CN113759722A - A parameter optimization method for unmanned aerial vehicle active disturbance rejection controller - Google Patents

Abstract

The invention discloses a method for optimizing the parameters of an active disturbance rejection controller (ADRC) of an unmanned aerial vehicle. In engineering practice, the active disturbance rejection controller needs to adjust more controller parameters than the PID controller, and the difference between the parameters is higher. It is difficult to adjust manually and it is difficult to achieve the optimal problem. The parameter optimization method of ADR controller of unmanned aerial vehicle is used to optimize the parameters of the controller. This method combines the fuzzy logic The characteristic is added to the particle swarm (PSO) algorithm, which improves the global and local exploration capabilities of the PSO algorithm, avoids particles falling into local optimal values, and improves the accuracy of the solution; the present invention solves the problem of automatic disturbance rejection controller adjustment. It improves the stability and robustness of the UAV control system, and greatly promotes the wide application of ADRC in practice.

Description

A parameter optimization method for unmanned aerial vehicle active disturbance rejection controller

technical field

The invention relates to the technical field of non-linear control of unmanned aerial vehicles, and in particular to a parameter optimization method of an active disturbance rejection controller of unmanned aerial vehicles.

Background technique

UAVs have many advantages, such as high degree of freedom, strong flexibility, strong adaptability to complex terrain, and low cost. They are often used to perform inspection and search and rescue tasks in dangerous areas or complex terrain environments. have a wide range of applications. Such as surveillance and reconnaissance tasks in the military field; electric power inspection, energy system inspection, bridge inspection, forest fire rescue and agricultural plant protection in the civilian field. How to realize the stable flight of the UAV is the premise of its ability to complete the designated inspection tasks. However, the UAV is a nonlinear, underactuated, and strongly coupled system, and it is difficult to establish its accurate mathematical model; how to design a highly stable and robust controller according to the system characteristics of the UAV is a It has always been a difficult point for engineers and technicians to study.

Active Disturbance Rejection Control (ADRC, Active Disturbance Rejection Control) is a new control method that is based on the principle of traditional PID controller and analyzes the advantages and disadvantages of PID controller and does not depend on the precise system model. The advantages of fast control, high control accuracy, strong anti-interference ability, and real-time estimation and compensation of various disturbances received by the system have been applied to many practices. The design of the UAV control system based on ADRC can solve the problem of many unknown disturbances in the flight process of the UAV, and realize the UAV control system with high stability and robustness.

However, in engineering practice, ADRC needs to adjust more controller parameters than the PID controller, and the parameters affect each other; manual adjustment is difficult and difficult to achieve optimal, which makes ADRC more effective in the actual UAV control system. Widespread application in the system has brought great obstacles.

In order to solve the above problems, Suiyuan Shen et al. (Attitude Active Disturbance Rejection Control of the quadrotor and its parameter tuning[J], International Journal of Aerospace Engineering) designed an ADRC-based quadrotor UAV attitude controller and adopted an adaptive genetic algorithm. - The particle swarm algorithm (AGA-PSO) optimizes the controller parameters and solves the problem that the controller parameters are difficult to adjust. Zhihao Cai et al. (Quadrotor trajectory tracking and obstacle avoidance by chaotic grey wolf optimization-based active disturbance rejection control[J], Mechanical Systems and Signal Processing) proposed a chaotic grey wolf optimization algorithm combining chaotic initialization and chaotic search (CGWO, chaotic grey wolf optimization) to obtain optimal parameters for attitude and position controllers. Wu Lei, Baohong, Du Jingli et al. (a learning algorithm for ADRC parameters [J]. Acta Automatica Sinica) Aiming at the problem that ADRC has many parameters and strong coupling, the parameters are difficult to be determined, combined the continuous action reinforcement learner (CARLA, Continuous action reinforcement learning automata) proposed an ADRC parameter self-learning algorithm CARLA-ADRC.

However, the methods mentioned above have the disadvantages of not wide optimization search range, low solution accuracy, too long solution time and easy to fall into local optimum.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a method for optimizing the ADRC parameters of an unmanned aerial vehicle, so as to solve the problem that the controller parameters are difficult to adjust in the ADRC-based unmanned aerial vehicle control system.

The technical scheme adopted in the present invention is, a kind of unmanned aerial vehicle ADRC parameter optimization method, this method has added fuzzy logic on the basis of traditional PSO algorithm, and is specifically implemented according to the following steps:

Step 1: Population initialization; it mainly includes population dimension, population size, the maximum number of iterations of the population, and the position and velocity of the initial particle. Among them, the population dimension is 7 dimensions, which correspond to the 7 parameters of ADRC: β ₀₁ , β ₀₂ , β ₀₃ , r, c, h ₁ , b ₀ ; the population size and the maximum number of iterations of the population are adjusted according to the actual needs of the project; The position and velocity of the initial particles are randomly generated based on the upper and lower bounds of the particle's position and velocity.

Step 2: Determine whether the maximum number of iterations is reached; if it is, record the global optimal particle, and the position value of the particle is the optimized controller optimal parameter; if not, go to step 3.

Step 3: Calculate the fitness value of each particle according to the fitness function, where the fitness function is defined as follows:

Since the rising stage of ADRC is mainly affected by the TD part, the present invention is based on the absolute error product criterion (IAE), and the designed fitness function is defined as the system response value from the rise time to the end of the sampling period. Compared with the cumulative sum of the expected value error, the designed fitness function can make the controller have better performance than other fitness functions. The mathematical expression of the fitness function is as follows:

Among them, the fitness value of particle J, t _r is the rise time of the system step response, T is the sampling period of the system, and e(t) is the difference between the controller response and the controller expected input at time t.

Step 4: Calculate the particle with the smallest fitness value according to the fitness of all particles in this iteration, and record the optimal value of the particle in this iteration; at the same time, compare with the global optimal value, if the optimal value of this iteration is If the global optimal value must be small, the global optimal value is updated, otherwise it is not updated.

Step 5: Calculate the population iteration process, population diversity, and population error.

Among them, the calculation method of the population iteration process is:

It is expressed in the form of a percentage to express the degree of PSO iteration, expressed in a normalized form, and the number of iterations after normalization is:

Among them, NI(k) is the population iteration degree at the k-th iteration, k is the algebra of the current iteration, and M is the largest population iteration algebra.

Among them, the calculation method of population diversity is:

The diversity of the population is expressed by the degree of dispersion between particles, which is obtained by measuring the average value of the Euclidean distance between each particle and the optimal particle. The population diversity D(k) is as follows:

为第k次迭代之前的全局最优粒子。种群多样性使用归一化 的形式来表示，对于归一化后的种群多样性定义为：in,

is the global optimal particle before the kth iteration. Population diversity is expressed in a normalized form, and the normalized population diversity is defined as:

The population error is defined as the average of the sum of the differences between the fitness of each particle and the fitness of the best particle; the population error E(k) is defined as:

The population error is expressed in the form of normalization, and the normalized population error is defined as:

Among them, k is the k-th iteration of PSO, M is the population size, and Fitness(x _i ) is the fitness value of particle i.

Step 6: Solve c ₁ and c ₂ according to the fuzzy logic system.

Among them, c ₁ and c ₂ are the learning factors of PSO, representing the weights of social cognition and self-cognition respectively; the defined value range of c ₁ and c ₂ is between 0.5 and 2.5.

Among them, the structure of the defined fuzzy logic system is a system with three inputs and two outputs; it should be noted that, before fuzzy inference, the fuzzy rules need to be defined according to the needs of the actual project.

Among them, for the fuzzy logic system, the iterative process, population diversity and population error obtained in step 5 are used as the input of the fuzzy logic system, and the learning factors c ₁ and c ₂ are used as the output of the fuzzy system.

Step 7: Update the velocity and position of the particles.

Among them, the particle velocity update formula is as follows:

Among them, α is an adjustable parameter, and the value range is between 0.6 and 0.8.

Among them, the position of the particle is updated as follows:

x _i (k+1)=x _i (k)+v _i (k+1) (8)

where k is the number of iterations; vi (k) is the velocity of particle _i at the k-th iteration, _xi (k+1) is the position of particle i at the k+1-th iteration, and p _i is the history of particle i The optimal value, g is the historical optimal value of all particles.

Step 8: Return to Step 2 for judgment.

The invention proposes a method for optimizing the parameters of the unmanned aerial vehicle active disturbance rejection controller. It has the advantages of high solution accuracy and not easy to fall into local optimum.

Compared with the PID controller, ADRC needs to adjust more controller parameters, and the parameters affect each other, so it is difficult to manually adjust and adjust the parameters manually. It is difficult to achieve the optimal dilemma, and can be widely used in the parameter adjustment of UAV ADRC. Compared with the controller without parameter optimization, after the controller parameters are optimized by this method, it can achieve high stability and robustness. Strong drone control system.

Description of drawings

In order to explain the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained according to these drawings without creative efforts.

Fig. 1 is a quadrotor unmanned aerial vehicle attitude control system designed by the present invention;

Fig. 2 is the implementation process flow of a kind of UAV ADRC parameter optimization method designed by the present invention;

Fig. 3 is the framework of the fuzzy logic system designed by the present invention.

Detailed ways

In order to make the purpose, technical solutions and advantages of the present application clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

The present invention takes the four-rotor unmanned aerial vehicle as an example, and analyzes the mathematical model of the four-rotor unmanned aerial vehicle according to the system characteristics of the four-rotor unmanned aerial vehicle; wherein, the mathematical model of the four-rotor unmanned aerial vehicle is as follows:

分别是机身沿x轴，y轴，z 轴移动的加速度；J_x,J_y,J_z分别是机身在三个方向的转动惯量；g是加速度(数值 为9.81)，m是机身的质量。Where J _r is the moment of inertia of the rotor, Ω _i is the rotational speed of the corresponding motor; φ, θ, ψ are the rotation angles of the fuselage around the x-axis, y-axis, and z-axis (counterclockwise);

are the acceleration of the fuselage moving along the x-axis, y-axis, and z-axis; J _x , J _y , J _z are the rotational inertia of the fuselage in three directions; g is the acceleration (the value is 9.81), m is the fuselage the quality of.

The definitions of U ₁ , U ₂ , U ₃ and U ₄ are as follows:

Among them, d is the arm length from the motor to the center of the UAV; c _T is the tension coefficient of the propeller; c _M is the torque coefficient.

Among them, the attitude control system based on ADRC quad-rotor UAV designed for quad-rotor UAV is shown in Figure 1;

Among them, the translational motion of the quadrotor UAV in the 3-dimensional space can be realized by changing the attitude angle, so the desired input of the control system includes three control variables, namely the desired roll angle φ _d , the desired pitch angle θ _d and the desired yaw angle ψ _d .

Among them, the attitude control loop of the quadrotor UAV includes ADRC-based attitude controller and control quantity conversion.

Among them, ADRC is mainly composed of three parts: tracking differentiator (TD), extended state observer (ESO) and nonlinear state error feedback control rate (NLSEF).

TD arranges the transition process for the input signal and solves the contradiction between the system overshoot and rapidity. The mathematical expression of the tracking differentiator for a second-order system is as follows:

Among them, fhan(·) is the fastest synthesis function, T is the sampling period of the control system, v _d , v ₁ , and v ₂ are the expected input signal, the expected input tracking signal, and the differential of the tracking signal, respectively. r and h are two adjustable parameters of the tracking differentiator; among them, r ₀ is the speed factor, increasing r ₀ will speed up the response speed and reduce the excessive process, but an excessively large value of r ₀ will make the tracking signal closer to the desired input signal , the meaning of the transition process is lost; h ₀ is the filtering factor, and increasing the value of h ₀ can improve the filtering effect, but also bring about a larger phase delay.

ESO is the core of ADRC. It does not depend on the precise mathematical model of the control object. It estimates the total disturbance of the system (uncertainty inside the system and disturbance outside the system) according to the input and output of the system and compensates it to the controller. The mathematical expression is as follows:

Among them, fal(·) is a nonlinear function α ₁ , and α ₂ is a variable parameter, which determines the interval length of the linear segment of the nonlinear function, and generally takes values α ₁ =0.5 and α ₂ =0.25. β ₀₁ , β ₀₂ , and β ₀₃ are determined by the sampling step size of the system.

NLSEF uses the TD stage and the ESO stage to generate the system tracking error signal, and generates control variables through a series of nonlinear combinations. The mathematical expression of NLSEF is as follows:

By compensating for the expanded state variable observed by ESO, the control quantity can be obtained:

Among them, r is the gain of the control quantity, generally taking a larger value, c is the damping factor, h ₁ is the precision factor, and b ₀ is the compensation factor.

To sum up, the parameters to be adjusted for ADRC are: β ₀₁ , β ₀₂ , β ₀₃ , r, c, h ₁ , b ₀ .

The specific implementation process of a UAV ADRC parameter optimization method is as follows, and the flowchart is shown in Figure 2:

Step 1: Population initialization; it mainly includes population dimension, population size, the maximum number of iterations of the population, and the position and velocity of the initial particle. Among them, the population dimension is 7 dimensions, which correspond to the 7 parameters of ADRC: β ₀₁ , β ₀₂ , β ₀₃ , r, c, h ₁ , b ₀ ; the population size and the maximum number of iterations of the population are adjusted according to the actual needs of the project; The position and velocity of the initial particles are randomly generated based on the upper and lower bounds of the particle's position and velocity.

Table 1 Particle range parameter Ranges parameter Ranges r [0, 400] β₀₁ [0,500] c [0, 400] β₀₂ [0, 4000] h₁ [0, 400] β₀₃ [0, 8000] b₀ [0, 100]

Step 2: Determine whether the maximum number of iterations is reached; if it is, record the global optimal particle, and the position value of the particle is the optimized controller optimal parameter; if not, go to step 3.

Among them, for this embodiment, the maximum number of iterations is set to 100 times.

Step 3: Calculate the fitness value of each particle according to the fitness function, where the fitness function is defined as follows:

Since the rising stage of ADRC is mainly affected by the TD part of ADRC, the present invention is based on the absolute error product criterion (IAE), and the designed fitness function is defined as the step response of the system during the period from the rise time to the end of the sampling period. The cumulative sum of the error of the response value and the expected value, the designed fitness function can make the controller have better performance than other fitness functions. The mathematical expression of the fitness function is as follows:

Among them, the fitness value of particle J, t _r is the rise time of the system step response, T is the sampling period of the system, and e(t) is the difference between the controller response and the controller expected input at time t.

Step 4: Calculate the particle with the smallest fitness value according to the fitness of all particles in this iteration, and record the optimal value of the particle in this iteration; at the same time, compare with the global optimal value, if the optimal value of this iteration is If the global optimal value must be small, the global optimal value is updated, otherwise it is not updated.

Step 5: Calculate the population iteration process, population diversity, and population error.

Among them, the calculation method of the population iteration process is:

It is expressed in the form of a percentage to express the degree of PSO iteration, expressed in a normalized form, and the number of iterations after normalization is:

Among them, NI(k) is the population iteration degree at the k-th iteration, k is the algebra of the current iteration, and M is the largest population iteration algebra.

Among them, the calculation method of population diversity is:

The diversity of the population is expressed by the degree of dispersion between particles, which is obtained by measuring the average value of the Euclidean distance between each particle and the optimal particle. The population diversity D(k) is as follows:

为第k次迭代之前的全局最优粒子。种群多样性使用归一化 的形式来表示，对于归一化后的种群多样性定义为：in,

is the global optimal particle before the kth iteration. Population diversity is expressed in a normalized form, and the normalized population diversity is defined as:

The population error is defined as the average of the sum of the differences between the fitness of each particle and the fitness of the best particle; the population error E(k) is defined as:

The population error is expressed in the form of normalization, and the normalized population error is defined as:

Among them, k is the k-th iteration of PSO, M is the population size, and Fitness(x _i ) is the fitness value of particle i.

Step 6: Solve c ₁ and c ₂ according to the fuzzy logic system.

Among them, c ₁ and c ₂ are the learning factors of PSO, respectively representing the weight of social cognition and self-cognition; the defined value of c ₁ and c ₂ ranges from 0.5 to 2.5.

Among them, the structure of the defined fuzzy logic system is shown in Figure 3.

Among them, for the fuzzy logic system, the iterative process, population diversity and population error obtained in step 5 are used as the input of the fuzzy logic system, and the learning factors c ₁ and c ₂ are used as the output of the fuzzy system.

Step 7: Update the velocity and position of the particles.

Among them, the particle velocity update formula is as follows:

Among them, α is a parameter, and the value range is between 0.6 and 0.8.

Among them, the position of the particle is updated as follows:

x _i (k+1)=x _i (k)+v _i (k+1) (22)

where k is the number of iterations; vi (k) is the velocity of particle _i at the k-th iteration, _xi (k+1) is the position of particle i at the k+1-th iteration, and p _i is the history of particle i The optimal value, g is the historical optimal value of all particles.

Step 8: Return to Step 2 for judgment.

The optimization results obtained in step 2 correspond to the seven controller parameters of ADRC, namely the optimal controller parameters.

The above is the theoretical analysis part of the present invention. Finally, simulation analysis needs to be carried out on the Matlab and Simulink platforms, and the experimental results are verified and compared.

Finally, it is necessary to deploy the optimized optimal controller parameters into the actual UAV hardware platform to observe whether the actual flight effect of the UAV meets the expectations.

The above disclosure is only a preferred embodiment of the present invention, and of course, it cannot limit the scope of rights of the present invention. Those of ordinary skill in the art can understand that all or part of the process for realizing the above-mentioned embodiment can be realized according to the rights of the present invention. The equivalent changes required to be made still belong to the scope covered by the invention.

Claims (5)

1. an unmanned aerial vehicle ADRC parameter optimization method, it is characterized in that, adopt a kind of particle swarm algorithm in conjunction with fuzzy logic to optimize the parameter of ADRC, specifically implement according to the following steps: Step 1: Population initialization; Step 2: Determine whether the maximum number of iterations is reached; if so, record the global optimal particle, and the position value of the particle is the optimized controller optimal parameter; if not, go to step 3; Step 3: Calculate the fitness value of each particle according to the fitness function; Step 4: Calculate the particle with the smallest fitness value according to the fitness of all particles in this iteration, and record the optimal value of the particle in this iteration; at the same time, compare with the global optimal value, if the optimal value of this iteration is If the global optimal value must be small, the global optimal value is updated, otherwise it is not updated; Step 5: Calculate the population iteration process, population diversity, and population error; Step 6: solve c ₁ , c ₂ according to the fuzzy logic system; Step 7: Update the velocity and position of the particles; Step 8: Return to Step 2 for judgment. 2. a kind of UAV ADRC parameter optimization method according to claim 1, is characterized in that, the population dimension in described step 1 is 7 dimensions, correspond to 7 parameters of ADRC respectively : β ₀₁ , β ₀₂ , β ₀₃ , r, c, h ₁ , b ₀ ; the size of the population and the maximum number of iterations of the population are adjusted according to the actual needs of the project; the position and velocity of the initial particle are based on the upper and lower limits of the position and velocity of the particle Randomly generated. 3. a kind of unmanned aerial vehicle active disturbance rejection controller parameter optimization method according to claim 1 is characterized in that, the designed fitness function can make the controller have better performance than other fitness functions, The mathematical expression of fitness function is as follows:

Among them, the fitness value of particle J, t _r is the rise time of the system step response, T is the sampling period of the system, and e(t) is the difference between the controller response and the controller expected input at time t. 4. a kind of UAV ADRC parameter optimization method according to claim 1, is characterized in that, described calculating population iteration process, population diversity, population error method are as follows: Among them, the calculation method of the population iteration process is: It is expressed in the form of a percentage to express the degree of iteration of the particle swarm optimization algorithm. It is expressed in the form of normalization. The number of iterations after normalization is:

Among them, NI(k) is the population iteration degree at the kth iteration, k is the algebra of the current iteration, and M is the largest population iteration algebra; among them, the calculation method of population diversity is: The diversity of the population is expressed by the degree of dispersion between particles, which is obtained by measuring the average value of the Euclidean distance between each particle and the optimal particle. The population diversity D(k) is as follows:

in,

is the global optimal particle before the k-th iteration; the population diversity is expressed in a normalized form, and the normalized population diversity is defined as:

The population error is defined as the average of the sum of the differences between the fitness of each particle and the fitness of the best particle; the population error E(k) is defined as:

The population error is expressed in the form of normalization, and the normalized population error is defined as:

Among them, k is the k-th iteration of particle swarm optimization, M is the population size, and Fitness(x _i ) is the fitness value of particle i. 5. a kind of UAV ADRC parameter optimization method according to claim 1, is characterized in that, the structure of described fuzzy logic system is a system of three inputs and two outputs; The iterative process, population diversity and population error obtained in step 5 are used as the input of the fuzzy logic system, and the learning factors c ₁ and c ₂ are used as the output of the fuzzy system.

Images