32)

[0146] Furthermore, according to the output formula The future output sequence can be obtained as follows:

[0147]

[0148]

[0149]

[0150]

[0151] (33)

[0152] Stack all predicted outputs into a vector according to time steps. This can be written in compact matrix form:

[0153] (34)

[0154] in, Here, represents the state prediction matrix, which shows the impact of the current state on future outputs. The control input prediction matrix describes the effect of future control variables on future outputs.

[0155] Its specific structure is as follows:

[0156] , (35)

[0157] The core mechanism of discrete-time model predictive control (including discrete integrator) is based on a rolling time-domain optimization strategy. At each sampling time, only the first control variable in the optimized control sequence is selected. The control input is applied to the controlled object and updated again at the next sampling time. The optimization algorithm assumes that when... and At that time, the control input remains constant, that is The aim is to minimize the following cost function to achieve the optimal control objective.

[0158] (36)

[0159] in, This is the performance metric function, i.e., the cost function. At the current discrete moment, Predict step size, Control the step size, Its weight matrix, , and They represent the times respectively. Given all measurement information, for time... The predicted values ​​of the controlled object's output, output setpoint trajectory, and control increment are given. This represents the increment of the predicted output.

[0160] Given the output predicted value vector Reference trajectory vector Control increment vector Its matrix formula is:

[0161] , , (37)

[0162] To facilitate the construction of the subsequent optimization problem, the cost function is reorganized into the following compact matrix form based on formula (37):

[0163] (38)

[0164] Further introduction of prediction models Substituting into the above formula, we get:

[0165] (39)

[0166] This can then be expanded into the standard quadratic form:

[0167] (40)

[0168] in, , The standard quadratic cost function can be written as:

[0169] (41)

[0170] in, Represents the optimization variable Irrelevant constant terms (constant bias).

[0171] Step S3. Optimize the model predictive control-based controller with series proportional-integral-derivative compensation;

[0172] In this embodiment, the algorithm for optimizing the model predictive control-based controller is as follows:

[0173] Model predictive control (MPC) possesses multivariable coordinated optimization and explicit constraint handling capabilities, enabling high-precision control by predicting future outputs and continuously optimizing control inputs. However, in multi-axis coupled systems, MPC is highly dependent on model accuracy, exhibiting lag in initial disturbance response, which can easily lead to error amplification. To address this, this invention proposes a series control strategy based on MPC-PID. This method introduces a nonlinear compensation stage into the existing MPC framework. The MPC generates the main control input, while the PID compensator corrects the prediction error in real time and forms the final control signal, thereby improving the system's transient response and steady-state accuracy. This structure combines the global optimization capabilities of MPC with the rapid compensation characteristics of PID, effectively suppressing initial overshoot, reducing steady-state error, improving the system's dynamic response and robustness, and enhancing the control accuracy and stability of the airborne remote sensing stabilization platform under complex operating conditions.

[0174] The output of a PID compensator can be expressed as a compensating control quantity, in the form of:

[0175] (42)

[0176] in, For PID compensation input, proportional gain Integral gain Differential gain , To compensate for errors, let the sampling time be... The current time is The discrete expression for the PID compensator is:

[0177] (43)

[0178] in, These parameters together determine the controller's response speed, steady-state error, and the system's dynamic characteristics.

[0179] In this embodiment, through Real-time correction of MPC prediction errors is performed to generate actual control inputs. , For MPC control input, The input for PID compensation is applied to the controlled object, and the system output is... The status feedback is then input into the controller to achieve closed-loop rolling optimization control.

[0180] This embodiment provides a control system for implementing the control method described above. Figure 1 The control system structure of an airborne remote sensing stabilization platform is demonstrated, comprising multiple functional units that work collaboratively. Specifically, these units include: a command input module, a status display module, a data display module, an airborne remote sensing stabilization platform controller, a power controller, motor drivers, a DC brushless torque motor, a transmission mechanism, a three-axis frame of the airborne remote sensing stabilization platform, and sensors. The sensors include a POS (Position & Orientation System or GNSS / INS integrated navigation system, primarily used in the airborne remote sensing stabilization platform to provide the macroscopic attitude and motion status of the aircraft / platform), gyroscopes, accelerometers, and photoelectric encoders. The three-axis frame of the airborne remote sensing stabilization platform includes a roll axis frame, a pitch axis frame, and a yaw axis frame. Structurally, the yaw axis frame is mounted on the pitch axis frame, which in turn is mounted on the roll axis frame, which is fixed to a base. Each frame's axis is equipped with a gyroscope and a photoelectric encoder for measuring angular velocity and angular position. This structural design facilitates system debugging and enables precise implementation of the various functions of the airborne remote sensing stabilization platform.

[0181] Figure 2 To optimize the basic structure of MPC-PID after model predictive control, it includes a model predictive control-based controller, PID discrete control (PID compensator), and the controlled object; wherein, the controller determines the controlled object based on the current state. and reference trajectory The future output is estimated through a predictive model, the optimal control variable change sequence is solved, and after being calculated by a discrete integrator, it is input into a PID compensator. Real-time correction of MPC prediction errors is performed to generate actual control inputs. It acts on the controlled object, and the system outputs... The status feedback is then input into the controller to achieve closed-loop rolling optimization control.

[0182] Figure 3 , Figure 4To compare the experimental results of roll axis attitude tracking with the curves, and to verify the effectiveness of the proposed MPC-PID series control strategy in a three-axis stabilization platform, a hardware-in-the-loop (HIL) platform based on a dual-axis precision rotary table was built to simulate the attitude changes of an aircraft during flight. The rotary table consists of a roll axis (inner axis) and a yaw axis (outer axis). In the experiment, a linear array aerial photography system was precisely mounted on the rotary table's worktable to ensure the accuracy of attitude compensation verification and the controllability of disturbance conditions. The experimental time was set to 20 seconds, and the initial angle of the attitude compensation unit was 5°. The computer controlled the roll axis of the rotary table to oscillate sinusoidally at a frequency of 0.3 Hz and an amplitude of 5°, while the yaw axis was locked to test the attitude compensation performance of the roll channel. Experimental results show that after introducing the MPC-PID series control strategy, the rolling channel's tracking ability of the reference trajectory is significantly enhanced, and the response process is smooth and has good periodicity. Compared with the original values, the root mean square error (RMSE) in the initial stage decreased from 0.891° to 0.765°, a reduction of 14.1%; the RMS error in the steady-state stage decreased from 0.523° to 0.412°, a reduction of 21.2%, without significant oscillations or drift. The results show that the proposed MPC-PID cascade control structure can effectively suppress initial deviations and transient fluctuations, significantly improving the stability and steady-state tracking accuracy of the roll channel.

[0183] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other forms without departing from the spirit or essential characteristics of the present invention.

[0184] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This way of describing the specification is only for clarity. The technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A multi-axis coupled control method for an airborne remote sensing stabilization platform based on model predictive control, characterized in that, The method includes the following steps: Step S1. Construct a multi-axis coupled dynamic model of the airborne remote sensing stabilization platform; Step S101. Taking into account the voltage balance equation, torque equation, torque balance equation of the supporting load, and gear transmission ratio of the brushless DC torque motor, construct the dynamic model of the single-axis brushless DC torque motor of the airborne remote sensing stabilization platform and obtain the torque equation of the single-axis brushless DC torque motor. Step S102. Based on the inertial coordinate system of the attitude compensation unit and the rotational relationship of the airborne remote sensing stabilization platform base, roll axis frame, pitch axis frame, and yaw axis frame, determine the angular velocity of each frame relative to the inertial coordinate system and the relative angular velocity of the airborne remote sensing stabilization platform. Based on the torque equation of each frame, obtain the comprehensive torque equation of the attitude compensation unit. Step S103. Based on the equations determined in steps S101 and S102, a multi-axis coupled dynamic model is obtained, wherein the multi-axis coupled dynamic model includes multi-axis coupled torque and Stribeck friction effect; Step S2. The model predictive control controller makes rolling predictions and calculates the optimal control quantity based on the current state and the reference trajectory; Step S3. Introduce a PID compensator on the model predictive control-based controller to correct the prediction error in real time and form the final control signal.

2. The multi-axis coupled control method for an airborne remote sensing stabilization platform based on model predictive control according to claim 1, characterized in that: The expression for the torque equation of the single-axis brushless DC torque motor in step S101 is as follows: ； in, The moment of inertia between the load and the frame. It is the equivalent load damping. It is the input torque of the load. It is the frictional torque of the platform. The angular acceleration of the platform's axis of rotation. The angular velocity of the platform's axis of rotation. This is the equivalent impedance of the armature inductance in the frequency domain. This represents the gear ratio. The torsional coefficient of a brushless DC torque motor. Armature voltage, For resistance, It is the back electromotive force coefficient. The rotational angular velocity of the brushless DC torque motor. This refers to the frictional torque at the motor end.

3. The multi-axis coupled control method for an airborne remote sensing stabilization platform based on model predictive control according to claim 2, characterized in that: The expression for the comprehensive torque equation of the attitude compensation unit in step S102 is as follows: ； in, , , The coupling moments between the pitch axis and roll / yaw axis, the roll axis and pitch / yaw axis, and the yaw axis and pitch / roll axis are respectively; the coupling moments between the base and the pitch axis, roll axis, and yaw axis are respectively. , , ; , The projection components of the moment of inertia of the yaw shaft frame relative to the inertial coordinate system on the x and z axes of the inertial coordinate system; , The projection components of the moment of inertia of the pitch pivot frame relative to the inertial coordinate system on the x and y axes of the inertial coordinate system. This is the projection component of the moment of inertia of the roll axis frame relative to the inertial coordinate system onto the y-axis of the inertial coordinate system. Let be the angular acceleration of the pitch axis about the x-axis of the inertial coordinate system. Angular acceleration of the roll axis about the y-axis of the inertial coordinate system. Let be the angular acceleration of the yaw axis about the z-axis of the inertial coordinate system. The equivalent driving torque acting on the pitch axis, The equivalent driving torque acting on the roll shaft, This is the equivalent driving torque acting on the yaw axis.

4. The multi-axis coupled control method for an airborne remote sensing stabilization platform based on model predictive control according to claim 3, characterized in that: The expression for the multi-axis coupled dynamics model in step S103 is as follows: ； in, The torque constant of the pitch axis motor is... This is the torque constant of the roll axis motor. Let be the torque constant of the yaw axis motor. Let be the back electromotive force constant of the pitch axis motor. Let be the back electromotive force constant of the roll axis motor. Let be the back electromotive force constant of the yaw axis motor. This is the control input voltage for the pitch axis motor. This is the control input voltage for the roll axis motor. This is the control input voltage for the yaw axis motor.

5. The multi-axis coupled control method for an airborne remote sensing stabilization platform based on model predictive control according to claim 4, characterized in that: Frictional torque of the platform at time t The friction is divided into two cases: static friction and dynamic friction. The Stribeck friction torque curve is used as the mathematical model for friction compensation. The specific relationship corresponding to the Stribeck friction torque curve is as follows: when At that time, the static friction is: ； when At that time, the kinetic friction is: ； in, Let t be the motor output driving torque. For the Coulomb friction of the platform, This is the proportionality coefficient for viscous friction torque. Let be the angular velocity of rotation at time t. For positive integers, For the maximum static friction force, Let be the angular acceleration of the platform's axis at time t.

6. The multi-axis coupled control method for an airborne remote sensing stabilization platform based on model predictive control according to claim 5, characterized in that: The model predictive control-based controller described in step S2 includes a predictive model, an optimizer, a discrete integrator, and the controlled object. The predictive model estimates the future output based on the current state and reference trajectory, and the optimizer solves for the optimal control quantity change sequence under given cost function and constraints. Then, the discrete integrator selects the first control quantity from the obtained control quantity change sequence. Apply to the controlled object.

7. The multi-axis coupled control method for an airborne remote sensing stabilization platform based on model predictive control according to claim 6, characterized in that: The controlled object is represented by the following discrete-time model: ； Wherein, the state transition matrix is The input matrix is The output matrix is The state variables are Control input is Controlled output is The reference trajectory is The state variable at the next moment is ; At each sampling time, for a given prediction time domain and control time domain, the model predictive control-based controller minimizes a cost function, said cost function The expression is: ； in, At the current discrete moment, Predict step size, Control the step size, This is the weight matrix. , and They represent the times respectively. Given all measurement information, for time... The predicted values ​​of the output of the controlled object, the trajectory of the output setpoint, and the increment of the control quantity.

8. The multi-axis coupled control method for an airborne remote sensing stabilization platform based on model predictive control according to claim 7, characterized in that: The discrete expression of the PID compensator is: ； Among them, the current time is Sampling time is , This represents the compensation error at time k. The compensation error at time i is represented by the proportional gain. Integral gain is The differential gain is , Let be the compensation control quantity at time k. This represents the compensation error at time k-1.

9. The multi-axis coupled control method for an airborne remote sensing stabilization platform based on model predictive control according to claim 8, characterized in that: The final control signal is the actual control input. .

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