Robust output feedback control method for three-degree-of-freedom helicopter based on adaptive variable parameters

Abstract

The present invention discloses a robust output feedback control method for a three-degree-of-freedom helicopter based on adaptive variable parameters, and belongs to the technical field of aircraft attitude control. The present invention is used to reduce the overshoot in the initial response stage by using an adaptive proportional-differential controller under the condition that the attitude angular velocity and angular acceleration are unmeasurable, so as to improve the transient response performance and steady-state performance of the closed-loop system. The present invention first establishes a mathematical model of a three-degree-of-freedom helicopter, and obtains a disturbed double integrator model by using feedback linearization technology; estimates the angular velocity and angular acceleration by using a finite-time convergence estimator, and designs a proportional-differential controller and a disturbance estimator; inputs the attitude angular velocity signal, the attitude angular acceleration signal, and the desired attitude angle signal into the controller; and introduces the control signal into the helicopter to complete attitude tracking. The present invention improves the transient response performance of the closed-loop system while ensuring the stability of the closed-loop system.

Description

Technical Field

[0001] The invention belongs to the technical field of aircraft attitude control, and in particular relates to a robust output feedback control method for a three-degree-of-freedom helicopter based on adaptive variable parameters. Background Art

[0002] Since unmanned helicopters can fly at low speeds, hover, and take off and land vertically, they have been widely used in military and civilian applications. However, due to economic and safety reasons, it is difficult to verify the performance of the flight controller through actual test flights, especially in the early stages of system design. In response to this, a company has developed an economical and practical 3-DOF helicopter experimental platform to verify the performance of various control methods. At the same time, the platform is widely used in teaching and research related to control theory. Although the experimental platform is only a simplified model of the actual aircraft, it retains the basic dynamic characteristics of the actual aircraft, such as strong coupling, under-actuation, and high nonlinearity. These characteristics, coupled with the influence of external interference and model uncertainty factors, make it difficult to design a flight controller with good performance.

[0003] At present, many nonlinear control methods have emerged for the attitude tracking problem of 3-DOF helicopter experimental platform, but most of them are relatively complicated, and most of them realize tracking control of one or two channels without considering the practical problem that angular velocity and angular acceleration are unmeasurable, or only have simulation results.

[0004] The finite time convergence estimator (FTC) can be used to calculate the angular velocity and angular acceleration information of the 3-DOF helicopter, but there is an estimation error in the initial stage. At the same time, in order to improve the robustness of the controller, the disturbance estimator (UDE) is introduced into the control method to suppress the influence of disturbances. At present, most of the parameter values ​​of the 3-DOF helicopter attitude controller are constants. The large angular velocity estimation error in the initial stage will be introduced into the control quantity, resulting in large overshoot of the system or even divergence. Summary of the invention

[0005] The invention provides a three-degree-of-freedom helicopter robust output feedback control method based on adaptive variable parameters, which can be used to improve the transient response performance and steady-state performance of a closed-loop system.

[0006] The technical solution adopted by the present invention is:

[0007] A robust output feedback control method for a three-degree-of-freedom helicopter based on adaptive variable parameters comprises the following steps:

[0008] Step 1, based on the sensor carried by the target object (three-degree-of-freedom helicopter), the real attitude angle of the target object is obtained, including: lift angle, pitch angle and yaw angle;

[0009] Step 2, input the expected trajectory of the target object, and extract the expected attitude angle of each time point in the expected trajectory, where the expected attitude angle includes the expected lift angle and the expected yaw angle; that is, the expected trajectory only involves the flight trajectory of two attitude angles;

[0010] Step 3, based on the set second-order finite-time convergence estimator and third-order finite-time convergence estimator, perform derivative estimation on the desired pitch angle and the desired yaw angle;

[0011] The desired pitch angle and the desired yaw angle are respectively input into a third-order finite time convergence estimator (third-order FTC estimator), and the second-order derivatives of the desired pitch angle and the desired yaw angle, i.e., the estimated value of the desired attitude angular acceleration signal, are obtained based on the output of the third-order FTC estimator.

[0012] The error between the desired lift angle and the actual lift angle is input into a second-order finite time convergence estimator (second-order FTC estimator), and the first-order derivative of the lift angle error, i.e., the estimated value of the attitude angular velocity error, is obtained based on its output;

[0013] The error between the desired yaw angle and the actual yaw angle is input into a second-order finite-time convergence estimator, and an estimated value of the yaw angular velocity error is obtained based on the output of the second-order finite-time convergence estimator;

[0014] Step 4, based on the adaptive time-varying control gain function of the set adaptive proportional-differential controller (APD), according to the obtained estimated value of the desired attitude angular acceleration signal and the estimated value of the attitude angular velocity error, the intermediate control amount of the pitch angle and the yaw angle is obtained;

[0015] According to the intermediate control quantities of the pitch angle and the yaw angle, the virtual control quantities of the pitch angle and the yaw angle are obtained;

[0016] According to the virtual control values ​​of the pitch angle and the yaw angle, the desired pitch angle is obtained based on the helicopter attitude angle kinematic model;

[0017] The error between the desired pitch angle and the actual pitch angle is input into a second-order finite-time convergence estimator, and an estimated value of the pitch angle velocity error is obtained based on the output of the second-order finite-time convergence estimator.

[0018] Inputting the desired pitch angle into a third-order finite-time convergence estimator, and obtaining an estimated value of the acceleration signal of the desired pitch angle based on the output of the third-order finite-time convergence estimator;

[0019] Based on an adaptive time-varying control gain function of a proportional-differential controller (PD controller), an intermediate control amount of the pitch angle is obtained according to an estimated value of the pitch angle velocity error and an estimated value of the acceleration signal of the desired pitch angle;

[0020] According to the intermediate control amount of the pitch angle, a virtual control amount of the pitch angle is obtained;

[0021] Step 5, converting the virtual control amount of the attitude angle into an actual control amount, and inputting the actual control amount into the controller of the target object, so that the controller controls the trajectory tracking of the target object according to the actual control amount currently input.

[0022] Furthermore, the helicopter attitude angle kinematic model is specifically:

[0023]

[0024]

[0025]

[0026]

[0027] in, They represent the second-order derivatives of the yaw angle, the lift angle, and the pitch angle respectively;

[0028] θ, ε, ψ represent the actual elevation, pitch, and travel angles of the target object acquired by the sensor, respectively, and the unit is rad;

[0029] d θ , d ε With d ψ Respectively represent the sum of the uncertainty and interference terms acting on the pitch channel, the lift channel and the yaw channel;

[0030] f s , f d They represent the resultant force and differential force generated by the two propellers of the helicopter, both in N;

[0031] The coefficients (constant parameters) a1 to a3 are: a1 = m h gl cd / I ε , a2=m′g / I ε , a3=m h gl cd / I θ ;

[0032] The coefficients (constant parameters) b1 to b4 are: b1 = l oc / I ε b2=l df / I θ , b3=l oc / I ψ , b4=l df / I ψ ;

[0033] The coefficient m' is: m' = -l obm c +l oc m h +l oa m b ;

[0034] I θ , I ε with I ψ Respectively represent the moment of inertia around the pitch axis, lift axis and yaw axis, all in kg·m 2 ;

[0035] l oa Indicates the distance between the longitudinal balance bar center of mass and the base, l oc Indicates the distance between the helicopter body connection point and the base, l ob Indicates the distance between the balance block and the base, l cd Indicates the distance between the longitudinal stabilizer bar and the helicopter body, l df Indicates the distance between a single motor and the longitudinal balance bar, in meters;

[0036] m h Represents the effective mass of the helicopter, m b Indicates the mass of the longitudinal balance bar, m c Indicates the mass of the balance block, and its unit is kg; g indicates the acceleration due to gravity, and its unit is m / s 2 ; The above parameters are all constant parameters.

[0037] The original nonlinear dynamic model (Formulas (1) to (3)) is transformed into a simpler linear double-integral model using feedback linearization technology:

[0038]

[0039] Among them, u ψ 、u ε and u θ Respectively represent the intermediate control quantities of yaw angle, lift angle and pitch angle;

[0040] Formula (1)-(3) can be simplified to the following formula by formula (5):

[0041]

[0042] in, represents the second derivative of the attitude angle, u ρ d ρ They respectively represent the intermediate control amount and interference amount of the attitude angle ρ (including yaw angle, lift angle and pitch angle).

[0043] Furthermore, the second-order finite-time convergence estimator and the third-order finite-time convergence estimator are specifically:

[0044] By defining virtual control quantities, the under-actuated characteristic problem of the target object (3-DOF helicopter) is solved, and the yaw and lift channel control is used as the outer loop, and the pitch channel is used as the inner loop, and the inner and outer loops are decoupled.

[0045] definition

[0046]

[0047]

[0048]

[0049] Among them, S(ρ) represents the generalized force driving matrix of the target object, g(ρ) represents the gravity vector of the target object, and u represents the actual control input, that is, the actual control amount;

[0050] Then the helicopter dynamics model (1)-(3) of the target object can be transformed into the following vector form:

[0051]

[0052] At the same time, define the virtual control volume:

[0053] [σ ψ ,σ ε ,σ θ ] T =S θ u=[sin(θ)f s ,cos(θ)f s , f d ] T (11)

[0054] Among them, σ ψ ,σ ε ,σ θ They represent the virtual control quantities of the yaw angle, the lift angle, and the pitch angle, i.e., the virtual control input of the attitude angle;

[0055] According to formula (11), the following desired pitch angle can be obtained, thereby realizing the decoupling of the inner and outer loops:

[0056]

[0057] At the same time, the actual control input u can be obtained according to formula (11):

[0058]

[0059] in, Represents intermediate calculation parameters.

[0060] According to the above decoupling method, an inner and outer loop control system can be established. Among them, the outer loop yaw and lift channel control system will generate the expected value of the pitch angle, and the finite time convergence estimator is used to generate the estimated value of the first-order derivative of the attitude angular velocity error and the estimated value of the expected attitude angular acceleration signal, which are used as the input of the controller to obtain the intermediate control value u of the yaw angle and the lift angle. ψ ,u ε , and then solve for f s and θ d θ d As the reference signal of the inner loop pitch angle control system, we get f d , and finally f s and f d Used to control the target object.

[0061] Therefore, the control objective of the design becomes: In the absence of angular velocity and angular acceleration measurement, design the control input u ρ ,ρ∈{ψ,ε,θ}, and then solve the virtual control input [σ ψ ,σ ε ,σ θ ] T :

[0062]

[0063] Among them, σ represents the virtual control amount of the attitude angle, S ε represents the partial decomposition matrix of S(ρ).

[0064] Then, we can use formula (13) to calculate f s and f d , to achieve attitude tracking control, that is, f s and f d It represents the actual control amount of the target object. The target object's controller controls the trajectory tracking of the target object according to the actual control amount currently input.

[0065] Set up the attitude angular velocity estimator (second-order finite time convergence estimator) and the attitude angular acceleration estimator (third-order finite time convergence estimator),

[0066] 1) The attitude angular velocity estimator is set as:

[0067] A second-order finite-time convergence estimator with the error between the attitude angle and its expected value as input outputs an estimated value of the attitude angular velocity error. The specific form of the estimator is:

[0068]

[0069] Among them, e ρ Represents the attitude angle tracking error signal, that is, the attitude angle error, and As the output signals of the second-order FTC estimator, they are e ρ and the first-order derivative The estimated value of the attitude angular velocity error can be known from the above definition e ρ As the input signal of the FTC estimator, λ i >0 and μ i >0(i=0,1) is the design parameter of the FTC estimator.

[0070] 2) The attitude angular acceleration estimator is:

[0071] A third-order finite-time convergence estimator with the desired attitude angle signal as input, which outputs an estimated value of the attitude angle signal, an estimated value of the desired attitude angular velocity signal, and an estimated value of the desired attitude angular acceleration signal. The specific form of the estimator is as follows:

[0072]

[0073] Among them, ρ d represents the desired attitude angle, z1, z2, z3 are the output signals of the third-order FTC estimator, and are the desired attitude angle ρ d , the first derivative of the desired attitude angle and the second derivative of the desired attitude angle The estimated value of . λ i >0 and μ i >0(i=0,1,2) is the design parameter of the FTC estimator.

[0074] Furthermore, the adaptive proportional-derivative controller (APD) is specifically:

[0075] The attitude angular velocity error estimation value and the expected attitude angular acceleration signal estimation value output by the attitude angular velocity and attitude angular acceleration estimator in step 3 are input into the APD controller, and the control signal generated by the APD controller is introduced into the controller of the target object.

[0076] The following controllers are designed for each attitude angle:

[0077]

[0078] in, For the PD controller designed for the undisturbed nominal system of equations (1)-(3), is the disturbance estimation value output by the disturbance estimator to enhance the robustness of the controller; that is, They represent the output signals of the proportional-derivative controller and the disturbance estimator at time t respectively.

[0079] The interference estimator is:

[0080]

[0081] The PD controller is designed as follows:

[0082]

[0083] in, is the estimated value of attitude angular acceleration at time t output by the attitude angular acceleration estimator, e ρ (t) is the attitude angle tracking error value at time t, is the estimated value of the attitude angular velocity error at time t output by the attitude angular velocity estimator, is the adaptive time-varying control gain of the PD controller, and its variation rule is as follows:

[0084]

[0085] where i∈{P,D}, for The upper bound of Infinity occurs, α i ,i=1,2,3 are constants, and α1,α2,α3>0.

[0086] Substituting equation (18) and equation (19) into equation (17), we can obtain:

[0087]

[0088] By setting The values ​​of α1, α2 and α3 can generate the three-channel control input u ρ (t), and thus solve for f s and f d , input into the 3-DOF helicopter to complete control.

[0089] The technical solution provided by the present invention brings at least the following beneficial effects:

[0090] (1) For a 3-DOF helicopter system, the present invention can effectively control the attitude angle of a three-DOF helicopter when the attitude angular velocity and angular acceleration are unmeasurable or cannot be completely measured.

[0091] (2) The present invention can effectively suppress the adverse effects caused by the estimation error in the initial stage of the finite time convergence estimator, reduce the overshoot in the initial response stage, improve the transient response performance of the closed-loop system, and enhance the system robustness.

[0092] (3) The present invention can effectively control both constant interference and time-varying interference.

[0093] (4) The present invention is simple and easy to use, and is convenient for engineering implementation.

[0094] (5) In the present invention, the disturbance estimator part is equivalent to adding an integral coefficient of The integral link transforms the original PD controller into a PID controller. and By making adjustments, the effect of adjusting the PID controller parameters at the same time can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0096] Figure 1 This is the schematic diagram of the three-degree-of-freedom helicopter experimental platform, where points E and F represent the left and right motors, f1 and f2 represent the lift generated by the left and right motors, the fuselage EF is connected to the balance bar BC through CD, and the fuselage can rotate around the bar BC, and the rotation angle is defined as the pitch angle (θ). The main rod AG is connected to the base G and is perpendicular to the ground. The balance bar BC can rotate around the main rod AG, and the rotation angle is defined as the yaw angle (ψ). By changing the speed of the two propellers at the same time, the fuselage can rotate around the lift axis AH to generate a lift angle (ε). There is a counterweight at the end of the balance bar to balance the lift torque generated by the fuselage, m h is the effective mass of the helicopter, m b is the mass of the longitudinal balance bar, m c is the mass of the balancing block, l oa is the distance between the center of mass of the longitudinal balance bar (point O) and the base, l oc is the distance between the helicopter body connection point and the base, l ob is the distance between the balancing block and the base, l cd is the distance between the longitudinal stabilizer bar and the helicopter body, l df is the distance between a single motor and the longitudinal balance bar.

[0097] Figure 2 is a schematic diagram of the posture control structure of the present invention, where ε d , ψ d ,θ d is the expected attitude angle (elevation angle, yaw angle and pitch angle) signal; ε, ψ, θ are the actual attitude angle signals; is the estimated value of the angular velocity error generated by the attitude angular velocity estimator; u is the angular acceleration estimate generated by the attitude angular acceleration estimator; ε ,u ψ The control signal generated for the lift channel and yaw channel; f s , f d The resultant force and differential force of the left and right motors of the 3-DOF helicopter generated by the controller.

[0098] Figure 3 Schematic diagram of the method for obtaining the estimated value of angular velocity error and the estimated value of angular acceleration.

[0099] Figure 4 Schematic diagram of the lifting axis angle tracking effect in numerical simulation.

[0100] Figure 5 Schematic diagram of the yaw axis angle tracking effect in numerical simulation.

[0101] Figure 6 Schematic diagram of the pitch axis angle tracking effect in numerical simulation.

[0102] Figure 7 Schematic diagram of the lifting axis angle tracking error in numerical simulation.

[0103] Figure 8 Schematic diagram of yaw axis angle tracking error in numerical simulation.

[0104] Fig. 9 Schematic diagram of pitch axis angle tracking error in numerical simulation.

[0105] Fig.10 Schematic diagram of the lift force of the left motor in the numerical simulation.

[0106] Fig.11 Schematic diagram of the lift force of the right motor in numerical simulation.

[0107] Fig.12 Schematic diagram of the tracking effect when there is constant interference on the lifting axis in the numerical simulation.

[0108] Fig.13 Schematic diagram of tracking error when there is constant interference on the lifting axis in numerical simulation.

[0109] Fig.14 Schematic diagram of the tracking effect when there is time-varying interference on the lifting axis in numerical simulation.

[0110] Fig.15 Schematic diagram of tracking error when there is time-varying interference on the lifting axis in numerical simulation.

[0111] Fig.16 This is a schematic diagram of the lifting axis angle tracking effect in the actual machine experiment.

[0112] Fig.17 Schematic diagram of the yaw axis angle tracking effect in the actual machine experiment.

[0113] Fig.18 Schematic diagram of the pitch axis angle tracking effect in the actual machine experiment.

[0114] Fig.19 Schematic diagram of the lifting axis angle tracking error in the actual machine experiment.

[0115] Fig. 20 Schematic diagram of yaw axis angle tracking error in actual machine experiment.

[0116] Fig.21 Schematic diagram of the pitch axis angle tracking error in the actual machine experiment.

[0117] Fig. 22 Schematic diagram of the lift force of the left motor in the actual machine experiment.

[0118] Fig.23 Schematic diagram of the lift of the right motor in the actual machine experiment. DETAILED DESCRIPTION

[0119] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0120] Based on the research, the present invention proposes a robust output feedback control method for a three-degree-of-freedom helicopter based on adaptive variable parameters. It is used to reduce the overshoot in the initial response stage by using an adaptive proportional-differential controller (APD) under the condition that the attitude angular velocity and angular acceleration are unmeasurable, and improve the transient response performance and steady-state performance of the closed-loop system. The concept of the present invention is: firstly, a mathematical model of a three-degree-of-freedom helicopter is established, and a disturbed double integrator model is obtained by using feedback linearization technology; the angular velocity and angular acceleration are estimated by using a finite time convergence estimator (FTC), and a proportional-differential (PD) controller and a disturbance estimator (UDE) are designed; the attitude angular velocity signal, the attitude angular acceleration signal, and the desired attitude angle signal are input into the controller; then, the control signal is introduced into the helicopter to complete the attitude tracking. In order to reduce the influence of the initial estimation error of the FTC on the control effect, an adaptive proportional-differential (APD) controller is specially designed to improve the transient response performance of the closed-loop system while ensuring the stability of the closed-loop system.

[0121] As a possible implementation, the three-degree-of-freedom helicopter robust output feedback control method based on adaptive variable parameters provided in an embodiment of the present invention specifically includes the following steps:

[0122] Step 1: Establish the helicopter attitude angle kinematic model and perform feedback linearization on it.

[0123] The mathematical model for the three-degree-of-freedom helicopter is as follows:

[0124]

[0125]

[0126]

[0127] in

[0128]

[0129] They represent the resultant force and differential force generated by the two propellers, and a1 = m h gl cd / I ε , a2=m′g / I ε , a3=m h gl cd / I θ , b1=l oc / I ε b2=l df / I θ , b3=l oc / I ψ , b4=l df / I ψ , m′=-l ob m c +l oc m h +l oa m b These are all constant parameters. The specific values ​​of the 3-DOF helicopter are shown in the following table:

[0130]

[0131] Among them, θ, ε, ψ correspond to the helicopter's elevation angle, pitch angle, and yaw angle, respectively, and the unit is rad; I θ , I ε with I ψ They are the moments of inertia around the lift axis, pitch axis and yaw axis, all in kg·m 2 ;d θ , d ε With d ψ are the sum of the uncertainty terms and interference terms acting on the lift channel, pitch channel and yaw channel respectively; f s With f d It is the resultant force and difference force of f1 and f2, both in N. m h is the effective mass of the helicopter, m bis the mass of the longitudinal balance bar, m c is the mass of the balance block, all in kg; g is the acceleration due to gravity, in m / s 2 ; l oa is the distance between the center of mass of the longitudinal balance bar and the base, l oc is the distance between the helicopter body connection point and the base, l ob is the distance between the balancing block and the base, l cd is the distance between the longitudinal stabilizer bar and the helicopter body, l df is the distance between a single motor and the longitudinal balance bar, all in m. Figure 1 shown.

[0132] See also Figure 2 The present invention utilizes feedback linearization technology to transform the original nonlinear dynamic model (22)-(24) into a simpler linear double integral model:

[0133] Make the following input transformations:

[0134]

[0135] Among them, u ε ,u ψ ,u θ They are the control signals generated for the elevator channel, yaw channel and pitch channel respectively.

[0136] Formula (22)-(24) can be simplified to the following formula by formula (26):

[0137]

[0138] Among them, u ρ d ρ Represent the intermediate control amount and interference amount of each angle respectively.

[0139] Step 2: By defining virtual control quantities, the 3-DOF under-actuated characteristic problem is solved. The yaw and lift channel control is used as the outer loop, and the pitch channel is used as the inner loop, and the inner and outer loops are decoupled.

[0140] definition

[0141]

[0142]

[0143]

[0144] Among them, S(ρ) represents the generalized force driving matrix of the target object, g(ρ) represents the gravity vector of the target object, and u represents the actual control input, that is, the actual control amount.

[0145] Then the 3-DOF helicopter dynamics model (22)-(24) can be transformed into the following vector form:

[0146]

[0147] At the same time, define the virtual control volume:

[0148] [σ ψ ,σ ε ,σ θ ] T =S θ u=[sin(θ)f s ,cos(θ)f s , f d ] T (32) According to formula (32), the following desired pitch angle can be obtained, thereby realizing the decoupling of the inner and outer loops:

[0149]

[0150] Among them, σ ψ , σ ε Represent the virtual control inputs for yaw and elevator channels respectively.

[0151] At the same time, the actual control input u can be obtained according to formula (32) as follows:

[0152]

[0153] According to the above decoupling method, an inner and outer loop control system can be established. Among them, the outer loop yaw and lift channel control system will generate the expected value of the pitch angle, and the finite time convergence estimator is used to generate the angular velocity error and the expected angular acceleration as the input of the controller to obtain u ψ ,u ε , and then solve for f s and θ d θ d As the reference signal of the inner loop pitch angle control system, we get f d , and finally f s and f d Used to control 3-DOF helicopters.

[0154] Therefore, the control objective of the design becomes: In the absence of angular velocity and angular acceleration measurement, design the control input u ρ ,ρ∈{ψ,ε,θ}, and then solve the virtual control input [σ ψ ,σ ε ,σ θ ] T :

[0155]

[0156] Then we can use the formula to calculate f s and f d , to achieve attitude tracking control. Among them, S ε represents the partial decomposition matrix of S(ρ).

[0157] Step 3: Design attitude angular velocity and angular acceleration estimators respectively.

[0158] 1) The attitude angular velocity estimator is designed as follows:

[0159] The second-order finite-time convergence estimator (such as Figure 3 As shown), this estimator outputs an estimated value of the attitude angular velocity error, and the specific form of the estimator is as follows:

[0160]

[0161] Among them, e ρ is the attitude angle tracking error signal, that is, e ρ (t) represents the attitude angle tracking error signal at time t, and e ρ (t) = ρ(t) - ρ d (t). ρ represents the attitude angle signal, ρ(t) is the attitude angle signal at time t (for the convenience of formula expression, ρ(t) can be simplified to ρ), ρ d (i.e., d (t)) represents the expected attitude angle signal. and As the output signals of the second-order FTC estimator, they are e ρ and The estimated value of e ρ As the input signal of the FTC estimator, λ i , μ i and They represent the three design parameters of the second-order finite-time convergence estimator, where λ i >0,μ i >0, and i=0,1,

[0162] 2) The attitude angular acceleration estimator is designed as follows:

[0163] A third-order finite-time convergent estimator (such as Figure 3 As shown), this estimator outputs an estimated value of an attitude angle signal, an estimated value of an expected attitude angular velocity signal, and an estimated value of an expected attitude angular acceleration signal. The specific form of the estimator is as follows:

[0164]

[0165] Among them, ρ d represents the desired attitude angle signal, z1, z2, z3 represent the three output signals of the third-order finite time convergence estimator, and are the desired attitude angle ρ d , desired attitude angle ρ d The first derivative of and the desired attitude angle ρ d The second derivative of The estimated value of As an estimate of the attitude angular acceleration λ i ′、μ i 'and They represent the three design parameters of the third-order finite-time convergence estimator, where λ i >0,μ i >0, and i=0,1,2,

[0166] The designed estimator parameters are shown in the following table:

[0167]

[0168] Step 4: Design an adaptive proportional-differential controller (APD), input the estimated value of the attitude angular velocity error and the expected attitude angular acceleration signal output by the attitude angular velocity and angular acceleration estimator in step 3 into the APD controller, and introduce the control signal generated by the APD controller into the helicopter mathematical model.

[0169] The following controllers are designed for each attitude angle:

[0170]

[0171] in, The PD controller designed for the undisturbed nominal system of systems (1)-(3) is: It is the disturbance estimation value output by the disturbance estimator to enhance the robustness of the controller.

[0172] The interference estimator part is designed as follows:

[0173]

[0174] in, They represent the first-order derivatives of the attitude angle signals collected by the sensor of the target object at time t and the initial time, respectively. represents the output signal of the proportional-derivative controller at time t, T ρ are the design parameters of the interference estimator.

[0175] The PD controller is designed as follows:

[0176]

[0177] in, is the attitude angular acceleration estimate output by the attitude angular acceleration estimator, e ρ (t) is the attitude angle tracking error value, is the estimated value of the attitude angular velocity error output by the attitude angular velocity estimator, is the adaptive time-varying control gain of the PD controller, and its variation rule is as follows:

[0178]

[0179] where i∈{P,D}, for The upper bound of Infinity occurs, α i , i=1,2,3 are constants, and α1,α2,α3>0. represents the gain of the control error amount, Represents the gain of the first-order derivative of the control error.

[0180] Substituting equation (18) and equation (19) into equation (17), we can obtain:

[0181]

[0182] By setting The values ​​of α1, α2, and α3 can generate the control input of the three channels, thereby solving f s and f d , input into the 3-DOF helicopter to complete control.

[0183] The specific aircraft model used in the physical experiment of the present invention can simulate the maneuvers such as take-off, landing, forward movement and rotation during the actual flight process. The platform can well reflect the strong coupling and strong nonlinearity of the aircraft and can effectively test the effectiveness of the control method. Figure 1 shown.

[0184] Experimental Example 1:

[0185] In the MATLAB simulation, PD and APD are used to perform robust control on the attitude of the 3-DOF helicopter to verify the robustness of the time-varying disturbance observer. Select the initial attitude angle of the three-degree-of-freedom helicopter (ψ(0), ε(0), θ(0)) = (0rad, -0.545rad, 0rad) and the initial attitude angular velocity Then track the desired pitch and yaw angles. The three-axis controller parameters in step 4 are shown in the following table, where (constant value) and (Constant) is the value set by PD in formula (40) value:

[0186]

[0187] The expected lift angle and actual lift angle tracking effect are shown in the attached Figure 4 , the expected yaw angle and the actual yaw angle tracking effect are shown in Figure 5 , the expected pitch angle and actual pitch angle tracking effect can be seen in Figure 6 The lifting angle tracking error is shown in Figure 7 , yaw angle tracking error see Figure 8 , the pitch angle tracking error is Fig. 9 The left motor lift signal is shown in Fig.10 , the lift signal of the right motor is Fig.11 .

[0188] The experimental results show that in the simulation, both PD and APD can complete trajectory tracking. At the same time, compared with PD, APD has a smaller overshoot in the initial time period and reaches a steady state quickly, which can well solve the adverse effects caused by the initial estimation error. Figure 6 , θ calculated by APD d The arc value is smaller, which is beneficial to avoid saturation in transient response. In addition, the lift of the left and right motors of APD is small at the transient moment, and the value changes steadily, which can ensure the tracking effect of the pitch axis, while ensuring the stability of the closed-loop steady-state system and improving the transient response performance of the closed-loop system.

[0189] Experimental Example 2:

[0190] In the MATLAB simulation, constant disturbance and time-varying disturbance are added respectively, and then PD and APD are used to perform robust control on the attitude of the 3-DOF helicopter to verify the robustness of the controller. Select the initial attitude angle (ψ(0), ε(0), θ(0)) = (0rad, -0.545rad, 0rad) and the initial attitude angular velocity of the 3-DOF helicopter Then the desired pitch angle and yaw angle are tracked. The controller parameters of this part of the experiment are the same as those in Example 1. The constant disturbance is set to d ρ =0.1rad / s 2 , the time-varying interference is set to d ρ =0.1sintrad / s 2 .

[0191] The tracking effect of the lifting axis when there is constant interference is shown in Fig.12 , tracking error see Fig.13 The tracking effect of the lifting axis in the presence of time-varying interference is shown in Fig.14 , tracking error see Fig.15 .

[0192] The experimental results show that the final tracking error is stable and bounded in the presence of constant interference or time-varying interference. At the same time, APD still has lower overshoot than PD, which reflects the advantages of APD.

[0193] Experimental Example 3:

[0194] The PD and APD are used to perform robust control on the attitude of a 3-DOF helicopter on a real machine to verify the robustness of the time-varying disturbance observer. Select the initial attitude angle of the three-degree-of-freedom helicopter (ψ(0), ε(0), θ(0)) = (0rad, -0.545rad, 0rad) and the initial attitude angular velocity Then track the desired pitch and yaw angles. Then track the desired pitch and yaw angles. The three-axis controller parameters in step 4 are shown in the following table, where (constant value) and (Constant) is the value set by PD in formula (40) value:

[0195]

[0196]

[0197] The expected lift angle and actual lift angle tracking effect can be seen in Fig.16 , the expected yaw angle and the actual yaw angle tracking effect are shown in Fig.17 , the expected pitch angle and actual pitch angle tracking effect can be seen in Fig.18 The lifting angle tracking error is shown in Fig.19 , yaw angle tracking error see Fig. 20 , the pitch angle tracking error is Fig.21 The left motor lift signal is shown in Fig. 22 , the lift signal of the right motor is Fig.23 .

[0198] The experimental results show that in the actual machine experiment, the APD control method designed in this patent can effectively track the expected attitude angle signal. In the initial response stage, the overshoot of the three axes is smaller than that of PD, and the steady state is reached quickly. Fig. 22 , θ calculated by APD d The arc value is smaller, which is helpful to avoid saturation in transient response. Figure 22-23In the initial response stage of APD, the motor lift force did not reach the saturation value and quickly ran to a smaller value. The lift force of APD changed more smoothly, while in the initial stage of PD, the motor lift force reached the saturation value many times and oscillated significantly. Therefore, APD can well solve the adverse effects caused by the initial estimation error, and improve the transient response performance of the closed-loop system while ensuring the stability of the closed-loop steady-state system.

[0199] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

[0200] The above are only some embodiments of the present invention. For those skilled in the art, several modifications and improvements can be made without departing from the creative concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A three-degree-of-freedom helicopter robust output feedback control method based on adaptive variable parameters, characterized in that: The following steps are involved: Step 1, obtaining the real attitude angle of the target object based on the sensor carried by the target object, including: lift angle, pitch angle and yaw angle; Step 2, input the expected trajectory of the target object, and extract the expected attitude angle of each time point in the expected trajectory, where the expected attitude angle includes the expected lift angle and the expected yaw angle; that is, the expected trajectory only involves the flight trajectory of two attitude angles; Step 3, based on the set second-order finite-time convergence estimator and third-order finite-time convergence estimator, perform derivative estimation on the desired pitch angle and the desired yaw angle; Inputting the desired pitch angle and the desired yaw angle into a third-order finite-time convergence estimator respectively, and obtaining an estimated value of an acceleration signal of the desired pitch angle and an estimated value of an acceleration signal of the desired yaw angle based on the output thereof; Input the error between the expected lift angle and the actual lift angle into a second-order finite-time convergence estimator, and obtain an estimated value of the lift angle error based on its output; The error between the desired yaw angle and the actual yaw angle is input into a second-order finite-time convergence estimator, and an estimated value of the yaw angular velocity error is obtained based on the output of the second-order finite-time convergence estimator; Step 4, based on the set adaptive time-varying control gain function of the adaptive proportional-differential controller, according to the obtained estimated value of the desired attitude angular acceleration signal and the estimated value of the attitude angular velocity error, the intermediate control amount of the pitch angle and the yaw angle is obtained; According to the intermediate control quantities of the pitch angle and the yaw angle, the virtual control quantities of the pitch angle and the yaw angle are obtained; According to the virtual control values ​​of the pitch angle and the yaw angle, the desired pitch angle is obtained based on the helicopter attitude angle kinematic model; The error between the desired pitch angle and the actual pitch angle is input into a second-order finite-time convergence estimator, and an estimated value of the pitch angle velocity error is obtained based on the output of the second-order finite-time convergence estimator. Inputting the desired pitch angle into a third-order finite-time convergence estimator, and obtaining an estimated value of the acceleration signal of the desired pitch angle based on the output of the third-order finite-time convergence estimator; An adaptive time-varying control gain function of an adaptive proportional-differential controller obtains an intermediate control amount of the pitch angle according to an estimated value of the pitch angle velocity error and an estimated value of the acceleration signal of the desired pitch angle; According to the intermediate control amount of the pitch angle, a virtual control amount of the pitch angle is obtained; Step 5, converting the virtual control amount of the attitude angle into an actual control amount, and inputting the actual control amount into the controller of the target object, so that the controller controls the trajectory tracking of the target object according to the actual control amount currently input.

2. The method according to claim 1, characterized in that The specific kinematic model of helicopter attitude angle is: you ψ =b3sin(θ)cos(ε)f s you ε =-a1cos(θ)sin(ε)-a2cos(ε)+b1cos(θ)f s you θ =-a3cos(ε)sin(θ)+b2f d f s =f1+f2 f d =f1-f2 Among them, u ψ 、u ε and u θ They represent the intermediate control quantities of the yaw angle, the lift angle, and the pitch angle, respectively. θ, ε, ψ represent the actual lift angle, pitch angle, and yaw angle of the target object acquired by the sensor, respectively. d θ , d ε With d ψ Respectively represent the sum of the uncertainty and interference terms acting on the pitch channel, the lift channel and the yaw channel; f s , f d They represent the resultant force and differential force generated by the two propellers of the target object respectively; The coefficients a1 to a3 are: a1 = m h gl cd / I ε , a2=m′g / I ε , a3=m h gl cd / I θ ; The coefficients b1 to b4 are: b1 = l oc / I ε b2=l df / I θ , b3=l oc / I ψ , b4=l df / I ψ ; The coefficient m' is: m' = -l ob m c +l oc m h +l oa m b ;I θ , I ε with I ψ Respectively represent the moment of inertia around the pitch axis, lift axis and yaw axis; l oa Indicates the distance between the longitudinal balance bar center of mass and the base, l oc Indicates the distance between the helicopter body connection point and the base, l ob Indicates the distance between the balance block and the base, l cd Indicates the distance between the longitudinal stabilizer bar and the helicopter body, l df Indicates the distance between a single motor and the longitudinal balance bar; m h Represents the effective mass of the helicopter, m b Indicates the mass of the longitudinal balance bar, m c represents the mass of the balance block, and g represents the acceleration due to gravity.

3. The method according to claim 2, characterized in that The second-order finite-time convergence estimator and the third-order finite-time convergence estimator are specifically: 1) Second-order finite-time convergence estimator: Among them, e ρ It represents the error between the expected attitude angle and the actual attitude angle, that is, the attitude angle error. and represents the two output signals of the second-order finite-time convergence estimator, and are the error quantities e ρ and the error e ρ The first derivative of The estimated value of As an estimate of the attitude angular velocity error λ i , μ i and They represent the three design parameters of the second-order finite-time convergence estimator, where λ i >0,μ i >0, and i=0,1, 2) Third-order finite-time convergence estimator: Among them, ρ d represents the desired attitude angle, z1, z2, z3 represent the three output signals of the third-order finite time convergence estimator, and are the desired attitude angle ρ d , desired attitude angle ρ d The first derivative of and the desired attitude angle ρ d The second derivative of The estimated value of As an estimate of the attitude angular acceleration λ i ′、μ i 'and They represent the three design parameters of the third-order finite-time convergence estimator, where λ i >0,μ i >0, and i=0,1,2, 4. The method according to claim 3, characterized in that The adaptive proportional-derivative controller is specifically: Set the controller for the attitude angle to: in, They represent the output signals of the proportional-derivative controller and the disturbance estimator at time t respectively; The interference estimator is set as: Among them, T ρ represents the design parameters of the disturbance estimator, and T ρ >0, They represent the first-order derivatives of the attitude angle signals collected by the sensor of the target object at time t and the initial time, respectively. Represents the output signal of the proportional-derivative controller at time τ; The proportional-derivative controller settings are: in, represents the estimated value of the acceleration signal of the desired attitude angle output by the third-order finite-time convergence estimator at time t, e ρ (t) represents the attitude angle error signal at time t, represents the estimated value of the attitude angular velocity error output by the second-order finite-time convergence estimator at time t, They represent the adaptive time-varying control gains of proportional control and differential control respectively, and their changing rules are as follows: where i∈{P,D}, is the adaptive time-varying control gain The upper bound of , the constant parameters α1~α3 are preset values, and their values ​​are all greater than 0.

5. The method according to claim 3, characterized in that In step 4, based on the adaptive time-varying control gain function of the adaptive proportional-differential controller, the intermediate control value u of the attitude angle ρ(t) is obtained. ρ (t) for; 6. The method according to claim 3, characterized in that In step 4, the virtual control quantities of the pitch angle and the yaw angle are obtained according to the intermediate control quantities of the pitch angle and the yaw angle, and then the desired pitch angle is obtained based on the helicopter attitude angle kinematic model. Specifically, Define σ ψ ,σ ε ,σ θ They represent the virtual control quantities of yaw angle, lift angle and pitch angle respectively; The intermediate control value u based on the attitude angle ρ ρ Calculate the virtual control amount σ of the attitude angle ρ : Among them, g(ρ) represents the gravity vector of the target object, S ε (ρ) represents the partial decomposition matrix of the generalized force driving matrix S(ρ) of the target object, and its calculation formula is as follows: According to the formula Get the desired pitch angle θ d ; And in step 5, according to the formula Get the actual control quantity u, where Represents intermediate calculation parameters.

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