A constraint-following control method for a preset performance level vertical take-off and landing underactuated aircraft

Abstract

The application discloses a constraint following control method for processing a preset performance plane vertical take-off and landing underactuated aircraft, relates to the field of aerospace control, and comprises the following steps: S1, a dynamic model of an underactuated PVTOL aircraft system is established; S2, servo constraints and preset performances are expressed as equality constraints and inequality constraints; S3, a conversion function is selected to process the inequality constraints, and a converted dynamic model is obtained; S4, converted equality constraints and constraint equations are established; S5, an adaptive robust constraint following control of a leakage type adaptive law is designed; and S6, performance simulation is performed. The constraint following control method for processing a preset performance plane vertical take-off and landing underactuated aircraft is adopted, the problem that system transient performance and steady-state performance cannot be preset is solved, the stability of the PVTOL aircraft vertical take-off and landing and the constraint following precision are improved, and through adjustable adaptive law parameters, the cost is reduced.

Description

Technical Field

[0001] This invention relates to the field of aerospace control, and in particular to a constrained following control method for handling underactuated vertical takeoff and landing aircraft with a preset performance plane. Background Technology

[0002] A planar vertical takeoff and landing (PVTOL) aircraft is a simplified version of a vertical takeoff and landing (VTOL) aircraft in two-dimensional space, possessing the basic dynamic characteristics of a VTOL aircraft. PVTOL aircraft can complete vertical takeoff and landing in a plane without a runway, making them highly adaptable to various complex application scenarios such as urban air traffic, emergency rescue, and cargo transportation in confined spaces. Furthermore, as a typical underactuated system (with fewer control inputs than the number of system degrees of freedom), PVTOL aircraft offer advantages over other aircraft, including fewer actuators, lower cost, lower energy consumption, greater flexibility, and higher control fault tolerance.

[0003] While PVTOL aircraft offer numerous advantages, they also face many challenges in control. The application scenarios for PVTOL aircraft demand high stability, requiring good in-plane motion performance while maintaining vertical takeoff and landing capabilities. However, due to the inherent underactuated nature of PVTOL aircraft, their control inputs are limited, directly leading to reduced controllability. This is often accompanied by problems such as high coupling, nonlinearity, and poor robustness.

[0004] Therefore, a control method is needed that enables the PVTOL aircraft to meet system constraints while also achieving good system performance. Summary of the Invention

[0005] The purpose of this invention is to provide a constrained following control method for underactuated vertical takeoff and landing (PVTOL) aircraft with a preset performance plane, solving the problems of unstable vertical takeoff and landing, low cruise accuracy, and poor controllability in traditional underactuated PVTOL aircraft control methods.

[0006] To achieve the above objectives, the present invention provides a constrained following control method for a vertical takeoff and landing underactuated aircraft with a preset performance plane, comprising the following steps: S1. Establish the dynamic model of the underactuated PVTOL aircraft system; S2. Represent the servo constraint as an equality constraint and the preset performance of the following error as an inequality constraint, so that the steady-state and transient characteristics of the system reach the preset values. S3. Select a transformation function to transform the inequality constraints in S2, and then merge the transformation result with the dynamic model in S1 to obtain the transformed dynamic model. S4. Based on the transformed dynamic model in S3, establish the transformed equality constraints and constraint equations; S5. Design a leakage-type adaptive law and combine it with a robust control structure to construct an adaptive robust constraint-following controller to compensate for system uncertainties. S6. Perform performance simulation on the underactuated PVTOL aircraft system.

[0007] Preferably, the dynamic model in S1 is: ; ; ; in, m For quality, J For rotational inertia, g It is the acceleration due to gravity. d 1. d 2. d 3 represents additional disturbances, and the system has a set of degrees of freedom. X , Y , There are only two control inputs. , ), X , Y These represent the horizontal and vertical displacements of the center of mass, respectively. This indicates the angle of rotation of the wing relative to the horizontal direction. , , These represent the corresponding accelerations and control inputs. To apply a force perpendicular to the wing at the bottom of the aircraft, The torque required to make the aircraft rotate It is the coupling coefficient between torque and lateral acceleration.

[0008] Preferably, the equation expression for the equality constraint in S2 is: e(q,t)=0; Where q is the position of the aircraft, t is time, and e is the constraint following error; The equation for the inequality constraint is: ; in, It is a continuously differentiable, bounded, and always positive decreasing function; choose make e ( q , t The initial value of ) satisfies the following equation: ; in, ， l For positive integers, Determine the convergence region. l Determines the convergence speed.

[0009] Preferably, the transformation function in S3 is the inverse hyperbolic tangent function, and the specific formula is as follows: z i = artanh ; in, z i For conversion functions, e i To constrain the following error, To address the inequality constraints for the constraint following error, z i As it approaches -∞, e i Approaching - ; z i As it approaches +∞, e i Approaching ; z i When =0, e i =0.

[0010] Preferably, the expression for the conversion result in S3 is as follows: q i = tanh z i + q d ; in, q i For the aircraft's position, q d This represents the desired trajectory of the aircraft.

[0011] Preferably, the transformed dynamic model in S3 is: M = ; C = ; G = ; B = ; in, M The inertia matrix, C For Coriolis force, G Including gravity, friction, and additional disturbances, B For the corresponding input matrix, , For inequality constraints, , To constrain the first derivative, , To constrain the second derivative, , For the first derivative of the transformation function, This represents the desired acceleration in the horizontal direction.

[0012] Preferably, the transformed equality constraints in S4 are as follows: ; ; in, , It is a constant.

[0013] Preferably, the specific steps of S5 are as follows: S51. Decompose the uncertainty part, the specific formula is as follows: ( = ; in, For general symbols, The first derivative of the system input matrix. For acceleration, These are uncertain parameters; S52. Construct an adaptive robust constraint-following control, the specific formula of which is as follows: ; in, For system input control, , , For control items, It is an estimate of the range of uncertainty; S53. Design an adaptive law. The specific expression of the adaptive law is as follows: ; in, For the design scalar, For the linear decomposition of the uncertain boundary with respect to the adaptive law, This is an expression containing constraint errors.

[0014] Therefore, the constraint following control method for a pre-defined performance plane vertical takeoff and landing underactuated aircraft, as described above, has the following beneficial effects: (1) The present invention introduces the concept of preset performance, processes the performance index e of the system, and converts the preset performance into inequality constraints about e, thereby making the transient and steady-state performance of the system controllable.

[0015] (2) The adaptive parameters in the controller of the present invention will be adjusted according to the time-varying trajectory error to prevent excessive control force and thus reduce control cost.

[0016] (3) The control method of the PVTOL underactuated aircraft of the present invention can effectively solve the problems of unstable vertical take-off and landing, low orbit determination and cruise accuracy, and slow speed from the initial position to the designated trajectory.

[0017] (4) Based on the transformed dynamic model and system constraints, the present invention uses a designed controller for control. The simulation results of Matlab show that the PVTOL underactuated aircraft system tracks the system constraints quickly, accurately, and stably.

[0018] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0019] Figure 1 This is a control flowchart of an embodiment of the constrained following control method for a pre-defined performance plane vertical takeoff and landing underactuated aircraft according to the present invention; Figure 2 This is a force model of an underactuated PVTOL aircraft system according to an embodiment of the constraint following control method for a pre-defined performance plane vertical takeoff and landing underactuated aircraft of the present invention; Figure 3 This is a graph showing the constraint following error of the underactuated PVTOL aircraft system in the X direction as a function of time, representing an embodiment of the constraint following control method for a pre-defined performance plane vertical take-off and landing underactuated aircraft system according to the present invention. Figure 4 This is a graph showing the transformed X-state variable versus time curve of a constrained following control method for a pre-defined performance plane vertical takeoff and landing underactuated aircraft system, according to an embodiment of the present invention. Figure 5 This is a simulation diagram of the underactuated PVTOL aircraft system hovering at a fixed point, which is an embodiment of the constraint following control method for a pre-defined performance plane vertical take-off and landing underactuated aircraft system of the present invention. The actual displacement of the aircraft in the X direction is a curve of time. Figure 6The diagram shows the constraint following error of the underactuated PVTOL aircraft system in the Y direction as a function of time, representing an embodiment of the constraint following control method for a pre-defined performance plane vertical take-off and landing underactuated aircraft system according to the present invention. Figure 7 This is a graph showing the transformed Y-state variable versus time curve of a constrained following control method for a pre-defined performance plane vertical take-off and landing underactuated aircraft system, according to an embodiment of the present invention. Figure 8 This is a simulation diagram of the underactuated PVTOL aircraft system hovering at a fixed point, which is an embodiment of the constraint following control method for a pre-defined performance plane vertical take-off and landing underactuated aircraft system of the present invention. The actual displacement of the aircraft in the Y direction is a curve of time. Figure 9 The graph shows the constraint following error of the underactuated PVTOL aircraft system as a function of time, representing an embodiment of the constraint following control method for a pre-defined performance plane vertical takeoff and landing underactuated aircraft system according to the present invention. Figure 10 This is a converted X-state variable versus time curve, representing an embodiment of the constrained following control method for a pre-defined performance plane vertical takeoff and landing underactuated aircraft system of the present invention. Figure 11 This is a simulation diagram of the orbit determination and cruise of an underactuated PVTOL aircraft system according to an embodiment of the constrained following control method for a pre-defined performance plane vertical take-off and landing underactuated aircraft system of the present invention. The actual displacement of the aircraft in the X direction is a curve of time. Figure 12 The diagram shows the constraint following error of the underactuated PVTOL aircraft system as a function of time, representing an embodiment of the constraint following control method for a pre-defined performance plane vertical takeoff and landing underactuated aircraft system according to the present invention. Figure 13 This is a converted curve of the Y-state variable versus time from a simulation diagram of the orbit determination and cruise of an underactuated PVTOL aircraft system, which is an embodiment of the constrained following control method for a pre-defined performance plane vertical takeoff and landing underactuated aircraft according to the present invention. Figure 14 This is a graph showing the actual displacement of the aircraft in the Y direction over time, representing an embodiment of the constrained following control method for a pre-defined performance plane vertical takeoff and landing underactuated aircraft system according to the present invention. Detailed Implementation

[0020] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0021] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0022] Example Please see Figures 1-14 This invention provides a constraint-following control method for underactuated vertical takeoff and landing (PVTOL) aircraft with preset performance planes. This method enables the underactuated PVTOL aircraft system to efficiently meet desired position and trajectory constraints. The method predetermines the system's steady-state and transient performance (i.e., preset performance), ensuring the system's convergence speed and residual set size. This means that while ensuring the system's uniform boundedness and uniform final boundedness, its steady-state and transient performance can also achieve the pre-defined effects. This guarantees that the PVTOL aircraft can stably, efficiently, and accurately reach the specified position or trajectory from its initial position, thus adapting to various complex working environments and high-precision tasks requiring high adaptability. Figure 1 As shown, the method includes the following steps: S1. Establish the dynamic model of the underactuated PVTOL aircraft.

[0023] ; ; ; in, m For quality, J For rotational inertia, g It is the acceleration due to gravity. d 1. d 2. d 3 represents additional disturbances, and the system has a set of degrees of freedom. X , Y , There are only two control inputs. , ), X , Y These represent the horizontal and vertical displacements of the center of mass, respectively, and represent the rotation angle of the wing relative to the horizontal direction. , , These represent the corresponding accelerations and control inputs. To apply a force perpendicular to the wing at the bottom of the aircraft, The torque required to make the aircraft rotate It is the coupling coefficient between torque and lateral acceleration.

[0024] S2. Represent servo constraints and preset performance as equality constraints and inequality constraints.

[0025] The equality constraints are constructed based on the dynamic model, and the specific equality constraint equations are as follows: e(q,t)=0; Where q is the position of the aircraft, t is time, and e is the constraint following error; The designed control should ensure that the system motion converges to the equality constraint equations. Let 'e' be defined as the system's constraint following error, i.e., the system's performance index. The preset performance, i.e., steady-state performance, requires the constraint following error 'e' to eventually converge to a predefined small region near 0. The transient performance requires the convergence rate to be no less than a specified value. This yields the mathematical expression for the preset performance, i.e., the inequality constraints. The specific inequality constraint equations are as follows: ; in, It is a continuously differentiable, bounded, and always positive decreasing function.

[0026] choose: ; in, ， l For positive integers, Determine the convergence region. l Determines the convergence speed. For the designer to decide to make e ( q , t The initial value of ) satisfies the above ρ ( t )equation.

[0027] The system's constraints are thus transformed into equality constraint equations and inequality constraint equations. In practical applications, the inequality constraint equations represent the accuracy of the underactuated PVTOL aircraft in tracking the target trajectory and its velocity from the initial position to the target trajectory position.

[0028] S3. Select a transformation function to process the inequality constraints.

[0029] To handle inequality constraints, a transformation function is constructed using the properties of the inverse hyperbolic tangent function: = artanh ; in, z i For conversion functions, e i To constrain the following error, To address the inequality constraints for the constraint following error, z i As it approaches -∞, e i Approaching - ; z i As it approaches +∞, e i Approaching ; z i When =0, e i =0; This transformation function is a smooth bijective. If the control makes it bounded and converges to 0, then it means that the dynamic model of the system satisfies the equality constraint equations and the inequality constraint equations.

[0030] S4. Establish the dynamic model of the converted underactuated PVTOL aircraft.

[0031] The transformation function is substituted into the dynamic model to obtain the transformed dynamic model of the underactuated PVTOL aircraft, and then new equality constraints and constraint equations are established.

[0032] Write out the transition functions for each state variable of the system: = artanh , = artanh ; Since the system's equality constraints are: X = X d , Y = Y d ; Therefore, we can further conclude that: ; Solving for: ; ; Differentiating, we get: ; ; ; ; Substituting these values ​​into the dynamic model yields a new dynamic model for the underactuated PVTOL aircraft: m ; m ; J ; Rewritten as the equations for a general underactuated mechanical system: ; in, M The inertia matrix, C Coriolis / centrifugal force, G Including gravity, friction, and additional disturbances, B is the corresponding input matrix. δ For the uncertain parameters of the system, τ To control the input, since it is an underactuated system, τ Dimensions less than q .

[0033] Summarized as follows: M = , C = , G = , B = ; in, , For inequality constraints, , To constrain the first derivative, , To constrain the second derivative, , For the first derivative of the transformation function, This represents the desired acceleration in the horizontal direction.

[0034] S5. Establish the transformed equality constraints and constraint equations.

[0035] The servo constraints of the converted system are: ; ; Arrange in matrix form: A c= 0, A b= 0; in: ; in, , It is a constant. A The coefficient matrix, c A first-order constraint vector. b It is a second-order constraint vector.

[0036] S6. Design an adaptive robust constraint following control with a leakage adaptive law.

[0037] By introducing servo-constrained following control into an underactuated uncertain system and decomposing the uncertainty into a matching part and a mismatch part, a novel adaptive robust controller with a leakage adaptive law is designed.

[0038] Breaking down the uncertainties: = ; in: , ; in, The general symbols are used to refer to C, G, B, etc. in the system. The first derivative of the system input matrix. For acceleration, The parameter is uncertain.

[0039] This is a general formula, in which C, G, and B can be substituted for C, G, and B in the model.

[0040] Adaptive robust constraint following control: ; , , ; in: , , , , , , ; in, For system input control, , , For control items, It is an estimate of the range of uncertainty. A The coefficient matrix, The inverse of the nominal mass matrix, Let C and G be the nominal matrices. This is the transpose of the nominal matrix of matrix B. This is the transpose of the coefficient matrix. For uncertain boundaries, This is a constant matrix adapted to the dimension. Here The term refers to nominal control, which is control based on model information. , The term compensates for initial conditions where the system does not meet constraints and for system uncertainties. In this context, β actually represents the system error and also signifies the system's performance.

[0041] Adaptive law: ; in, For the design scalar, For the linear decomposition of the uncertain boundary with respect to the adaptive law, This is an expression containing constraint errors.

[0042] Here, the adaptive law is related to the system error β and consists of two terms. When the system error is large, the first term dominates to compensate for the system error. As the system error decreases to a certain extent, the second term dominates, thereby reducing the adaptive law and avoiding excessive control costs.

[0043] S7. Perform performance simulation on the underactuated PVTOL aircraft system.

[0044] Simulation of hovering performance of underactuated PVTOL aircraft system: like Figures 3-8The diagram shows a simulation of an underactuated PVTOL aircraft system hovering at a fixed point. It can be seen that, under the control of the controller in S6, the system error *e* in both the X and Y directions is within the pre-set inequality constraints. This means the system can achieve the pre-set transient and steady-state performance. Consequently, both the transformed state variable *z* and the original state variable *q* can quickly and stably converge to the specified constraints. In practical terms, the underactuated PVTOL aircraft can quickly and stably move from an initial state deviating from the specified position to the specified position and maintain hovering, indicating that the designed controller has good control performance.

[0045] Simulation of orbit determination and cruise performance of underactuated PVTOL aircraft system: like Figures 9-14 The figure shows a simulation diagram of the orbit determination and cruise of the underactuated PVTOL aircraft system. It can be seen that the system error e can also satisfy the inequality constraint and move quickly from the initial position deviating from the constraint to the specified trajectory, and move stably according to the specified trajectory. This also proves the rationality of the controller design.

[0046] Therefore, the present invention employs the aforementioned constraint following control method for a pre-defined performance plane vertical takeoff and landing (PVTOL) underactuated aircraft. While ensuring the system's consistent boundedness and consistent final boundedness, it solves the problem that the system's transient and steady-state performance cannot be pre-set. This makes the speed at which the underactuated PVTOL aircraft moves from its initial position deviating from the constraint to the designated trajectory controllable. It also improves the stability of the PVTOL aircraft's vertical takeoff and landing, as well as the constraint following accuracy. Furthermore, by using adjustable adaptive law parameters, the control force is synchronously adjusted according to the constantly changing system error, thus solving the problem of excessively high control costs.

[0047] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A constrained following control method for a pre-defined performance plane vertical takeoff and landing underactuated aircraft, characterized in that, Includes the following steps: S1. Establish the dynamic model of the underactuated PVTOL aircraft system; S2. Represent the servo constraint as an equality constraint and the preset performance of the following error as an inequality constraint, so that the steady-state and transient characteristics of the system reach the preset values. S3. Select a transformation function to transform the inequality constraints in S2, and then merge the transformation result with the dynamic model in S1 to obtain the transformed dynamic model. S4. Based on the transformed dynamic model in S3, establish the transformed equality constraints and constraint equations; S5. Design a leakage-type adaptive law and combine it with a robust control structure to construct an adaptive robust constraint-following controller to compensate for system uncertainties. S6. Perform performance simulation on the underactuated PVTOL aircraft system.

2. The constrained following control method for a pre-defined performance plane vertical takeoff and landing underactuated aircraft according to claim 1, characterized in that, The dynamic model in S1 is: ； ； ； in, m For quality, J For rotational inertia, g It is the acceleration due to gravity. d 1. d 2. d 3 represents additional disturbances, and the system has a set of degrees of freedom. X , Y , There are only two control inputs ( , ), X , Y These represent the horizontal and vertical displacements of the center of mass, respectively, and represent the rotation angle of the wing relative to the horizontal direction. , , These represent the corresponding accelerations and control inputs. To apply a force perpendicular to the wing at the bottom of the aircraft, The torque required to make the aircraft rotate It is the coupling coefficient between torque and lateral acceleration.

3. The constraint-following control method for a pre-defined performance plane vertical takeoff and landing underactuated aircraft according to claim 2, characterized in that, The equation expression for the equality constraint in S2 is: e(q,t)=0; Where q is the position of the aircraft, t is time, and e is the constraint following error; The equation for the inequality constraint is: ； in, It is a continuously differentiable, bounded, and always positive decreasing function; choose make e ( q , t The initial value of ) satisfies the following equation: ； in, ， l For positive integers, Determine the convergence region. l Determines the convergence speed.

4. The constraint-following control method for a pre-defined performance plane vertical takeoff and landing underactuated aircraft according to claim 3, characterized in that, The transformation function in S3 is the inverse hyperbolic tangent function, and the specific formula is as follows: z i = artanh ； in, z i For conversion functions, e i To constrain the following error, To address the inequality constraints for the constraint following error, z i As it approaches -∞, e i Approaching - ; z i As it approaches +∞, e i Approaching ; z i When =0, e i =0.

5. The constrained following control method for a pre-defined performance plane vertical takeoff and landing underactuated aircraft according to claim 4, characterized in that, The specific expression for the conversion result in S3 is as follows: q i = fishy z i + q d ; in, q i For the aircraft's position, q d This represents the desired trajectory of the aircraft.

6. The constrained following control method for a pre-defined performance plane vertical takeoff and landing underactuated aircraft according to claim 5, characterized in that, The transformed dynamic model in S3 is as follows: M = ； C = ； G = ； B = ； in, M The inertia matrix, C For Coriolis force, G Including gravity, friction, and additional disturbances, B For the corresponding input matrix, , For inequality constraints, , To constrain the first derivative, , To constrain the second derivative, , For the first derivative of the transformation function, This represents the desired acceleration in the horizontal direction.

7. The constrained following control method for a pre-defined performance plane vertical takeoff and landing underactuated aircraft according to claim 6, characterized in that, The transformed equality constraints in S4 are as follows: ； ； in, , It is a constant.

8. The constrained following control method for a pre-defined performance plane vertical takeoff and landing underactuated aircraft according to claim 7, characterized in that, The specific steps of S5 are as follows: S51. Decompose the uncertainty part, the specific formula is as follows: ( = ； in, For general symbols, The first derivative of the system input matrix. For acceleration, These are uncertain parameters; S52. Construct an adaptive robust constraint-following control, the specific formula of which is as follows: ； in, For system input control, , , For control items, It is an estimate of the range of uncertainty; S53. Design an adaptive law. The specific expression of the adaptive law is as follows: ； in, For the design scalar, For the linear decomposition of the uncertain boundary with respect to the adaptive law, This is an expression containing constraint errors.

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