Hierarchical control method and system for deicing vehicle under airplane idling condition

Abstract

The invention belongs to the technical field of airplane nonlinear system control, and discloses a deicing vehicle hierarchical control method and system under an airplane idling condition. According to the method, a deicing vehicle overall dynamic model under incomplete constraint is constructed based on a Lagrange equation, a vehicle-arm combined trajectory tracking error state model is constructed, a cost function of a model prediction controller is designed according to a control target of deicing vehicle combined trajectory tracking, a quadratic programming problem is constructed on an upper layer to solve an optimal virtual control quantity, and the optimal virtual control quantity is calculated. And the lower layer analyzes the virtual control quantity into control input which can actually act on an execution mechanism by designing a self-adaptive fuzzy logic strategy so as to realize trajectory tracking control. According to the invention, a hierarchical control strategy is provided by combining model predictive control and an adaptive fuzzy logic system (FLS), the stability and high efficiency of system operation are ensured, and the deicing vehicle is ensured to always maintain a stable operation state in a complex and changeable operation environment.

Description

Technical Field

[0001] The present invention belongs to the technical field of aircraft nonlinear system control, and in particular relates to a de-icing vehicle stratification control method and system under aircraft idling conditions. Background Art

[0002] Idle deicing refers to the de-icing / anti-icing operations performed by a de-icing vehicle on an aircraft while the aircraft engine is idling. Idle deicing is faster and more efficient. However, engine idling will form a complex three-dimensional risk zone, and the wake turbulence will affect the de-icing vehicle's operation difficulty. There is also a risk of de-icing fluid being inhaled into the engine. Therefore, conducting research on the joint trajectory tracking control of the de-icing vehicle at aircraft idling has certain engineering significance. Aircraft de-icing vehicles are an essential operational safety vehicle for airports or airlines in cold regions, used to remove ice from the aircraft fuselage and wings.

[0003] Traditional de-icing typically involves collaboration between a de-icing operator and a vehicle operator. However, this approach often requires high operator skill, and the de-icing environment is often harsh, significantly impacting the operator's health. Currently, some international companies have developed intelligent spray systems, automatic flow monitoring systems, and single-operator operation systems. Intelligent systems are an inevitable trend in the development of aircraft de-icing vehicles.

[0004] During aircraft idling de-icing operations, de-icing vehicles must operate in extreme weather conditions. The mobile platform has poor adhesion, and the vehicle body is subject to wake turbulence interference. The forces generated by the de-icing fluid spray also affect the dynamic characteristics of the entire system. Furthermore, the operational trajectories are often complex, high-order, and nonlinear, resulting in complex performance constraints.

[0005] The above analysis reveals the following problems and shortcomings of existing technologies: In the aviation support sector, de-icing operations at idle aircraft require extremely high performance from de-icing vehicles. The complex operating conditions, coupled with the intertwined parameters and multiple constraints, significantly restrict operational efficiency and stability. Summary of the Invention

[0006] To overcome the challenges of related technologies, the present invention discloses a hierarchical control method and system for de-icing vehicles operating at idle speed. This invention addresses the challenges of nonlinear factors, complex uncertainties, and complex trajectory constraints during system operation, and proposes a hierarchical control strategy by combining model prediction and adaptive fuzzy logic.

[0007] The technical solution is as follows: A de-icing vehicle layer control method under aircraft idling conditions, comprising the following steps:

[0008] S1, considering the inherent strong nonlinear characteristics of the de-icing vehicle system and the close coupling relationship between variables, the overall dynamic model of the de-icing vehicle under nonholonomic constraints is constructed based on the Lagrange equation;

[0009] S2, based on the constructed de-icing vehicle overall dynamics model and considering the complex constraints of the overall trajectory, a vehicle-arm joint trajectory tracking error state model is constructed;

[0010] S3, linearize the constructed vehicle-arm joint trajectory tracking error state model and design a hierarchical control framework to achieve trajectory tracking of the de-icing vehicle under aircraft idling conditions;

[0011] In S4, the upper layer of the controller constructs a quadratic programming problem to obtain the optimal virtual control variable, focusing on the key indicators of maximizing de-icing efficiency and optimizing energy consumption, while taking into account the dynamic constraints of aircraft surface temperature fluctuations and de-icing fluid spray rate limits;

[0012] S5, the lower layer of the controller designs a fuzzy logic system FLS to resolve the virtual control quantity into a control input that can actually act on the actuator to achieve trajectory tracking control.

[0013] In step S1, the de-icing vehicle is a multi-rigid body system, and the Lagrange equation is used to develop the overall dynamic model of the de-icing vehicle under nonholonomic constraints. The expression is:

[0014] (1)

[0015] Where, is a symmetric positive definite mass matrix, The lifting degree of the de-icing vehicle's boom. is the lifting speed of the de-icing vehicle's boom, is the acceleration of the de-icing vehicle's boom lifting, For centripetal force and scientific force, is the gravity term, is the unknown external interference term, Input torque for the de-icing vehicle, is the input transformation matrix, is the constraint matrix, is the Lagrange multiplier;

[0016]

[0017]

[0018]

[0019] Where, is the coordinate of the center point of the de-icing vehicle, express Transpose, is the horizontal axis, is the vertical axis, is the yaw angle of the de-icing vehicle, is the displacement of the de-icing vehicle, express Transpose, is the front wheel turning angle, is the rear wheel turning angle, Joint 1 to joint The rotation angle of .

[0020] Furthermore, the nonholonomic constraint is , the expression is:

[0021] (2)

[0022] Where, represents the matrix related to the constraints, for Transpose the matrix, is the wheel radius, is the distance from the center of the de-icing vehicle's mobile platform to the driving wheel, is the distance from the center of the mobile platform to the center of mass of the mobile platform;

[0023] Pick dimensional full rank matrix for A basis for the null space of for Transpose the matrix, is its first-order derivative, then Established, is the position of the system after transformation, is the transformed joint angular velocity, is the transformed joint angular acceleration; taking the time derivatives on both sides of the equation, we get: , substitute into formula (1), and multiply both sides of the equation by , then:

[0024] (3)

[0025] in,

[0026] (4)

[0027] The overall dynamic model of the de-icing vehicle system is obtained as follows:

[0028] (5)

[0029] Where, is the transformed symmetric positive definite mass matrix, are the transformed centripetal force and kinetic force terms, is the transformed gravity term, is the unknown external interference term after transformation, Enter the torque for the transformed de-icing vehicle.

[0030] In step S2, a vehicle-arm joint trajectory tracking error state model is constructed, including:

[0031] Move the de-icing arm to the desired position With actual location To construct, the position error of the system is , the speed error is , the acceleration error is , de-icing vehicle system state variables and speed error The linear combination of ,in, is the desired position of the system, is the desired speed of the system, is the desired acceleration of the system, is the position of the system after transformation, is the velocity of the system after transformation, is the acceleration of the system after transformation, for OK A diagonal matrix of columns, is the derivative, is the second-order derivative, and the above formula is differentiated to obtain:

[0032]

[0033]

[0034] Where, is the speed error of the system, is the acceleration error of the system, for OK A diagonal matrix of columns, represents its inverse matrix;

[0035] The vehicle-arm joint trajectory tracking error state model is obtained as:

[0036] (6)

[0037] (7)

[0038] Where, Auxiliary control input for de-icing vehicle system, For one OK a column-diagonal matrix, For one OK The identity matrix of the columns, The transformed symmetric positive definite mass matrix, Its inverse matrix, is the transformed de-icing vehicle input torque;

[0039] The state equation of the de-icing vehicle system is:

[0040] (8)

[0041]

[0042] Where, is the state variable, is the output variable, is the state matrix, are all input matrices, is the state variable, is its derivative.

[0043] In step S3, the constructed vehicle-arm joint trajectory tracking error state model is linearized, including:

[0044] Perform discretization to obtain the discrete state space expression at time K:

[0045] (10)

[0046] Where, is the sampling step length, is the state variable of the discrete system, is the control quantity of the discrete system, is the output of the discrete system, For the moment.

[0047] In step S4, the controller's cost function as follows:

[0048] (11)

[0049] Where, is the time variable, For Time-predicted The state quantity at the moment, To control the input increment, For Time-predicted The amount of control at any moment, is the length of the forecast interval, is the weight coefficient, is the relaxation factor, is the tracking error weight matrix, the value is greater than 0, is the weight matrix of the input increment, the value is greater than 0, for The moment tracking error weight matrix, the value is greater than 0; is the length of the prediction interval.

[0050] In step S4, the virtual control variable is parsed into a control input that can actually act on the actuator, including:

[0051] (1) Each joint of the de-icing vehicle has an extreme angle, and the hard constraints added to the control quantity are:

[0052] (12)

[0053] Where, are the minimum and maximum constraints of the control quantity respectively; are the minimum and maximum constraints for the control increment respectively; are the minimum and maximum constraints of the state quantity respectively;

[0054] The cost function of formula (11) is converted into a standard quadratic form and solved using the adaptive MPC algorithm. The following vector is defined:

[0055] (13)

[0056]

[0057] (14)

[0058] in, is the length of the prediction interval, is the state vector, is the control vector, Control input increment, there is the following equation:

[0059] (15)

[0060] in,

[0061]

[0062]

[0063] The objective function of the optimal control of the de-icing vehicle system is:

[0064] (16)

[0065] Where, is the weight matrix of the input increment;

[0066] (2) According to the goal of optimizing the objective function of the de-icing vehicle system control, the quadratic programming problem is constructed as follows:

[0067] (17)

[0068] in, is the cost function of the controller, represents the coefficient matrix of the quadratic term in the quadratic programming, represents the coefficient matrix of the linear term in the quadratic programming, Represent the transformed tracking error weight matrix and the input increment weight matrix respectively;

[0069] (3) The optimal virtual control quantity is obtained and solved in each tracking control cycle to obtain a series of optimal control variables in the control time domain.

[0070] In step (3), a series of optimal control variables in the control domain are obtained. for:

[0071] (18)

[0072] Where, For the The optimal control variable at the moment, the first element of the above optimal control variable acts on the de-icing vehicle system: The above calculation is performed in each control cycle.

[0073] In step S5, the strategy for designing the fuzzy logic system FLS is as follows:

[0074] definition is the time, and the torque error is: , the derivative is ;in, Auxiliary control input for de-icing vehicle system, is the actual value obtained by the sensor and combined with formula (14);

[0075] The de-icing vehicle system equation is:

[0076] (19)

[0077] Select control torque As the fuzzy controller output, As the input of the controller, a fuzzy controller is established, and the membership function of the fuzzy set is designed to be a Gaussian function The formula is as follows:

[0078] (20)

[0079] Where, For the In the fuzzy system The mean of the Gaussian function corresponding to the fuzzy rules, For the In the fuzzy system The Gaussian function variance corresponding to the fuzzy rules, the input-output relationship of the fuzzy system is:

[0080] (twenty one)

[0081] (twenty two)

[0082] (twenty three)

[0083] (twenty four)

[0084] Where, is the estimated value of the control output, To sum the variables, For the In the fuzzy system The weight vector corresponding to the fuzzy rule, For the The estimated value of the weight matrix corresponding to the fuzzy system, For the In the fuzzy system The fuzzy basis vectors corresponding to the fuzzy rules are: For the The fuzzy basis matrix corresponding to the fuzzy system is is the number of fuzzy sets;

[0085] Adaptive algorithm is used to adjust the parameters Make an estimate, To set the constant, is a positive definite matrix, For the The torque error, For the The derivative of the estimated value of the weight matrix corresponding to the fuzzy system, the system adaptive update rate can be expressed as follows:

[0086] (25).

[0087] Another object of the present invention is to provide a de-icing vehicle stratification control system under aircraft idle conditions, the system implementing the de-icing vehicle stratification control method under aircraft idle conditions, the system comprising:

[0088] The model building module considers the inherent strong nonlinear characteristics of the de-icing vehicle system and the close coupling relationship between variables. It constructs a non-holonomic constrained overall dynamic model of the de-icing vehicle based on the Lagrange equation. Based on the constructed overall dynamic model of the de-icing vehicle, it considers the complex constraints of the overall trajectory and constructs a vehicle-arm joint trajectory tracking error state model.

[0089] The hierarchical controller module linearizes the constructed vehicle-arm joint trajectory tracking error state model and designs a hierarchical control framework to achieve trajectory tracking of the de-icing vehicle under aircraft idling conditions. The upper layer of the controller constructs a quadratic programming problem to obtain the optimal virtual control quantity, focusing on the key indicators of maximizing de-icing efficiency and optimizing energy consumption, while taking into account the dynamic constraints of aircraft surface temperature fluctuations and de-icing fluid spraying rate limits. The lower layer of the controller realizes trajectory tracking control by designing a fuzzy logic system FLS to resolve the virtual control quantity into control inputs that can actually act on the actuator.

[0090] Combining all of the above technical solutions, the present invention achieves the following beneficial effects: To address the complex parameter perturbations and constraints faced by de-icing vehicles operating at aircraft idle speed, the present invention proposes a hierarchical control strategy by combining model predictive control (MPC) and an adaptive fuzzy logic system (FLS). This strategy ensures stable and efficient system operation, ensuring the de-icing vehicle maintains stable operation in complex and changing operating environments. By combining the forward-looking advantages of MPC with the precise adjustment capabilities of the adaptive fuzzy logic system (FLS), the present invention constructs a hierarchical control strategy suitable for de-icing vehicles. First, considering the nonlinear characteristics of the system and the strong coupling between variables, a nonholonomically constrained overall dynamic model of the de-icing vehicle is established using the Lagrangian equations. Next, a hierarchical control strategy is constructed. The upper layer, relying on the MPC framework, constructs a quadratic programming problem to determine the optimal virtual control variable, focusing on key indicators such as maximizing de-icing efficiency and optimizing energy consumption, while also considering dynamic constraints such as aircraft surface temperature fluctuations and de-icing fluid spray rate limits. The lower layer employs an adaptive fuzzy logic strategy to accurately convert the virtual control variable into actuator control inputs. Its built-in fuzzy logic module dynamically compensates for parameter perturbations caused by modeling uncertainty and external interference in real time, ensuring stable and efficient system operation.

[0091] The present invention studies in detail the principle and algorithm implementation process of the strategy for generating optimal control inputs based on specified optimization indicators and dynamic constraints, and analyzes its control effects in different operating scenarios and de-icing vehicle states, including the improvement of de-icing vehicle trajectory tracking accuracy, de-icing efficiency, etc., as well as its effectiveness in dealing with strong nonlinearity and parameter uncertainty. First, the proposal of the present invention realizes the full automation of de-icing operations, reduces dependence on manual labor, and reduces labor costs. Secondly, precise de-icing control reduces the waste of de-icing agents and reduces operating costs. Finally, the efficient operation of the equipment can shorten the aircraft's stay on the ground, improve the punctuality of flights, and bring additional economic benefits. Based on current market demand and technological development trends, the promotion and development of the technology of the present invention can also drive the development of other related businesses in the field of aviation equipment, such as integrated research and development with other aviation equipment, thereby further improving the company's economic benefits.

[0092] New technologies for aircraft ground de-icing operations are gaining popularity. The traditional engine-off de-icing method (de-icing with the aircraft engines shut down) is gradually being replaced by slow-run de-icing (de-icing without shutting down the aircraft engines). While slow-run de-icing is faster than engine-off de-icing, it places higher demands on aircraft ice accumulation detection and operational control speed accuracy, requirements that existing technologies no longer meet. Currently, some international companies have developed intelligent spray systems, automatic flow monitoring systems, and single-operator operating systems. Intelligent systems are an inevitable trend in the development of aircraft de-icing vehicles. The present invention proposes a hierarchical control method and system, taking into account the impact of engine wake turbulence, weak ground adhesion in icy and snowy environments, unavoidable self-coupling effects, and the reaction force of de-icing fluid spraying when the aircraft is idling on the ground. The upper layer, relying on a model predictive control framework, constructs a quadratic programming problem to determine the optimal virtual control variable, focusing on key indicators such as maximizing de-icing efficiency and optimizing energy consumption, while also taking into account dynamic constraints such as aircraft surface temperature fluctuations and de-icing fluid spray rate limits. The lower layer employs an adaptive fuzzy logic strategy to accurately convert the virtual control variable into actuator control inputs. Its built-in fuzzy logic module dynamically compensates for parameter perturbations caused by modeling uncertainty and external interference in real time, ensuring stable and efficient system operation. This allows for efficient and safe de-icing even at idle. Precise control ensures the quality and effectiveness of de-icing operations, thoroughly clearing the ice from the aircraft surface, ensuring excellent aerodynamic performance and control stability during takeoff, and effectively avoiding flight accidents caused by incomplete de-icing, providing a solid guarantee for the safety of passengers and property, as well as for aviation transportation safety.

[0093] This invention addresses the significant system uncertainty and measurement noise present in practical systems, as well as the influence of factors such as ground mechanics and environmental compliance. A hierarchical control method and system are proposed. The upper layer, relying on a model predictive control framework, constructs a quadratic programming problem to solve the optimal virtual control variable, focusing on key metrics such as maximizing deicing efficiency and optimizing energy consumption, while also taking into account dynamic constraints such as aircraft surface temperature fluctuations and deicing fluid spray rate limits. The lower layer employs an adaptive fuzzy logic strategy to accurately convert the virtual control variable into actuator control inputs. Its built-in fuzzy logic module dynamically compensates for parameter perturbations caused by modeling uncertainty and external interference in real time, ensuring stable and efficient system operation. This method enables efficient and safe deicing even when the aircraft is idling. This invention enables fully automated deicing operations, promotes the automation of deicing vehicles, and supports intelligent management of airport equipment. By employing advanced sensor technology, intelligent control algorithms, and high-precision positioning techniques, the system achieves automated and intelligent trajectory tracking control of deicing vehicles. This provides a reference and technical support for the future automation upgrade of other airport ground service vehicles and equipment, promoting the intelligent and efficient development of airports and enhancing the level of modern airport management. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present disclosure and, together with the description, serve to explain the principles of the present disclosure;

[0095] Figure 1 This is a flow chart of a de-icing vehicle layer control method under aircraft idling conditions provided by an embodiment of the present invention;

[0096] Figure 2 It is a structural diagram of the de-icing vehicle layered control strategy under aircraft idling conditions of the present invention;

[0097] Figure 3 This is a schematic diagram of a de-icing vehicle model of the present invention;

[0098] Figure 4 Graph showing the tracking of joint angle 1 position trajectory using the hierarchical control strategy of the present invention compared with the adaptive fuzzy control;

[0099] Figure 5 2 is a diagram showing the tracking of joint angle 2 position trajectory of the hierarchical control strategy of the present invention compared with the adaptive fuzzy control;

[0100] Figure 6 Graph showing the convergence of joint angle 1 position tracking error of the hierarchical control strategy of the present invention compared with the adaptive fuzzy control;

[0101] Figure 7 Graph showing the convergence of joint angle 2 position tracking error of the hierarchical control strategy of the present invention compared with the adaptive fuzzy control;

[0102] Figure 8 Graph showing the position trajectory tracking of a mobile platform using the hierarchical control strategy of the present invention compared with the adaptive fuzzy control;

[0103] Figure 9 Graph showing the convergence of the lateral position tracking error of the mobile platform using the hierarchical control strategy of the present invention compared with the adaptive fuzzy control;

[0104] Figure 10 Graph showing the convergence of the longitudinal position tracking error of the mobile platform using the hierarchical control strategy of the present invention compared with the adaptive fuzzy control;

[0105] Figure 11 This is a diagram of the control torque signal of joint 1 angle and joint 2 angle of the present invention;

[0106] Figure 12 This is a diagram of the control torque signal of the mobile platform of the present invention. DETAILED DESCRIPTION

[0107] To make the above-mentioned objects, features, and advantages of the present invention more readily apparent, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings. The following description sets forth numerous specific details to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways than those described herein, and those skilled in the art may make similar modifications without departing from the scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0108] The present invention fully considers the nonlinear factors, the interference of uncertain complex environment and the complex trajectory constraints during the system operation. By combining the model prediction strategy and the adaptive fuzzy logic strategy, a hierarchical control strategy for the mobile de-icing robot arm under aircraft idling conditions is proposed. The system innovation lies in:

[0109] Example 1, as Figure 1 As shown, the de-icing vehicle stratification control method under aircraft idling conditions provided by an embodiment of the present invention includes the following steps:

[0110] S1, considering the inherent strong nonlinear characteristics of the de-icing vehicle system and the close coupling relationship between variables, the overall dynamic model of the de-icing vehicle under nonholonomic constraints is constructed based on the Lagrange equation;

[0111] S2, based on the constructed de-icing vehicle overall dynamics model and considering the complex constraints of the overall trajectory, a vehicle-arm joint trajectory tracking error state model is constructed;

[0112] S3, linearize the constructed vehicle-arm joint trajectory tracking error state model and design a hierarchical control framework to achieve trajectory tracking of the de-icing vehicle under aircraft idling conditions;

[0113] In S4, the upper layer of the controller constructs a quadratic programming problem to obtain the optimal virtual control variable, focusing on the key indicators of maximizing de-icing efficiency and optimizing energy consumption, while taking into account the dynamic constraints of aircraft surface temperature fluctuations and de-icing fluid spray rate limits;

[0114] S5, the lower layer of the controller designs a fuzzy logic system FLS to resolve the virtual control quantity into a control input that can actually act on the actuator to achieve trajectory tracking control.

[0115] For example, Figure 2 This figure illustrates the structure of the proposed layered control strategy for de-icing vehicles under aircraft idling conditions. First, a controller is designed within a model predictive control framework, taking into account the joint constraints of the mobile de-icing arm's operation and optimizing the control objectives. Second, an adaptive fuzzy logic strategy is employed to transform the resulting optimal auxiliary control input into an additional motor torque that can actually act on the mobile de-icing arm's actuators.

[0116] For example, in step S1, in order to solve the strong nonlinearity, strong coupling and parameter uncertainty of the de-icing vehicle during the idling de-icing operation, it is considered that the de-icing vehicle is composed of an n-2 degree-of-freedom manipulator and an Ackerman mobile chassis with 2 degrees of freedom and nonholonomic constraints. Figure 3 As shown, P C is the center of mass of the platform, P 0 The center of the platform;

[0117] At the same time, considering the influence of external disturbances, assuming that no joints are deformed, that is, the entire de-icing vehicle can be regarded as a multi-rigid body system, the overall dynamic model of the de-icing vehicle under non-holonomic constraints using the Lagrange equation is as follows:

[0118] (1)

[0119] Where, for is a OK A matrix of columns, for The transpose of a matrix, for The inverse of a matrix, for The true value of the matrix, for Estimated values ​​of the matrix; is the unified generalized coordinate of the de-icing vehicle, is the joint angle, is the joint angular velocity, is the joint angular acceleration; The coordinates of the center point of the de-icing vehicle's mobile platform; is the displacement of each joint, including the front wheel angle and rear wheel rotation; is a symmetric positive definite inertia matrix; For centripetal force and scientific force; is the gravity term; is the unknown external interference term; Control torque for each joint; is the input transformation matrix, is the constraint matrix; is the Lagrange multiplier.

[0120]

[0121]

[0122]

[0123] Where, is the coordinate of the center point of the de-icing vehicle, express Transpose, is the horizontal axis, is the vertical axis, is the yaw angle of the de-icing vehicle, is the displacement of the de-icing vehicle, express Transpose, is the front wheel turning angle, is the rear wheel turning angle, Joint 1 to joint The rotation angle of .

[0124] The nonholonomic constraints are , the expression is:

[0125] (2)

[0126] Where, represents the matrix related to the constraints, for Transpose the matrix, is the wheel radius, is the distance from the center of the de-icing vehicle's mobile platform to the driving wheel, is the distance from the center of the mobile platform to the center of mass of the mobile platform;

[0127] Pick dimensional full rank matrix for A basis for the null space of for Transpose the matrix, is its first-order derivative, then Established, is the position of the system after transformation, is the transformed joint angular velocity, is the transformed joint angular acceleration; take the time derivatives on both sides to get , substitute the above expression into formula (1) and multiply it from the left ,get:

[0128] (3)

[0129] in,

[0130] (4)

[0131] The overall dynamic model of the de-icing vehicle system is obtained as follows:

[0132] (5)

[0133] Where, is the transformed symmetric positive definite mass matrix, are the transformed centripetal force and kinetic force terms, is the transformed gravity term, is the unknown external interference term after transformation, Enter the torque for the transformed de-icing vehicle.

[0134] Exemplarily, in step S2, a vehicle-arm joint trajectory tracking error state model is constructed, including:

[0135] Move the de-icing arm to the desired position With actual location To construct, the position error of the system is , the speed error is , the acceleration error is , de-icing vehicle system state variables and speed error The linear combination of ,in, is the desired position of the system, is the desired speed of the system, is the desired acceleration of the system, is the position of the system after transformation, is the velocity of the system after transformation, is the acceleration of the system after transformation, for OK A diagonal matrix of columns, is the derivative, is the second-order derivative, and the above formula is differentiated to obtain:

[0136]

[0137]

[0138] Where, is the speed error of the system, is the acceleration error of the system, for OK A diagonal matrix of columns, represents its inverse matrix;

[0139] The vehicle-arm joint trajectory tracking error state model is obtained as:

[0140] (6)

[0141] (7)

[0142] Where, Auxiliary control input for de-icing vehicle system, For one OK a column-diagonal matrix, For one OK The identity matrix of the columns, The transformed symmetric positive definite mass matrix, Its inverse matrix, is the transformed de-icing vehicle input torque;

[0143] The state equation of the de-icing vehicle system is:

[0144] (8)

[0145] (9)

[0146] Where, is the state variable, is the output variable, is the state matrix, are all input matrices, is the state variable, is its derivative.

[0147] In step S3, the constructed vehicle-arm joint trajectory tracking error state model is linearized, including:

[0148] Perform discretization to obtain the discrete state space expression at time K:

[0149] (10)

[0150] Where, is the sampling step length, is the state variable of the discrete system, is the control quantity of the discrete system, is the output of the discrete system, For the moment.

[0151] In step S4, the controller's cost function as follows:

[0152] (11)

[0153] Where, is the time variable, For Time-predicted The state quantity at the moment, To control the input increment, For Time-predicted The amount of control at any moment, is the length of the forecast interval, is the weight coefficient, is the relaxation factor, is the tracking error weight matrix, the value is greater than 0, is the weight matrix of the input increment, the value is greater than 0, for The moment tracking error weight matrix, the value is greater than 0; is the length of the prediction interval.

[0154] In step S4, a quadratic programming problem is constructed to obtain the optimal virtual control quantity, including:

[0155] (1) Since each joint of the de-icing vehicle has an extreme angle, the hard constraint added to the control quantity is:

[0156] (12)

[0157] Where, are the minimum and maximum constraints of the control quantity, are the minimum and maximum constraints for controlling the increment, are the minimum and maximum constraints of the state quantity respectively.

[0158] The cost function of formula (11) is converted into a standard quadratic form and solved using the adaptive MPC algorithm. The following vector is defined:

[0159] (13)

[0160]

[0161] (14)

[0162] in, is the length of the prediction interval, is the state vector, is the control vector, Control input increment, there is the following equation:

[0163] (15)

[0164] in,

[0165]

[0166]

[0167] The objective function of the optimal control of the de-icing vehicle system is:

[0168] (16)

[0169] Where, is the weight matrix of the input increment;

[0170] (2) According to the goal of optimizing the objective function of the de-icing vehicle system control, the quadratic programming problem is constructed as follows:

[0171] (17)

[0172] in, is the cost function of the controller, represents the coefficient matrix of the quadratic term in the quadratic programming, represents the coefficient matrix of the linear term in the quadratic programming, Represent the transformed tracking error weight matrix and the input increment weight matrix respectively;

[0173] (3) The optimal virtual control quantity is obtained and solved in each tracking control cycle to obtain a series of optimal control variables in the control time domain.

[0174] In step (3), a series of optimal control variables in the control domain are obtained. for:

[0175] (18)

[0176] Where, For the The optimal control variable at the moment, the first element of the above optimal control variable acts on the de-icing vehicle system: The above calculation is performed in each control cycle.

[0177] In step S5, the strategy for designing the fuzzy logic system FLS is as follows:

[0178] definition is the time, and the torque error is: , the derivative is ;in, Auxiliary control input for de-icing vehicle system, is the actual value obtained by the sensor and combined with formula (14);

[0179] The de-icing vehicle system equation is:

[0180] (19)

[0181] The present invention selects the control torque As the fuzzy controller output, As the input of the controller, a fuzzy controller is established. Define NB, NM, NS, ZO, PS, PM, and PB as negative large, negative medium, negative small, zero, positive small, positive medium, and positive large. The fuzzy rule design is:

[0182] if is NB then is NB ,

[0183] if is NM then is NM ,

[0184] if is NS then is NS ,

[0185] if is ZO then is ZO ,

[0186] if is PS then is PS ,

[0187] if is PM then is PM ,

[0188] if is PB then is PB ;

[0189] The membership function designed for the fuzzy set is a Gaussian function. This smooth and continuous function better aligns with the actuator's motion control during de-icing vehicle trajectory tracking, reducing shock and vibration. It also provides a natural gradient for fuzzy concepts.

[0190] The membership function designed as a fuzzy set is a Gaussian function. The Gaussian function is smooth and continuous. When performing de-icing vehicle trajectory tracking control, it is more in line with the motion control of the actuator, can reduce shock and vibration, and is also very beneficial for fuzzy concepts with natural gradients. The membership function designed as a fuzzy set is a Gaussian function. The formula is as follows:

[0191] (20)

[0192] Where, For the In the fuzzy system The mean of the Gaussian function corresponding to the fuzzy rules, For the In the fuzzy system The Gaussian function variance corresponding to the fuzzy rules, the input-output relationship of the fuzzy system is:

[0193] (twenty one)

[0194] Where, is the estimated value of the control output, To sum the variables, For the In the fuzzy system The weight vector corresponding to the fuzzy rule, For the The estimated value of the weight matrix corresponding to the fuzzy system, For the In the fuzzy system The fuzzy basis vectors corresponding to the fuzzy rules are: For the The fuzzy basis matrix corresponding to the fuzzy system is is the number of fuzzy sets;

[0195] (twenty two)

[0196] (twenty three)

[0197] (twenty four)

[0198] Adaptive algorithm is used to adjust the parameters Make an estimate, To set the constant, is a positive definite matrix, For the The torque error, For the The derivative of the estimated value of the weight matrix corresponding to the fuzzy system, the system adaptive update rate can be expressed as follows:

[0199] (25).

[0200] The fuzzy logic module in the adaptive fuzzy logic strategy has a specific fuzzy rule base, which is optimized based on a large amount of actual data and experience of deicing operations to further improve the compensation accuracy of uncertain factors.

[0201] Exemplarily, the present invention performs stability analysis on the designed adaptive fuzzy logic strategy and defines the Lyapunov function V :

[0202] (26)

[0203] in, , then the derivative of the above formula can be obtained as the derivative of the Lyapunov function :

[0204] (27)

[0205] According to formula (15) (16), it is easy to obtain:

[0206] (28)

[0207] make , we can get:

[0208] (29)

[0209] (30)

[0210] in is a skew-symmetric matrix that satisfies The above equation can be further written as:

[0211] (31)

[0212] Combining (30) and (31) we can get:

[0213] (32)

[0214] Combined adaptive rate We can get:

[0215] (33)

[0216] in, is a small positive real number and ,therefore , the adaptive rate converges asymptotically and the controller is globally asymptotically stable.

[0217] In embodiment 2, a de-icing vehicle layered control system for an aircraft under idle conditions provided by the present invention includes:

[0218] The model building module considers the inherent strong nonlinear characteristics of the de-icing vehicle system and the close coupling relationship between variables. It constructs a non-holonomic constrained overall dynamic model of the de-icing vehicle based on the Lagrange equation. Based on the constructed overall dynamic model of the de-icing vehicle, it considers the complex constraints of the overall trajectory and constructs a vehicle-arm joint trajectory tracking error state model.

[0219] The hierarchical controller module linearizes the constructed vehicle-arm joint trajectory tracking error state model and designs a hierarchical control framework to achieve trajectory tracking of the de-icing vehicle under aircraft idling conditions. The upper layer of the controller constructs a quadratic programming problem to obtain the optimal virtual control quantity, focusing on the key indicators of maximizing de-icing efficiency and optimizing energy consumption, while taking into account the dynamic constraints of aircraft surface temperature fluctuations and de-icing fluid spraying rate limits. The lower layer of the controller realizes trajectory tracking control by designing a fuzzy logic system FLS to resolve the virtual control quantity into control inputs that can actually act on the actuator.

[0220] Experimental Example: The present invention uses a four-degree-of-freedom mobile manipulator model for MATLAB simulation, considering the state equation of the de-icing vehicle system (8):

[0221] ,

[0222] in

[0223]

[0224] Expected trajectory of chassis and robotic arm joints The settings are as follows:

[0225]

[0226] Then the above state equation is discretized according to formula (10), where The cost function of the model predictive controller is designed as Equation (11): , the weight matrix , .

[0227] In this simulation, the tracking error is required to satisfy the constraints shown in formula (12), where i=1,2,3,4

[0228]

[0229] According to the objective function of the de-icing vehicle system, a quadratic programming problem is constructed as Equation (17) to solve it, and an MPC controller is created to obtain the optimal virtual control quantity. The optimal control variable is solved in each tracking control cycle to obtain a series of optimal control variables in the control time domain. The first element of the optimal control variable is applied to the de-icing vehicle system, and steps (1) to (3) are calculated in each control cycle. The change of the tracking error of each joint is as follows: Figure 6 Figure 7 As shown in Figure 2, the tracking error of the platform in the task space is as follows: Figure 9 Figure 10 shown.

[0230] The adaptive fuzzy logic strategy at the lower level of the controller selects the control torque As the fuzzy controller output, As the input of the controller, a fuzzy controller is established. Define NB, NM, NS, ZO, PS, PM, and PB as negative large, negative medium, negative small, zero, positive small, positive medium, and positive large. The fuzzy rule design is:

[0231]

[0232] As shown in formula (20), the membership function of the fuzzy set is designed to be a Gaussian function:

[0233]

[0234] The simulation analysis is carried out according to the input-output relationship of the controller (21), where the parameters The adaptive algorithm (25) is used for estimation, where =[9000,8000,550,650], the simulation results are as follows Figure 4-10 As shown in Figure 4 and Figure 5 The expected and actual motion trajectories of joint 1 and joint 2 are shown respectively. The expected and actual trajectories of the platform are shown in Figure 2. Figure 8 shown. Figure 11 and Figure 12 They are the optimal joint control torque and the optimal platform control torque respectively.

[0235] The present invention conducted an experimental comparison between the de-icing vehicle layered control method under aircraft idling conditions and the single adaptive fuzzy control of the prior art, as follows:

[0236] Figure 4 and Figure 5The expected and actual motion trajectories of joints 1 and 2 are shown, respectively. Clearly, the proposed controller performs better during joint motion, achieving a tracking accuracy of 97.8%. The maximum tracking error of the robot arm does not exceed 0.03 m.

[0237] Figure 6 and Figure 7 The changes in tracking error for joints 1 and 2 are shown separately. It can be seen that the hierarchical control strategy designed in this paper outperforms the adaptive fuzzy control in all dynamic performance aspects. Although slight chattering still occurs when the joint angles are near the desired values, overall, the hierarchical multi-loop control reduces the chattering amplitude by 82.3% and improves tracking accuracy by approximately 53.4% ​​compared to the adaptive fuzzy controller.

[0238] The expected and actual trajectories of the platform are as follows: Figure 8 As shown in Figure 2, it can be seen that in the path segment with large curvature, this method shows better tracking performance than the traditional adaptive fuzzy control. The tracking accuracy is as high as 98.3%. The tracking error of the platform in the task space is shown in Figure 2. Figure 9 and Figure 10 As shown in the figure, the longitudinal tracking error converges to 0 within 0.023 seconds, while the lateral error is improved by 78.5% compared to the adaptive fuzzy control. The maximum trajectory tracking error does not exceed 0.04m.

[0239] Figure 11 and Figure 12 These are the optimal joint control torque and the optimal platform control torque, respectively. Their output is continuous and stable, not exceeding the structural limits of the mobile de-icing arm and meeting the control specifications of existing mobile de-icing arms at airports. A cycle of approximately 100 seconds satisfies the response speed of actual actuators.

[0240] In summary, the hierarchical control strategy designed in this paper has good anti-interference ability and robustness when the de-icing vehicle is affected by joint friction and external interference. At the same time, the tracking error is small during trajectory tracking and it has a faster convergence speed.

[0241] The above description is only a preferred specific implementation method of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with this technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered by the scope of protection of the present invention.

Claims

1. A de-icing vehicle stratification control method under aircraft idling conditions, characterized in that: The method comprises the following steps: S1, considering the inherent strong nonlinear characteristics of the de-icing vehicle system and the close coupling relationship between variables, the overall dynamic model of the de-icing vehicle under nonholonomic constraints is constructed based on the Lagrange equation; S2, based on the constructed de-icing vehicle overall dynamics model and considering the complex constraints of the overall trajectory, a vehicle-arm joint trajectory tracking error state model is constructed; S3, linearize the constructed vehicle-arm joint trajectory tracking error state model and design a hierarchical control framework to achieve trajectory tracking of the de-icing vehicle under aircraft idling conditions; In S4, the upper layer of the controller constructs a quadratic programming problem to obtain the optimal virtual control variable, focusing on the key indicators of maximizing de-icing efficiency and optimizing energy consumption, while taking into account the dynamic constraints of aircraft surface temperature fluctuations and de-icing fluid spray rate limits; S5, the lower layer of the controller designs a fuzzy logic system FLS to resolve the virtual control quantity into a control input that can actually act on the actuator to achieve trajectory tracking control.

2. The de-icing vehicle stratification control method under aircraft idling conditions according to claim 1, characterized in that: In step S1, the de-icing vehicle system is a multi-rigid body system, and the Lagrange equation is used to develop the overall dynamic model of the de-icing vehicle under nonholonomic constraints. The expression is: （1）； Where, is a symmetric positive definite mass matrix, is the generalized location of the de-icing vehicle system, is the generalized speed of the de-icing vehicle system, is the generalized acceleration of the de-icing vehicle system, For centripetal force and scientific force, is the gravity term, is the unknown external interference term, Input torque for the de-icing vehicle, is the input transformation matrix, represents the matrix related to the constraints, for The transposed matrix of is the Lagrange multiplier; ； ； ； Where, is the coordinate of the center point of the de-icing vehicle, express The transpose of is the horizontal axis, is the vertical axis, is the yaw angle of the de-icing vehicle, is the displacement of the de-icing vehicle, express The transpose of is the front wheel turning angle, is the rear wheel turning angle, Joint 1 to joint The rotation angle of .

3. The de-icing vehicle stratification control method under aircraft idling conditions according to claim 2, characterized in that: The nonholonomic constraints are , the expression is: （2）； Where, represents the matrix related to the constraints, for The transposed matrix of is the wheel radius, is the distance from the center of the de-icing vehicle's mobile platform to the driving wheel, is the distance from the center of the mobile platform to the center of mass of the mobile platform; Pick dimensional full rank matrix for A basis for the null space of for Transpose the matrix, is its first-order derivative, then Established, is the position of the de-icing vehicle system after the transformation, is the speed of the de-icing vehicle system after transformation, is the acceleration of the de-icing vehicle system after transformation; taking the time derivatives on both sides of the equation, we get: , substitute into formula (1), and multiply both sides of the equation by , then: （3）； in, （4）； The overall dynamic model of the de-icing vehicle system is obtained as follows: （5）； Where, is the transformed symmetric positive definite mass matrix, are the transformed centripetal force and kinetic force terms, is the transformed gravity term, is the unknown external interference term after transformation, Enter the torque for the transformed de-icing vehicle.

4. The de-icing vehicle stratification control method under aircraft idling conditions according to claim 3, characterized in that: In step S2, constructing the vehicle-arm joint trajectory tracking error state model includes: Move the de-icing arm to the desired position With actual location The position error of the de-icing vehicle system is constructed as , the speed error is , the acceleration error is , de-icing vehicle system state variables and speed error The linear combination of ,in, Desired location for the de-icing vehicle system, is the desired speed of the de-icing vehicle system, is the expected acceleration of the de-icing vehicle system, is the position of the de-icing vehicle system after the transformation, is the speed of the de-icing vehicle system after transformation, is the acceleration of the de-icing vehicle system after transformation, for OK A diagonal matrix of columns, is the derivative, is the second-order derivative, and the above formula is differentiated to obtain: ； ； Where, is the speed error of the de-icing vehicle system, is the acceleration error of the de-icing vehicle system, for OK A diagonal matrix of columns, represents its inverse matrix; The vehicle-arm joint trajectory tracking error state model is obtained as: （6）； （7）； Where, Auxiliary control input for de-icing vehicle system, For one OK a column-diagonal matrix, For one OK The identity matrix of the columns, The transformed symmetric positive definite mass matrix, Its inverse matrix, is the transformed de-icing vehicle input torque; The state equation of the de-icing vehicle system is: （8）； （9）； Where, is the state variable, is the output variable, is the state matrix, are all input matrices, is the state variable, is its derivative.

5. The de-icing vehicle stratification control method under aircraft idling conditions according to claim 4, characterized in that: In step S3, the constructed vehicle-arm joint trajectory tracking error state model is linearized, including: After discretization, we get The discrete state space expression at time: （10）； Where, is the sampling step length, is the state variable of the discrete system, is the control quantity of the discrete system, is the output of the discrete system, For the moment.

6. The de-icing vehicle stratification control method under aircraft idling conditions according to claim 1, characterized in that: In step S4, the controller's cost function as follows: （11）； Where, is the time variable, For Time-predicted The state quantity at the moment, To control the input increment, For Time-predicted The amount of control at any moment, is the length of the prediction interval, is the weight coefficient, is the relaxation factor, is the tracking error weight matrix, the value is greater than 0, is the weight matrix of the input increment, the value is greater than 0, for The moment tracking error weight matrix, the value is greater than 0; is the length of the prediction interval.

7. The de-icing vehicle stratification control method under aircraft idling conditions according to claim 6, characterized in that: In step S4, the virtual control variable is parsed into a control input that can actually act on the actuator, including: (1) Each joint of the de-icing vehicle has an extreme angle, and the hard constraints added to the control quantity are: （12）； Where, are the minimum and maximum constraints of the control quantity respectively; are the minimum and maximum constraints for the control increment respectively; are the minimum and maximum constraints of the state quantity respectively; The cost function of formula (11) is converted into a standard quadratic form and solved using the adaptive MPC algorithm. The following vector is defined: （13）； ； （14）； in, is the length of the prediction interval, is the state vector, is the control vector, Control input increment, there is the following equation: （15）； in, ； ； The objective function of the optimal control of the de-icing vehicle system is: （16）； Where, is the weight matrix of the input increment; (2) According to the goal of optimizing the objective function of the de-icing vehicle system control, the quadratic programming problem is constructed as follows: （17）； in, is the cost function of the controller, represents the coefficient matrix of the quadratic term in the quadratic programming, represents the coefficient matrix of the linear term in the quadratic programming, Represent the transformed tracking error weight matrix and the input increment weight matrix respectively; (3) The optimal virtual control quantity is obtained and solved in each tracking control cycle to obtain a series of optimal control variables in the control time domain.

8. The de-icing vehicle stratification control method under aircraft idling conditions according to claim 7, characterized in that: In step (3), a series of optimal control variables in the control time domain are obtained for: （18）； Where, For the The optimal control variable at the moment, the first element of the above optimal control variable acts on the de-icing vehicle system: The above calculation is performed in each control cycle.

9. The de-icing vehicle stratification control method under aircraft idling conditions according to claim 1, characterized in that: In step S5, the strategy for designing the fuzzy logic system FLS is as follows: definition is the time, and the torque error is: , the derivative is ;in, Auxiliary control input for de-icing vehicle system, is the actual value obtained by the sensor and combined with formula (14); The de-icing vehicle system equation is: （19）； Select control torque As the fuzzy controller output, As the input of the controller, a fuzzy controller is established, and the membership function of the fuzzy set is designed to be a Gaussian function The formula is as follows: （20）； Where, For the In the fuzzy system The mean of the Gaussian function corresponding to the fuzzy rules, For the In the fuzzy system The Gaussian function variance corresponding to the fuzzy rules, the input-output relationship of the fuzzy system is: （21）； （22）； （23）； （24）； Where, is the estimated value of the control output, To sum the variables, For the In the fuzzy system The weight vector corresponding to the fuzzy rule, For the The estimated value of the weight matrix corresponding to the fuzzy system, For the In the fuzzy system The fuzzy basis vectors corresponding to the fuzzy rules are: For the The fuzzy basis matrix corresponding to the fuzzy system is is the number of fuzzy sets; Adaptive algorithm is used to adjust the parameters Make an estimate, To set the constant, is a positive definite matrix, For the The torque error, For the The derivative of the estimated value of the weight matrix corresponding to the fuzzy system, the adaptive update rate of the de-icing vehicle system can be expressed as follows: （25）。 10. A de-icing vehicle layer control system under aircraft idling conditions, characterized in that: The de-icing vehicle stratification control system implements the de-icing vehicle stratification control method under aircraft idle conditions according to any one of claims 1 to 9, the system comprising: The model building module considers the inherent strong nonlinear characteristics of the de-icing vehicle system and the close coupling relationship between variables. It constructs a non-holonomic constrained overall dynamic model of the de-icing vehicle based on the Lagrange equation. Based on the constructed overall dynamic model of the de-icing vehicle, it considers the complex constraints of the overall trajectory and constructs a vehicle-arm joint trajectory tracking error state model. The hierarchical controller module linearizes the constructed vehicle-arm joint trajectory tracking error state model and designs a hierarchical control framework to achieve trajectory tracking of the de-icing vehicle under aircraft idling conditions. The upper layer of the controller constructs a quadratic programming problem to obtain the optimal virtual control quantity, focusing on the key indicators of maximizing de-icing efficiency and optimizing energy consumption, while taking into account the dynamic constraints of aircraft surface temperature fluctuations and de-icing fluid spraying rate limits. The lower layer of the controller realizes trajectory tracking control by designing a fuzzy logic system FLS to resolve the virtual control quantity into control inputs that can actually act on the actuator.

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