A model predictive control method for a three-degree-of-freedom motion control system of a wind tunnel aircraft model

Abstract

The present invention belongs to the field of precision motion control, and discloses a model predictive control method for a three-degree-of-freedom motion control system of a wind tunnel aircraft model. A mechanism dynamics model is constructed based on the constructed three-degree-of-freedom motion control system of the aircraft model; theoretical models are constructed for various types of nonlinear factors generated during the load-resistant motion of the piezoelectric actuator, and parameters are calibrated based on experimental data to form a system model of multiple cascaded nonlinear dynamic links. The real-time force and position information of the system is obtained through a monitoring system composed of multiple sensors, and the real-time prediction of the mechanism motion state is realized based on the system model. A tolerance constraint of a multi-dimensional instantaneous load-driving force is established, and the deviation of the aircraft motion is used as the optimization target. The real-time optimal drive amount is obtained through the Adam-GA rolling optimization strategy. A control system fault-tolerant mechanism is constructed to filter and screen the input data, and the control rate is adjusted according to the amplitude of the sudden change interference to achieve high-precision and stable control of the aircraft model motion.

Description

Technical Field

[0001] The invention belongs to the field of precision motion control, and designs a predictive control method of a nonlinear cascade model for a three-degree-of-freedom motion control system of an aircraft model in a wind tunnel test. Background Art

[0002] Modern flight missions place higher demands on the maneuverability and stability of high-speed aircraft. However, the flight speed of such aircraft is extremely high and the service environment is complex. The high maneuverability of the aircraft can easily induce aerodynamic load changes and cause system instability. Therefore, the dynamic stability of the aerodynamic layout must be evaluated during the aircraft design phase to ensure the safety and effectiveness of the aerodynamic design. As the most practical and accurate stability test technology currently available, dynamic derivative testing plays a key role in the development of new aircraft models.

[0003] In order to meet the needs of stability assessment of high-speed aircraft under high maneuvers in complex aerodynamic environments, high-speed wind tunnel dynamic derivative tests need to have multi-degree-of-freedom actuation capabilities to obtain accurate, reliable, and complete dynamic derivative judgment criteria. However, in a hypersonic flow field environment, the nonlinear factors inside the controlled system are coupled and overlapped, and external interference changes dramatically. Therefore, high-precision stability control of the motion control system is a difficult problem for dynamic derivative testing.

[0004] In 2014, the team of T. Loeser of the German-Dutch Wind Tunnel Organization (DNW) published a paper entitled "UCAV model design and static experimental investigations to estimate control device effectiveness and control capabilities". Aiming at the multi-degree-of-freedom motion simulation needs of the model, the team developed a model motion control system for the low-speed wind tunnel NWB. The device uses a hybrid PID to control the rotary motor and the six-degree-of-freedom parallel platform, which can achieve three-degree-of-freedom excitation at a 3Hz actuation frequency at 0.26 Mach, with an angular displacement accuracy of up to 0.005°. In 2022, the team of Mou Weiqiang of the China Aviation Industry Aerodynamics Research Institute published a paper entitled "Development of a Three-Degree-of-Freedom Large-Scale Oscillation Test System for the FL-51 Wind Tunnel", which proposed a three-degree-of-freedom large-scale oscillation test system for the external tail support of a low-speed wind tunnel, which can achieve three-degree-of-freedom motion simulation within 1.5Hz. The device uses a PID-based integrated control algorithm with an angle control accuracy of ±0.05°, but it is only suitable for low-speed flow field and low-frequency actuation working scenarios.

[0005] The above motion simulation scheme is based on model-free control theories such as PID algorithm and fuzzy control. It is often suitable for relatively stable and low-response low-speed wind tunnels. The combined influence of tracking target frequency change and external interference transient in high-speed complex flow fields greatly reduces the control accuracy. Therefore, it is necessary to propose a multi-degree-of-freedom motion control method for aircraft models in complex aerodynamic environments of high-speed wind tunnels. Summary of the invention

[0006] In order to overcome the deficiencies of the prior art, the present invention proposes a model predictive control strategy that takes into account the time-varying nonlinear cascade of the system for the three-degree-of-freedom motion control system of the aircraft model. Based on the method of dynamic modeling and offline training of the machine learning model, a nonlinear interconnected model of piezoelectric hysteresis-rotational friction-transmission deformation is constructed to achieve modeling and real-time prediction of the motion system with multiple nonlinear link cascades. The time-varying law of high-speed flow field load disturbance is studied, and an aerodynamic load estimation model is established. Based on the principle of instantaneous load balancing, load-driving force tolerance constraints are constructed, and a time-domain rolling optimization strategy is established to achieve real-time optimization of the driving voltage solution space taking into account load disturbances, form a time-varying load balancing anti-disturbance method, and achieve real-time anti-disturbance control that adapts to sudden changes in loads. A nonlinear cascade model fault-tolerant mechanism is constructed to filter the pathological input information caused by sudden changes in disturbances, constrain the adjustment rate of the control output, reduce the model prediction deviation, and improve the stability of the control system.

[0007] The technical solution of the present invention:

[0008] A model predictive control method for a three-degree-of-freedom motion control system of a wind tunnel aircraft model, the steps are as follows:

[0009] Firstly, based on the constructed three-degree-of-freedom motion control system of the aircraft model, the mechanism dynamics model is constructed to describe the dynamic process of the mechanism in the anti-load motion; secondly, based on the actuator drive experimental data and the mechanism friction experimental data, the drive hysteresis and friction nonlinear model is constructed, and finally a cascade model of multiple nonlinear dynamic links is formed. Then, the real-time force and position information of the system is obtained through a monitoring system composed of multiple sensors such as angle encoders, strain sensors, and piezoelectric balances, and the real-time prediction of the mechanism motion state is realized based on the above cascade model; then, based on the existing mechanism state parameters, a multi-dimensional instantaneous load-driving force tolerance constraint is established, and the deviation of the aircraft model motion is taken as the optimization target. The real-time optimal drive quantity is obtained through the Adams-GA rolling optimization strategy; finally, a control system fault-tolerant mechanism is constructed to filter and screen the sudden pathological input data, and the control rate is adjusted according to the sudden change interference amplitude to achieve high-precision and stable control of the aircraft model motion.

[0010] (1) Building a three-degree-of-freedom motion control system for an aircraft model: Install the angle encoder 1 on the inner side of the vibration cylinder and on the yaw axis to form a three-degree-of-freedom angular displacement monitoring system 2, which is connected to the angle monitoring card of the data acquisition module 3; Install the piezoelectric actuator 8 in the three-degree-of-freedom motion mechanism, connect its drive circuit to the power amplifier 6, and connect the strain sensor embedded in the piezoelectric actuator 8 to the actuator displacement acquisition card of the data acquisition module 3; The piezoelectric balance 7 is matched with the aircraft model through a conical surface, and is connected to the multi-dimensional force acquisition card and angle monitoring card of the data acquisition module 3 corresponding to the three-degree-of-freedom angular displacement monitoring system 2 to measure multi-dimensional dynamic force and multi-degree-of-freedom motion angle data; Connect the data acquisition module 3, the power amplifier 6, and the host computer 5 to the real-time controller 4 to form a physical quantity measurement acquisition circuit, an actuator control drive circuit, and a data transmission visualization circuit, thereby completing the construction of a three-degree-of-freedom motion control system for an aircraft model;

[0011] (2) Based on the open-loop drive experiment, the driving voltage, actuator strain, multi-dimensional dynamic force and multi-degree-of-freedom motion angle of the motion control system under different load conditions are collected, and the actuator strain is converted into the actuator displacement value, and then the mapping curves of driving voltage-actuator displacement and multi-dimensional dynamic force-actuator displacement-multi-degree-of-freedom motion angle are obtained respectively. The training data set of the piezoelectric actuator 8 is established by collecting the driving voltage and actuator displacement, and the training data set of the three-degree-of-freedom motion mechanism is obtained by collecting the multi-dimensional dynamic force-actuator displacement-multi-degree-of-freedom motion angle; based on the kinematic pair friction experiment, the dynamic and static friction coefficients of the kinematic pair are recorded to obtain the kinematic pair friction experiment data;

[0012] (3) Based on the geometric constraint relationship between the components of the three-degree-of-freedom motion mechanism, the dynamic model of the transmission mechanism is constructed. The three-degree-of-freedom motion mechanism consists of three motion chains, among which the pitch direction motion chain contains the transmission node - And transmission rod - ; Yaw direction kinematic chain, including transmission nodes - And transmission rod - ; Rolling direction kinematic chain, including transmission nodes - And transmission rod - and ; Among them, in the pitch direction, Provides linear displacement for the piezoelectric actuator 8, One end and Articulated, The other end , exist Articulated at The other end is connected to the node , The other end Connect to Node , The other end is connected to the node ,pass Linear displacement drive , , Turn, realize Around the Node Rotation; in yaw direction, The piezoelectric actuator 8 has one end connected to the node Hinge, the other end Articulated at the node , Same as three transmission rods The first end is hinged to the node , The second end is connected to the node , The third end exist Contact in the form of point-to-surface friction, Last same node Articulated, through Output linear displacement, transmitted to Node ,pass At the node The displacement in the orthogonal direction is magnified, driving Around the Node Rotation; Roll direction, pass , Amplify the displacement to ,same exist Contact in the form of point-to-surface friction, driving Around the Node Rotation; each transmission rod forms a kinematic pair at the transmission node; the geometric constraint equation and force analysis in the dynamic model are shown in formulas (1) and (2) respectively:

[0013]

[0014]

[0015] in, to is the space vector of the nine transmission rods, to is the output displacement of the three piezoelectric actuators 8, and Respectively represent transmission rods The horizontal and vertical angles of space vectors, For transmission rod The initial horizontal angle of the space vector, , , are the pitch angle, yaw angle and roll angle of the three-degree-of-freedom motion mechanism, to is the positioning dimension between components in the transmission chain, to For each transmission rod to bear force, is the force on the piezoelectric actuator, , , Transmission node , , The friction torque at , Transmission node , The friction force at , is the moment arm in the yaw and roll directions, to is the moment in the three directions of pitch, yaw and roll;

[0016] Based on the horizontal angle of the space vector of each transmission rod obtained by formula (1), the rotation angular velocity of each transmission rod is derived, and the relative velocity of the kinematic pair composed of the transmission rods can be obtained, as shown in the following formula:

[0017]

[0018] in, , , Indicates the transmission rod The angular velocity of rotation and The radius and relative speed of the corresponding kinematic pair; the dynamic model of the transmission mechanism can be obtained by combining equations (1), (2) and (3);

[0019] (4) Based on the driving voltage, displacement data, multi-dimensional dynamic force data and kinematic pair friction experimental data of the piezoelectric actuator 8, nonlinear modeling of the piezoelectric actuator 8 and nonlinear modeling of the kinematic pair friction are performed respectively, the input-output relationship of the model is determined, and finally a nonlinear cascade model of the system is formed; the driving voltage, strain data and multi-dimensional dynamic force data of the piezoelectric balance 7 are respectively obtained from the data acquisition module 3;

[0020] The nonlinear model of the piezoelectric actuator 8 is established by a NARX neural network, with the displacement time series of the piezoelectric actuator 8 and the time series of the driving voltage as input, and the output is the predicted value of the actuator displacement; its NARX form is as follows:

[0021]

[0022] in, is the predicted value of the actuator displacement, a is the number of displacement time series of the piezoelectric actuator 8, to is the displacement time series of the piezoelectric actuator 8, to is the time series of the driving voltage;

[0023] Transmission nodes in the kinematic chain of a three-degree-of-freedom motion mechanism - There are kinematic pairs everywhere. The nonlinear friction model of the kinematic pair is established by the LuGre friction model, and its function form is as follows:

[0024]

[0025] In the formula, is the friction coefficient, z represents the Coulomb friction coefficient, is the friction force, is the relative sliding velocity; , , , All are constant coefficients, set to 100000 N / m, 400Ns / m, 0.01, and 2 respectively; is the Stribeck speed, which is a scaling factor that determines the transition speed range of friction from static friction to dynamic friction; and are the dynamic and static friction coefficients respectively;

[0026] Through the predicted value of the actuator displacement, the force analysis based on formula (2) is used to obtain the force on each transmission rod: to , defining the contact force of the kinematic pair is the contact force generated by the connection of each transmission rod at the transmission node, and its magnitude is equal to the minimum force of each transmission rod at the transmission node; Substitute the forces of the transmission rods on both sides corresponding to each kinematic pair into the contact force of the kinematic pair. , based on formula (3), the relative sliding velocity of the corresponding kinematic pair is obtained ; The dynamic and static friction coefficients are determined through the kinematic pair friction test data, and the kinematic pair friction force is obtained through formula (5): ,this is the predicted value of the friction force of the kinematic pair;

[0027] The nonlinear cascade model is segmented and parameterized through the training data set of the three-degree-of-freedom motion mechanism to verify the stability of the nonlinear cascade model; the function form of the nonlinear cascade model is as follows:

[0028]

[0029] in, represents the nonlinear cascade model of the system, where U, S, and F are the driving voltage, actuator displacement, and multi-dimensional dynamic force, respectively. , , They respectively represent the NARX neural network of the piezoelectric actuator 8, the LuGre friction model of the kinematic pair, and the dynamic model of the transmission mechanism; the predicted displacement of the actuator can be substituted into the dynamic model of the transmission mechanism to solve the relative displacement and velocity of each transmission rod, and then substituted into the LuGre friction model of the kinematic pair to obtain the predicted value of the friction force of the kinematic pair, and finally substituted back into the dynamic model of the transmission mechanism to solve the predicted value of the force-position state of the transmission mechanism, including the predicted value of the angular displacement and the relative displacement, velocity and force predicted value of each transmission rod. (5) Based on the nonlinear cascade model of the system, a model predictive control strategy is constructed. Through the obtained predicted value of the force-position state of the transmission mechanism, the tolerance constraint of the instantaneous load-driving force and the optimization goal of minimizing the driving displacement error are designed. The optimization problem is shown in the following formula (7). The Adam-GA algorithm is used for time domain rolling optimization to realize real-time predictive control taking into account the external time-varying large load;

[0030]

[0031] in, is the objective function, which is defined as the weighted addition of the mean square error between the angular displacement prediction value and the target value and the sum of the squares of the output quantity in the control time domain; , are the predicted value and target value of the angular displacement at time step e, , is the voltage output value and change value at time step e; , are the upper and lower limits of the voltage output value, , is the limit value, which should be adjusted according to the actual working conditions. , , T are load, driving force and system inertia respectively; n is the time step number of the output voltage, e Indicates e Time step, a is the weight of the voltage output mean square term;

[0032] (6) Design a fault-tolerant mechanism for the nonlinear cascade model, design a moving window, and establish an identification and screening mechanism for the ill-conditioned input of the state quantity in the time domain through variance analysis; the functional form of the ill-conditioned input identification mechanism is as follows:

[0033]

[0034] Among them, q is the variance of the time domain data in the window, m is the number of time domain data in the window, is the kth data, is the mean of window data;

[0035] The prediction output of the nonlinear cascade model is shown in equation (9):

[0036]

[0037] in, , are the nonlinear cascade model outputs at time t and t-1 respectively, is the preset variance threshold;

[0038] At the same time, the adjustment rate of the model predictive control is dynamically adjusted according to the external sudden change disturbance amplitude. The function is shown in the following formula (10):

[0039]

[0040] Among them, rate is the adjustment rate, the unit is Hz; is the preset rate, q is the variance of the time domain data within the window, m is the number of time domain data in the window.

[0041] Beneficial effects of the present invention: The present invention realizes real-time prediction of system status by nonlinear cascade modeling of the three links of piezoelectric hysteresis-rotational friction-transmission deformation in the three-degree-of-freedom motion control system of the wind tunnel aircraft model; by constructing a model predictive control strategy, designing the tolerance constraints of the instantaneous load-driving force and the optimization goal of minimizing the angular displacement error, and realizing model predictive control through real-time rolling prediction-optimization-correction. Compared with the existing model-free control method, it has better frequency-varying adaptability and anti-interference ability, and can ensure higher accuracy in multi-dimensional motion tasks under complex flow fields. Because it adopts forward rolling prediction optimization, its control lag is also significantly lower than that of traditional control methods, and it is easier to resist interference caused by sudden impact loads. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is an overall flow chart of a model predictive control method for a three-degree-of-freedom motion simulation device for a wind tunnel aircraft model of the present invention.

[0043] Figure 2 It is a connection diagram of the three-degree-of-freedom excitation control system of the present invention.

[0044] Figure 3 This is the actuator voltage-actuator displacement mapping curve of the present invention.

[0045] Figure 4 It is the actuator displacement-mechanism angular displacement mapping curve of the present invention.

[0046] Figure 5 This is the relationship diagram between the geometric constraints and forces of the pitch excitation transmission chain.

[0047] Figure 6 This is the relationship diagram between the geometric constraints and forces of the yaw excitation transmission chain.

[0048] Figure 7 This is the relationship diagram between the geometric constraints and forces of the rolling excitation transmission chain.

[0049] Figure 8 It is a schematic diagram of the system nonlinear dynamics model of the present invention.

[0050] Fig. 9 Iterative optimization flowchart of the Adam-GA optimization algorithm.

[0051] Fig.10 This is the model predictive control result diagram of the three-degree-of-freedom excitation system.

[0052] In the figure: 1 angle encoder; 2 three-degree-of-freedom angular displacement monitoring system; 3 data acquisition module; 4 real-time controller; 5 host computer; 6 power amplifier; 7 piezoelectric balance; 8 piezoelectric actuator. DETAILED DESCRIPTION

[0053] The specific implementation of the present invention is described in detail below in conjunction with specific embodiments and drawings.

[0054] (1) Build a three-degree-of-freedom motion control system for an aircraft model designed for a 2.4-meter wind tunnel: Figure 1 As shown in the assembly diagram of the three-degree-of-freedom motion control system, the angle encoder 1 is installed on the inner side of the vibration cylinder and on the yaw axis to form a three-degree-of-freedom angular displacement monitoring system 2, which is connected to the angle monitoring card of the data acquisition module 3. The piezoelectric actuator 8 is installed in the three-degree-of-freedom motion mechanism, and its driving circuit is connected to the power amplifier 6. At the same time, the strain sensor embedded in the piezoelectric actuator 8 is connected to the actuator displacement acquisition card of the data acquisition module 3. The piezoelectric balance 7 is connected to the aircraft model through a conical surface fit, and is connected to the multi-dimensional force acquisition card and angle monitoring card of the data acquisition module 3 corresponding to the three-degree-of-freedom angular displacement monitoring system 2, for measuring multi-dimensional dynamic force and multi-degree-of-freedom motion angle data.

[0055] In addition, the data acquisition module 3, the power amplifier 6 and the host computer 5 are all connected to the real-time controller 4 to form a physical quantity measurement acquisition circuit, an actuator control drive circuit and a data transmission visualization circuit, and finally complete the construction of the three-degree-of-freedom motion control system of the aircraft model. The schematic diagram of the system is shown in Figure 2 shown.

[0056] (2) Conduct an open-loop drive experiment of the three-degree-of-freedom motion control system, and collect the driving voltage, actuator strain, multi-dimensional dynamic force, and multi-degree-of-freedom motion angle data of the motion control system under different load conditions. The actuator strain is converted into the actuator displacement value to obtain the mapping curves between the driving voltage and the actuator displacement, the multi-dimensional dynamic force and the actuator displacement, and the multi-degree-of-freedom motion angle. The training data set of the piezoelectric actuator 8 is established through the collected driving voltage and actuator displacement data; the training data set of the three-degree-of-freedom motion mechanism is constructed through the collected multi-dimensional dynamic force, actuator displacement, and multi-degree-of-freedom motion angle data. In addition, in the kinematic pair friction experiment, the dynamic friction coefficient and static friction coefficient of the kinematic pair are recorded to obtain the friction experiment data of the kinematic pair. Combined with the driving voltage data, the characteristic curves of the actuator voltage-actuator displacement and the actuator displacement-multi-degree-of-freedom motion angle are constructed respectively to obtain the dynamic response information of the motion control system. The characteristic curves are analyzed and the system characteristics are identified. The characteristic curves of the actuator voltage-actuator displacement and the actuator displacement-multi-degree-of-freedom motion angle are shown as follows: Figure 3 , Figure 4 shown.

[0057] (3) Based on the geometric constraint relationship between the components of the three-degree-of-freedom motion mechanism, the dynamic model of the transmission mechanism is constructed. The three-degree-of-freedom motion mechanism contains three motion chains: the motion chain in the pitch direction includes the transmission node - And its corresponding transmission rod - ; The kinematic chain in the yaw direction contains the transmission nodes - And its corresponding transmission rod - ; The kinematic chain in the rolling direction contains the transmission nodes - And related transmission rods - and In the pitch direction, Provides linear displacement for the piezoelectric actuator 8, One end and Articulated, The other end , exist Articulated at The other end is connected to the node , The other end Connect to Node , The other end is connected to the node ,pass Linear displacement drive , , Turn, realize Around the Node Rotation; in yaw direction, The piezoelectric actuator 8 has one end connected to the node Hinge, the other end Articulated at the node , Same as three transmission rods The first end is hinged to the node , The second end is connected to the node , The third end exist Contact in the form of point-to-surface friction, Last same node Articulated, through Output linear displacement, transmitted to Node ,pass At the node The displacement in the orthogonal direction is magnified, driving Around the Node Rotation; Roll direction, pass , Amplify the displacement to ,same exist Contact in the form of point-to-surface friction, driving Around the Node Rotate; Substitute the length of each rod vector, the geometric constraint equation and force analysis in the dynamic model are shown in formulas (11) and (12) respectively:

[0058]

[0059]

[0060] in, , , are the axial forces acting on the long and short rods and the piezoelectric actuator in the pitch transmission chain respectively; , , , are the tangential forces on the high pair contacts of the four levers in the yaw and roll transmission chain, The piezoelectric actuator is subjected to force.

[0061] Based on the horizontal angle of the space vector of each transmission rod obtained by formula (11), the rotation angular velocity of each transmission rod can be obtained by derivation, as shown in formula (3), and the relative velocity between the kinematic pairs can be obtained. Combining formula (3) with (11) and (12), the dynamic model of the transmission mechanism can be constructed to fully describe its dynamic characteristics and motion behavior, where Figure 5 , Figure 6 , Figure 7 These are the geometric constraints and force relationship diagrams of the pitch transmission chain, yaw transmission chain, and roll transmission chain.

[0062] (4) Based on the driving voltage, actuator displacement data, multi-dimensional dynamic force data of the piezoelectric actuator 8 collected by the data acquisition module 3, and the experimental data obtained from the kinematic pair friction experiment, nonlinear modeling of the piezoelectric actuator 8 and nonlinear modeling of the kinematic pair friction are performed respectively to determine the input-output relationship of the model, and finally a nonlinear cascade model of the system is formed. Figure 8 Schematic diagram of the nonlinear cascade model.

[0063] Specifically, the nonlinear model of the piezoelectric actuator 8 is established using the NARX neural network, with the displacement time series of the piezoelectric actuator 8 and the time series of the driving voltage as input, and the output is the predicted value of the actuator displacement. In the motion chain of the three-degree-of-freedom motion mechanism, there are kinematic pairs at the transmission nodes, and their friction nonlinear model is established using the LuGre friction model. Through the predicted value of the actuator displacement, combined with formula (2), force analysis is performed to obtain the force conditions of each transmission rod, and the corresponding forces of the transmission rods on both sides are substituted to calculate the contact force of the kinematic pair. Based on formula (3), the relative sliding speed of the corresponding kinematic pair can be obtained, and the dynamic friction coefficient and static friction coefficient are determined through the kinematic pair friction experimental data. Based on formula (5), the predicted value of the kinematic pair friction force is further obtained. Subsequently, the stability of the nonlinear cascade model is verified by performing segmented verification and parameter correction on the training data set of the three-degree-of-freedom motion mechanism. The predicted displacement of the actuator can be substituted into the dynamic model of the transmission mechanism to solve the relative displacement and velocity of each transmission rod, and then substituted into the LuGre friction model of the kinematic pair to obtain the predicted value of the friction force of the kinematic pair. Finally, it is substituted back into the dynamic model of the transmission mechanism to solve the predicted value of the force-position state of the transmission mechanism, including the predicted value of the angular displacement and the predicted values ​​of the relative displacement, velocity and force of each transmission rod.

[0064] (5) Based on the nonlinear cascade model of the motion control system formed in step (5), a model predictive control strategy is constructed. Through the predicted value of the force and position state of the transmission mechanism, the tolerance constraint of the instantaneous load-driving force is designed, and the minimization of the driving displacement error is taken as the optimization goal. The optimization problem can be expressed as formula (7). In order to realize real-time predictive control of external time-varying large loads, the Adam-GA algorithm is used for time domain rolling optimization to realize real-time predictive control taking into account the external time-varying large loads. The algorithm flow is as follows: Fig. 9 As shown, the optimization objective is shown in formula (4).

[0065] (6) Design a fault-tolerant mechanism for the nonlinear cascade model, establish a moving window, and establish an identification and screening mechanism for the time-domain pathological input of the state quantity through variance analysis. The function form of the pathological input identification mechanism can be expressed as formula (8), and the predicted output of the nonlinear cascade model is shown in formula (9). At the same time, according to the change in the amplitude of the external sudden change interference, the adjustment rate of the model predictive control is dynamically adjusted to prevent the continuous adjustment when the system is not in a stable state from causing the system to overshoot. Its function form is shown in formula (10). Finally, a model predictive control method for piezoelectric ceramic actuators under time-varying loads is formed, and the final control result is as follows: Fig.10 shown.

[0066] Compared with the traditional method, this control method improves the control accuracy of the motion control device under the conditions of motion frequency change and drastic interference, and can realize the real-time and accurate prediction of the state quantity of the motion control device. By solving the optimal output in the control time domain through the predictive control strategy, the real-time rolling prediction-optimization-correction of the three-degree-of-freedom composite motion simulation of the aircraft model can be realized. The control effect of the multi-dimensional motion control system in the wind tunnel environment is obvious, the test data is accurately obtained, and the reliable evaluation of the dynamic stability of the aircraft can be guaranteed. The invention can be applied to many types of piezoelectric driven motion control systems.

Claims

1. A model predictive control method for a three-degree-of-freedom motion control system of a wind tunnel aircraft model, characterized in that: Here are the steps: (1) Building a three-degree-of-freedom motion control system for an aircraft model: installing an angle encoder (1) into a vibration cylinder and a yaw axis to form a three-degree-of-freedom angular displacement monitoring system (2), and connecting the three-degree-of-freedom angular displacement monitoring system (2) to an angle monitoring card of a data acquisition module (3); installing a piezoelectric actuator (8) in a three-degree-of-freedom motion mechanism, connecting its driving circuit to a power amplifier (6), and connecting a strain sensor embedded in the piezoelectric actuator (8) to an actuator displacement acquisition card of a data acquisition module (3); matching a piezoelectric balance (7) with the aircraft model through a conical surface, and correspondingly connecting the piezoelectric balance (7) to a multi-dimensional force acquisition card and an angle monitoring card of a data acquisition module (3) to measure multi-dimensional dynamic force and multi-degree-of-freedom motion angle data; connecting the data acquisition module (3), the power amplifier (6), and the host computer (5) to a real-time controller (4) to form a physical quantity measurement acquisition circuit, an actuator control drive circuit, and a data transmission visualization circuit, thereby completing the construction of a three-degree-of-freedom motion control system for an aircraft model; (2) Based on the open-loop drive experiment, the driving voltage, actuator strain, multi-dimensional dynamic force and multi-degree-of-freedom motion angle of the motion control system under different load conditions are collected, and the actuator strain is converted into the actuator displacement value, and then the mapping curves of driving voltage-actuator displacement and multi-dimensional dynamic force-actuator displacement-multi-degree-of-freedom motion angle are obtained respectively. The training data set of the piezoelectric actuator (8) is established by collecting the driving voltage and actuator displacement, and the training data set of the three-degree-of-freedom motion mechanism is obtained by collecting the multi-dimensional dynamic force-actuator displacement-multi-degree-of-freedom motion angle; Based on the kinematic pair friction experiment, the dynamic and static friction coefficients of the kinematic pair are recorded to obtain the kinematic pair friction experiment data; (3) Based on the geometric constraint relationship between the components of the three-degree-of-freedom motion mechanism, the dynamic model of the transmission mechanism is constructed. The three-degree-of-freedom motion mechanism consists of three motion chains, among which the pitch direction motion chain contains the transmission node - And transmission rod - ; Yaw direction kinematic chain, including transmission nodes - And transmission rod - ; Rolling direction kinematic chain, including transmission nodes - And transmission rod - and ; Among them, in the pitch direction, Provides a linear displacement for the piezoelectric actuator (8). One end and Articulated, The other end , exist Articulated at The other end is connected to the node , The other end Connect to Node , The other end is connected to the node ,pass Linear displacement drive , , Turn, realize Around the Node Rotation; in yaw direction, is a piezoelectric actuator (8), one end of which is connected to the node Hinge, the other end Articulated at the node , Same as three transmission rods The first end is hinged to the node , The second end is connected to the node , The third end exist Contact in the form of point-to-surface friction, Last same node Articulated, through Output linear displacement, transmitted to Node ,pass At the node The displacement in the orthogonal direction is magnified, driving Around the Node Rotation; Roll direction, pass , Amplify the displacement to ,same exist Contact in the form of point-to-surface friction, driving Around the Node Rotation; each transmission rod forms a kinematic pair at the transmission node; the geometric constraint equation and force analysis in the dynamic model are shown in formulas (1) and (2) respectively: in, to is the space vector of the nine transmission rods, to is the output displacement of the three piezoelectric actuators (8), and Respectively represent transmission rods The horizontal and vertical angles of space vectors, For transmission rod The initial horizontal angle of the space vector, , , are the pitch angle, yaw angle and roll angle of the three-degree-of-freedom motion mechanism, to is the positioning dimension between components in the transmission chain, to For each transmission rod to bear force, is the force on the piezoelectric actuator, , , Transmission node , , The friction torque at , Transmission node , The friction force at , is the moment arm in the yaw and roll directions, to is the moment in the three directions of pitch, yaw and roll; Based on the horizontal angle of the space vector of each transmission rod obtained by formula (1), the rotation angular velocity of each transmission rod is derived, and the relative velocity of the kinematic pair composed of the transmission rods can be obtained, as shown in the following formula: in, , , Indicates the transmission rod The angular velocity of rotation and The radius and relative speed of the corresponding kinematic pair; the dynamic model of the transmission mechanism can be obtained by combining equations (1), (2) and (3); (4) Based on the driving voltage of the piezoelectric actuator (8), the displacement data of the actuator, the multi-dimensional dynamic force data and the kinematic pair friction experimental data, the nonlinear modeling of the piezoelectric actuator (8) and the nonlinear modeling of the kinematic pair friction are respectively performed to determine the input-output relationship of the model, and finally form a nonlinear cascade model of the system; the driving voltage, strain data and the multi-dimensional dynamic force data of the piezoelectric balance (7) are respectively obtained from the data acquisition module (3); The nonlinear model of the piezoelectric actuator (8) is established by a NARX neural network, with the displacement time series of the piezoelectric actuator (8) and the driving voltage time series as input, and the output is the predicted value of the actuator displacement; its NARX form is as follows: in, is the predicted value of the actuator displacement, a is the number of displacement time series of the piezoelectric actuator (8), to is the displacement time series of the piezoelectric actuator (8), to is the time series of the driving voltage; Transmission nodes in the kinematic chain of a three-degree-of-freedom motion mechanism - There are kinematic pairs everywhere. The nonlinear friction model of the kinematic pair is established by the LuGre friction model, and its function form is as follows: In the formula, is the friction coefficient, z represents the Coulomb friction coefficient, is the friction force, is the relative sliding velocity; , , , All are constant coefficients, set to 100000 N / m, 400Ns / m, 0.01, and 2 respectively; is the Stribeck speed, which is a scaling factor that determines the transition speed range of friction from static friction to dynamic friction; and are the dynamic and static friction coefficients respectively; Through the predicted value of the actuator displacement, the force analysis based on formula (2) is used to obtain the force on each transmission rod: to , defining the contact force of the kinematic pair is the contact force generated by the connection of each transmission rod at the transmission node, and its magnitude is equal to the minimum force of each transmission rod at the transmission node; Substitute the forces of the transmission rods on both sides corresponding to each kinematic pair into the contact force of the kinematic pair. Based on formula (3), the relative sliding speed of the corresponding kinematic pair is obtained; through the kinematic pair friction experimental data, the dynamic and static friction coefficients are determined, and the kinematic pair friction force is obtained through formula (5): ,this is the predicted value of the friction force of the kinematic pair; The nonlinear cascade model is segmented and parameterized through the training data set of the three-degree-of-freedom motion mechanism to verify the stability of the nonlinear cascade model; the function form of the nonlinear cascade model is as follows: in, represents the nonlinear cascade model of the system, where U, S, and F are the driving voltage, actuator displacement, and multi-dimensional dynamic force, respectively. , , The NARX neural network, the LuGre friction model of the kinematic pair, and the dynamic model of the transmission mechanism respectively represent the piezoelectric actuator (8); based on the predicted values ​​of the actuator displacement and the kinematic pair friction force, they are substituted into the dynamic model of the transmission mechanism to solve and obtain the predicted values ​​of the force-position state of the transmission mechanism, including the predicted values ​​of the angular displacement and the relative displacement, velocity, and force of each transmission rod; (5) Based on the nonlinear cascade model of the system, a model predictive control strategy is constructed. By obtaining the predicted value of the force-position state of the transmission mechanism, the tolerance constraint of the instantaneous load-driving force and the optimization goal of minimizing the driving displacement error are designed. The optimization problem is shown in equation (7). The Adam-GA algorithm is used for time domain rolling optimization to achieve real-time predictive control taking into account the external time-varying large load; in, is the objective function, which is defined as the weighted addition of the mean square error between the angular displacement prediction value and the target value and the sum of the squares of the output quantity in the control time domain; , are the predicted value and target value of the angular displacement at time step e, , is the voltage output value and change value at time step e; , are the upper and lower limits of the voltage output value, , is the limit value, which should be adjusted according to the actual working conditions. , , T are load, driving force and system inertia respectively; n is the time step number of the output voltage, e Indicates e Time step, a is the weight of the voltage output mean square term; (6) Design a fault-tolerant mechanism for the nonlinear cascade model, design a moving window, and establish an identification and screening mechanism for the ill-conditioned input of the state quantity in the time domain through variance analysis; the functional form of the ill-conditioned input identification mechanism is as follows: Among them, q is the variance of the time domain data in the window, m is the number of time domain data in the window, is the kth data, is the mean of window data; The nonlinear cascade model prediction output is shown as follows: in, , are the nonlinear cascade model outputs at time t and t-1 respectively, is the preset variance threshold; At the same time, the adjustment rate of the model predictive control is dynamically adjusted according to the external sudden change disturbance amplitude. The function is shown in the following formula (10): Among them, rate is the adjustment rate, the unit is Hz; is the preset rate, q is the variance of the time domain data within the window, m is the number of time domain data in the window.

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