Unmanned aerial vehicle active-disturbance-rejection flight control method based on lead-lag adjustment and multi-objective optimization

Abstract

The invention discloses an unmanned aerial vehicle active-disturbance-rejection flight control method based on lead-lag adjustment and multi-objective optimization, and belongs to the technical field of flight control systems. Aiming at the problem that the traditional active disturbance rejection controller parameter design depends on pole assignment and cannot directly guarantee frequency domain indexes, a lead-lag link is embedded in a control loop, a multi-objective optimization model is established, a frequency domain amplitude-phase margin is set as a hard constraint, time domain performance is set as a soft constraint, and parameters are synchronously set through an optimization algorithm. For pitching and rolling attitude control, a unified design framework is constructed, frequency characteristic indexes are brought into a design stage, the phenomenon that later indexes are substandard is effectively avoided, and while the advantage of self-reactance disturbance dynamic suppression is maintained, parameter adjustment complexity is remarkably reduced, and control precision and dynamic quality under complex disturbance are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of flight control systems, and in particular relates to an unmanned aerial vehicle (UAV) active disturbance rejection flight control method based on lead-lag regulation and multi-objective optimization. Background Art

[0002] In UAV flight control, active disturbance rejection control (ADRC) improves system robustness by estimating and compensating for lumped disturbances through an extended state observer. Traditional designs use a fixed ratio of 3 to 5 times the controller bandwidth to the observer bandwidth for parameter adjustment. While this simplifies parameter selection, it has significant limitations: while increasing the observer bandwidth improves time-domain tracking performance, it degrades the phase margin, leading to oscillations and even instability risks. Furthermore, the limited number of adjustable parameters makes it difficult to account for practical constraints such as sensor latency, filtering characteristics, and actuator dynamics. To this end, while retaining the advantages of ADRC for disturbance rejection, it is necessary to restructure the control architecture to incorporate frequency-domain indicators (such as amplitude / phase margin) and enhance the flexibility and systematic nature of parameter adjustment, thereby achieving coordinated optimization of stability and performance under complex operating conditions.

[0003] The present invention proposes a UAV flight control method that integrates auto-disturbance rejection control and lead-lag compensation. In order to solve the problem that the parameter design of traditional auto-disturbance rejection controller relies on pole configuration and cannot directly guarantee the frequency domain indicators, a lead-lag link is embedded in the control loop to improve the freedom of parameter adjustment. A multi-objective optimization model is established, the frequency domain amplitude and phase margin is set as a hard constraint, and the time domain performance is used as a soft constraint, and the parameters are synchronously adjusted through the optimization algorithm. This method constructs a unified design framework in the pitch and roll attitude control channels, incorporates frequency characteristic indicators into the design stage, effectively avoids the phenomenon of substandard indicators in the later stage, and significantly reduces the complexity of parameter adjustment while maintaining the disturbance suppression advantage of auto-disturbance rejection, thereby improving the control accuracy and dynamic quality under complex disturbances. Summary of the Invention

[0004] The present invention proposes a UAV self-disturbance rejection control method based on lead-lag compensation and multi-objective optimization, aiming to improve the anti-disturbance performance of attitude control while taking into account frequency domain stability. The method adopts a hierarchical control architecture: the inner loop constructs an angular rate control loop based on a second-order extended state observer (ESO) to realize disturbance estimation and compensation; the outer loop uses nonlinear dynamic inversion (NDI) to complete attitude tracking control. The crossover frequency and phase margin of the inner loop open-loop transfer function are obtained through frequency domain analysis, and the lead-lag link is designed accordingly to expand the parameter adjustment freedom. In the optimization stage, the frequency domain indicators (such as the minimum phase margin) are set as hard constraints, and the time domain performance indicators are used as soft constraints. A multi-objective optimization problem is constructed to solve the optimal control parameters, thereby improving the dynamic response quality while ensuring robustness.

[0005] Beneficial effects of the present invention:

[0006] A UAV auto-disturbance rejection flight control method based on lead-lag regulation and multi-objective optimization includes the following parts:

[0007] Step S1: Building a pitch attitude angle and roll attitude angle control framework based on active disturbance rejection control;

[0008] Step S2: adding a lead-lag link to the attitude control loop of the pitch angle and the roll angle to form a lead-lag adjustment control framework;

[0009] Step S3: defining time domain and frequency domain indicators as soft constraints and hard constraints of the control framework, respectively, to form the optimization objective function;

[0010] Step S4: Optimize the objective function to obtain a control gain that satisfies the time zone and frequency domain indicators.

[0011] Furthermore, the step S1 includes the following steps:

[0012] Step S1.1: Build the pitch rate and roll rate control laws

[0013] For pitch angular rate and roll angular rate, the controlled object is roll angular rate or pitch angular rate, and an active disturbance rejection control model is built. Consider the first-order controlled object:

[0014]

[0015] Where y is the measured output, u is the controlled variable, b0 is the control effectiveness parameter, and f is the lumped disturbance. The extended state observer treats the model's internal uncertainty as internal disturbance, external disturbance factors as external disturbance, and the sum of internal and external disturbances as the lumped disturbance. The extended state space of the controlled object shown in formula (1) is expressed as:

[0016]

[0017] Among them, x1 and x2 represent the controlled state and the lumped disturbance state, respectively. The lumped disturbance state x2 is estimated and the state observer is constructed using the output feedback method. Its expression is:

[0018]

[0019] Among them, z1 and z2 are the estimated values ​​of x1 and x2 respectively, and β1 and β2 are the observer gains. The final control law output is:

[0020]

[0021] Where R is the command signal, l1 is the control law gain, that is, the control bandwidth. For pitch angle rate control:

[0022]

[0023] Among them, q c is the pitch angle rate command, q is the pitch angle rate feedback, is the elevator to pitch rate control derivative. For roll rate control:

[0024]

[0025] Among them, p c is the roll angular rate command, p is the roll angular rate feedback, is the aileron to roll rate control derivative.

[0026] Step S1.2: Build the pitch and roll control laws

[0027] The pitch and roll angles serve as the outer loop of the angular rate control, outputting pitch rate and roll rate commands to the inner loop angular rate control law, respectively. Considering that in actual flight control, angular rate and attitude angles can be directly measured by inertial navigation equipment, a nonlinear dynamic inversion method is used to control the pitch and roll angles. The output pitch rate command is:

[0028]

[0029] Among them, k θ is the pitch angle control gain, θ c is the pitch angle command, θ is the pitch angle feedback, r and φ are the yaw rate and roll angle feedback respectively. The output roll rate command is:

[0030] p c =k φ (φ c -φ)-tanθ(qsinφ+rcosφ) (8)

[0031] Among them, k φ is the roll angle control gain, φ c is the roll angle command, and φ is the roll angle feedback.

[0032] Furthermore, step S2 includes the following steps:

[0033] Build a lead-lag link and expand the control architecture described in S1. The lead-lag link llm is expressed as:

[0034]

[0035] Where τ is the time constant of the leading link, k g is the lead-lag link gain, a1 is the lead link gain, s is the Laplace operator, τ gis the time constant of the lag link, and a2 is the gain of the lag link. The lead-lag link is placed after the output of the control variable u, forming an active disturbance rejection attitude and angular rate control framework with a lead-lag link, aiming to improve the control loop phase margin and dynamic response quality. Parameter a1 is calculated as follows:

[0036]

[0037] in, To increase the maximum phase margin of the control loop, the time constant τ is calculated as follows:

[0038]

[0039] Among them, ω c is the crossover frequency of the angular rate control loop in step S1.1. The parameters of the hysteresis link are calculated as:

[0040] a2=a1,τ g =kτ (12)

[0041] Wherein, k is the adjustment factor, and k>1.

[0042] Furthermore, step S3 includes the following steps:

[0043] Step S3.1: Construct amplitude margin and phase margin as hard indicator constraints

[0044] The flight quality standard MIL-F-9490D specifies the amplitude margin and phase margin indicators. The time delay in the UAV flight control system is a key factor affecting its stability and performance, including sensor delay, communication delay, calculation delay, and actuator delay. Therefore, the control system needs to have a certain phase margin to ensure the stability of the system under the phase lag caused by the delay. The amplitude margin and phase margin at the angular rate feedback are defined as GM and GM, respectively. o and PM o , define the amplitude margin and phase margin at the control quantity output as GM i and PM i , then the margin index is expressed as:

[0045]

[0046] Among them, Gm i and Gm o are the minimum amplitude margin requirements at the input and output, respectively, Pm i and Pm o are the minimum phase margin requirements at the input and output, respectively.

[0047] Step S3.2: Construct the time domain objective function as a soft indicator constraint

[0048] The desired dynamics between the attitude angle command and the attitude angle response are characterized by a standard second-order transfer function, which is expressed as:

[0049]

[0050] Among them, B c (s) and B(s) represent the Laplace transform of attitude angle command and attitude angle response respectively. The attitude angle includes roll angle and pitch angle, ω t and ζ t denote the frequency and damping ratio of the desired closed-loop response of the attitude control loop. t and ζ t The value of , changes the time domain tracking indicator.

[0051] Step S3.3: Constructing the comprehensive objective function

[0052] The frequency domain indicators including amplitude margin and phase margin are used as hard constraints, and the expected standard second-order dynamic response transfer function including rise, overshoot and steady-state error is used as soft constraints. The normalized soft constraint indicator is defined as F i (c) and hard constraint index G j (c), where the subscripts i and j represent the number of constraint indicators, c is the control parameter to be optimized, and c min <c<c max , then the optimization problem is described as:

[0053]

[0054] Among them, c min and c max are the minimum and maximum limits for the parameter.

[0055] Furthermore, step S4 includes the following steps:

[0056] The objective function proposed in step 3 is optimized to obtain control parameters that meet the soft constraint indicators and hard constraint indicators within the parameter constraint range.

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] (1) Improved control performance: By integrating active disturbance rejection and lead-lag compensation, the dynamic response quality of the system is significantly improved while maintaining strong disturbance suppression capability;

[0059] (2) Innovation in design methods: Breaking through the limitations of traditional pole placement, building an optimization design framework that includes frequency domain indicators (amplitude and phase margin), and achieving systematic tuning of control parameters;

[0060] (3) Enhanced engineering practicality: The unified design architecture effectively reduces the complexity of parameter adjustment, avoids the problem of substandard indicators in the later stage, and improves the control accuracy and stability in complex disturbance environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is the longitudinal pitch angle attitude closed loop control loop;

[0062] Figure 2 is the open-loop response Bode diagram of the control loop;

[0063] Figure 3 It is to increase the lead-lag longitudinal pitch angle attitude closed loop control loop;

[0064] Figure 4 is the Bode plot of the open-loop response in the original form and lead-lag;

[0065] Figure 5 is the pitch angle step response diagram in original form and lead-lag;

[0066] Figure 6 It is the Bode plot of the open-loop response in the original form, lead-lag and parameter optimization;

[0067] Figure 7 is the pitch angle step response diagram under the original form, lead-lag and parameter optimization; DETAILED DESCRIPTION

[0068] The present invention will be further described below in conjunction with the embodiments.

[0069] The present invention proposes a UAV flight control method that integrates auto-disturbance rejection control and lead-lag compensation. In view of the problem that the parameter design of traditional auto-disturbance rejection controller relies on pole configuration and cannot directly guarantee the frequency domain indicators, a lead-lag link is embedded in the control loop to improve the degree of freedom of parameter adjustment. A multi-objective optimization model is established, the frequency domain amplitude and phase margin is set as a hard constraint, and the time domain performance is used as a soft constraint, and the parameters are synchronously adjusted through the optimization algorithm. This method constructs a unified design framework in the pitch and roll attitude control channels, incorporates the frequency characteristic indicators into the design stage, effectively avoids the phenomenon of substandard indicators in the later stage, and significantly reduces the complexity of parameter adjustment while maintaining the advantages of auto-disturbance rejection suppression, thereby improving the control accuracy and dynamic quality under complex disturbances. The following takes the pitch control channel as an example and the pitch angle of the UAV as the controlled object to introduce the implementation process of the present invention.

[0070] Step S1: Building a pitch angle control framework based on active disturbance rejection control:

[0071] The longitudinal small disturbance motion equation of the UAV can be expressed as:

[0072]

[0073] Where α is the angle of attack, q is the pitch rate, θ is the pitch angle, δ e Represents the elevator deflection angle. For the pitch rate control, a self-disturbance rejection control model is built. Referring to the formula (1), the pitch rate dynamics model is rewritten as:

[0074]

[0075] in The lumped disturbance f = -10.2α - 1.8q. Referring to formula (2), the expanded state space of the controlled object shown in formula (17) is expressed as:

[0076]

[0077] Among them, x1=q,x2=f, The state observer is constructed by output feedback, and its expression is:

[0078]

[0079] Where z1 and z2 are estimates of q and f respectively, β1 and β2 are observer gains, and β1 = 6 and β2 = 20 are selected. The final control law output is:

[0080]

[0081] Where r = q c is the pitch angle rate command, l1 is the control law gain, that is, the control bandwidth, and l1=6.

[0082] Step S1.2: Build the pitch angle control law

[0083] For single-loop pitch angle control, the pitch angle control outputs the pitch angle rate command, which is expressed as:

[0084] q c =k θ (θ c -θ) (21)

[0085] It should be noted that formula (21) does not consider the coupling of lateral and heading directions, but only considers the pitch control channel. θ =1, establish Figure 1 The control block diagram is shown. Figure 1 Where SFC is the structural filter, expressed as:

[0086]

[0087] Figure 1Where ACT is the servo transfer function, expressed as:

[0088]

[0089] Figure 1 Where DELAY is the first-order pade approximation of the delay, expressed as:

[0090]

[0091] Among them, τ d is the delay time, here it is set to 0.04. Figure 1 As shown, the loop is disconnected at u to obtain the open-loop Bode diagram of the control system, as shown in Figure 2 As shown, from Figure 2 It can be seen that the amplitude crossover frequency of the control loop is 8.2Hz, the amplitude margin is 6.2dB, and the phase margin is 42deg.

[0092] Step S2: Expand the pitch attitude angle control framework of the active disturbance rejection control, add a lead-lag link in the loop, and build a control framework including lead-lag adjustment;

[0093] Build the lead-lag link, the lead-lag link llm can be expressed as:

[0094]

[0095] Select k g =1, According to formula (10) and formula (11), the parameters a1 and τ can be calculated to be 1.89 and 0.0884 respectively. According to formula (12), k = 10, we can get a2 and τ g are 1.89 and 0.884 respectively, and we get Figure 3 The lead-lag link shown in is:

[0096]

[0097] Figure 4 and Figure 5 The frequency domain and time domain responses after adding the lead-lag link are given respectively. Figure 4 It shows that after adding the lead-lag link, the amplitude margin becomes 99deg, the phase margin becomes 9.4dB, and the crossover frequency is 5.64rad / s. Both the amplitude margin and the phase margin are improved. Figure 5 It can be seen from the step command response that after adding the lead-lag link, the pitch angle overshoot increases from 2.4% to 5.5%.

[0098] Step S3: defining time domain and frequency domain indicators, which are used as soft and hard constraints to form an objective function and as parameter optimization objects of a lead-lag adjustment pitch angle control framework.

[0099] Step S3.1: Construct amplitude margin and phase margin as hard indicator constraints

[0100] like Figure 3 As shown, set δ ec The amplitude margin at ≮6dB and the phase margin at ≮45deg;

[0101] like Figure 3 As shown, set q sfc The amplitude margin at ≮6dB and the phase margin at ≮45deg.

[0102] Step S3.2: Construct the time domain objective function as a soft indicator constraint

[0103] The desired dynamics between the attitude angle command and the attitude angle response are characterized by a standard second-order transfer function, which can be expressed as:

[0104]

[0105] Step S3.3: Constructing the comprehensive objective function

[0106] Select the parameters and ranges to be optimized:

[0107] (1) The lead-lag link adjustment factor k, 1≤k≤100, with an initial value of 1;

[0108] (2) Lead-lag link gain k g , 0.1≤k≤2, initial value is 1;

[0109] (3) Expanded observer gain β1, 1≤β1≤20, initial value is 6;

[0110] (4) Expanded observer gain β2, 1≤β2≤40, initial value is 20.

[0111] Then the optimization problem can be described as:

[0112]

[0113] Among them, c min and c max are the minimum and maximum limits of the parameters. The hard constraint index is expressed as:

[0114] G i (c) = (6 / G m (δ ec )) 2 +(6 / G m (q sfc )) 2 +(45 / P m (δ ec)) 2 +(45 / P m (q sfc )) 2 (29)

[0115] Among them, G m (δ ec ) and P m (δ ec ) are δ ec The amplitude margin and phase margin at G m (q sfc ) and P m (q sfc ) are q sfc The amplitude margin and phase margin at . The soft constraint index is expressed as:

[0116] F i (c) = ITAE(θ I -θ F ) (30)

[0117] Among them, θ I is the response of the standard second-order transfer function to the step pitch angle command expressed by formula (27), and θ F It is the response of the constructed pitch angle control framework with lead-lag link to the step pitch angle command, and the ITAE index of the difference between the two constitutes the soft constraint cost function.

[0118] In step S4, the comprehensive objective function is optimized to obtain the controller gain under the new active disturbance rejection control framework that adds a lead-lag link on the basis of the traditional active disturbance rejection control, and the controller gain satisfies both the frequency domain performance index and the time domain performance index.

[0119] The optimized controller gain is obtained:

[0120] (1) The lead-lag link adjusts the initiator k, 1≤k≤100, and the optimization result is 1.6;

[0121] (2) Lead-lag link gain k g , 0.1≤k≤2, the optimization result is 0.56;

[0122] (3) The expanded observer gain β1, 1≤β1≤20, the optimization result is 4.5;

[0123] (4) The expanded observer gain β2, 1≤β2≤40, the optimization result is 22.1.

[0124] like Figure 6 As shown in the figure, the optimized phase margin is 50deg, the amplitude margin is 12.5dB, and the crossover frequency is 4.8rad / s, which meets the index requirements. Figure 7The overshoot shown is 3.3% due to the direct increase in lead-lag compensation of 5.5%.

[0125] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. An autonomous anti-disturbance flight control method for UAV based on lead-lag regulation and multi-objective optimization, characterized by: Includes the following sections: Step S1: Building a pitch attitude angle and roll attitude angle control framework based on active disturbance rejection control; Step S2: adding a lead-lag link to the attitude control loop of the pitch angle and the roll angle to form a lead-lag adjustment control framework; Step S3: defining time domain and frequency domain indicators as soft constraints and hard constraints of the control framework, respectively, to form the optimization objective function; Step S4: Optimize the objective function to obtain a control gain that satisfies the time zone and frequency domain indicators.

2. The UAV active disturbance rejection flight control method based on lead-lag adjustment and multi-objective optimization according to claim 1 is characterized in that: The step S1 comprises the following steps: Step S1.1: Build the pitch rate and roll rate control laws For pitch angular rate and roll angular rate, the controlled object is the roll angular rate or pitch angular rate, and an active disturbance rejection control model is built; considering the first-order controlled object: Where y is the measured output, u is the controlled variable, b0 is the control effectiveness parameter, and f is the lumped disturbance. The extended state observer takes the model internal uncertainty as the internal disturbance, the external disturbance factor as the external disturbance, and the sum of the internal disturbance and the external disturbance as the lumped disturbance. The extended state space of the controlled object shown in formula (1) is expressed as: Among them, x1 and x2 represent the controlled state quantity and the lumped disturbance state quantity respectively; the lumped disturbance state quantity x2 is estimated, and the state observer is constructed by output feedback, and its expression is: Among them, z1 and z2 are the estimated values ​​of x1 and x2 respectively, β1 and β2 are the observer gains; the final control law output is: Where R is the command signal, l1 is the control law gain, that is, the control bandwidth; for pitch angle rate control: Among them, q c is the pitch angle rate command, q is the pitch angle rate feedback, is the elevator to pitch rate control derivative; For roll rate control: Among them, p c is the roll angular rate command, p is the roll angular rate feedback, is the aileron to roll rate control derivative; Step S1.2: Build the pitch and roll control laws The pitch angle and roll angle serve as the outer loop of the angular rate control, outputting pitch rate and roll rate commands to the inner loop angular rate control law, respectively. Considering that in actual flight control, angular rate and attitude angle can be directly measured by inertial navigation equipment, a nonlinear dynamic inversion method is used to control the pitch angle and roll angle. The output pitch rate command is: Among them, k θ is the pitch angle control gain, θ c is the pitch angle command, θ is the pitch angle feedback, r and φ are the yaw rate and roll angle feedback respectively; the output roll rate command is: p c =k φ (f c -φ)-tanθ(qsinφ+rcosφ) (8) Among them, k φ is the roll angle control gain, φ c is the roll angle command, and φ is the roll angle feedback.

3. The UAV active disturbance rejection flight control method based on lead-lag adjustment and multi-objective optimization according to claim 1 is characterized in that: The step S2 comprises the following steps: Build a lead-lag link and expand the control architecture described in S1. The lead-lag link llm is expressed as: Where τ is the time constant of the leading link, k g is the lead-lag link gain, a1 is the lead link gain, s is the Laplace operator, τ g is the time constant of the lag link, and a2 is the gain of the lag link. The lead-lag link is placed after the output of the control variable u, forming an active disturbance rejection attitude and angular rate control framework with a lead-lag link, aiming to improve the phase margin and dynamic response quality of the control loop. The parameter a1 is calculated as follows: in, To increase the maximum phase margin of the control loop, the time constant τ is calculated as follows: Among them, ω c is the crossover frequency of the angular rate control loop in step S1.1; the parameters of the lag link are calculated as: a2=a1,τ g =kτ(12) Wherein, k is the adjustment factor, and k>1.

4. The UAV active disturbance rejection flight control method based on lead-lag adjustment and multi-objective optimization according to claim 1 is characterized in that: The step S3 comprises the following steps: Step S3.1: Construct amplitude margin and phase margin as hard indicator constraints The control system needs to have a certain phase margin to ensure the stability of the system under the phase lag caused by time delay; the amplitude margin and phase margin at the angular rate feedback are defined as GM and GM respectively. o and PM o , define the amplitude margin and phase margin at the control quantity output as GM i and PM i , then the margin index is expressed as: Among them, Gm i and Gm o are the minimum amplitude margin requirements at the input and output, respectively, Pm i and Pm o are the minimum phase margin requirements at the input and output respectively; Step S3.2: Construct the time domain objective function as a soft indicator constraint The desired dynamics between the attitude angle command and the attitude angle response are characterized by a standard second-order transfer function, which is expressed as: Among them, B c (s) and B(s) represent the Laplace transform of attitude angle command and attitude angle response respectively. The attitude angle includes roll angle and pitch angle, ω t and ζ t They represent the frequency and damping ratio of the desired closed-loop response of the attitude control loop respectively; by changing ω t and ζ t The value of , changes the time domain tracking indicator; Step S3.3: Constructing the comprehensive objective function The frequency domain indicators including amplitude margin and phase margin are used as hard constraints, and the expected standard second-order dynamic response transfer function including rise, overshoot and steady-state error is used as soft constraints; the normalized soft constraint indicator is defined as F i (c) and hard constraint index G j (c), where the subscripts i and j represent the number of constraint indicators, c is the control parameter to be optimized, and c min <c<c max , then the optimization problem is described as: Among them, c min and c max are the minimum and maximum limits for the parameter.

5. The UAV active disturbance rejection flight control method based on lead-lag adjustment and multi-objective optimization according to claim 1 is characterized in that: The step S4 includes the following steps: optimizing the objective function proposed in step 3 to obtain control parameters that meet the soft constraint indicators and hard constraint indicators within the parameter constraint range.

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