CN113759722A - Parameter optimization method for active disturbance rejection controller of unmanned aerial vehicle - Google Patents
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Abstract
The invention discloses an unmanned aerial vehicle Active Disturbance Rejection Controller (ADRC) parameter optimization method, aiming at the problems that in engineering practice, the ADRC has more parameters to be adjusted compared with a PID (proportion integration differentiation) controller, the parameters are mutually influenced, manual adjustment is difficult, and the optimal parameters are difficult to achieve, the parameter optimization method of the ADRC is adopted to optimize the parameters of the controller, the fuzzy logic characteristic is added into a Particle Swarm Optimization (PSO) algorithm, the global and local exploration capacity of the PSO algorithm is improved, and the solving precision is improved while the particles are prevented from falling into a local optimal value; the method solves the problem of parameter adjustment of the active disturbance rejection controller, improves the stability and robustness of the unmanned aerial vehicle control system, and greatly promotes the wide application of the active disturbance rejection controller in practice.
Description
Technical Field
The invention relates to the technical field of nonlinear control of unmanned aerial vehicles, in particular to a parameter optimization method for an active disturbance rejection controller of an unmanned aerial vehicle.
Background
The unmanned aerial vehicle has the advantages of high degree of freedom, strong flexibility, strong adaptability to complex terrains, low cost and the like, is commonly used for executing routing inspection and search and rescue tasks in dangerous areas or complex terrain environments, and is widely applied to the civil and military fields at present. Such as surveillance and reconnaissance missions in the military field; the method is applied to power inspection, energy system inspection, bridge inspection, forest fire rescue, agricultural plant protection and the like in the civil field. How to realize the stable flight of unmanned aerial vehicle is its prerequisite that can accomplish appointed task of patrolling and examining. However, the drone is a nonlinear, under-actuated, strongly coupled system and it is difficult to build an accurate mathematical model thereof; how to design a controller with high stability and strong robustness aiming at the characteristics of an unmanned system is a difficult point studied by engineering technicians all the time.
An Active Disturbance Rejection Controller (ADRC) is a novel Control method which is provided based on the principle of the traditional PID controller and analyzes the advantages and disadvantages of the PID controller and does not depend on an accurate system model, has the advantages of high tracking speed, high Control precision, strong anti-interference capability, capability of estimating and compensating various disturbances suffered by the system in real time and the like, and is applied to a plurality of practices at present. Design unmanned aerial vehicle control system based on ADRC can solve unmanned aerial vehicle and have more unknown disturbance problem in flight process, realizes the high and strong unmanned aerial vehicle control system of robustness of stability.
However, in engineering practice, ADRC needs more parameters to adjust than PID controllers, and the parameters affect each other; manual adjustment is difficult and difficult to achieve the optimum, which brings great hindrance to the wide application of ADRC in the actual unmanned aerial vehicle control system.
In order to solve the above problems, an Attitude controller of an ADRC-based quad-rotor unmanned aerial vehicle is designed by Suiyuan Shen et al (Attitution Active Disturbance Rejection Control of the quadrotor and the parameter tuning [ J ], International Journal of aeronautical Engineering), and an adaptive genetic algorithm-particle swarm algorithm (AGA-PSO) is adopted to optimize the parameters of the controller, so that the problem that the parameters of the controller are difficult to adjust is solved. Zhihao Cai et al (Quadrotor transmitter tracking and object architecture by chaotic vector optimization-based active diversity estimation control [ J ], Mechanical Systems and Signal Processing) propose a chaotic grey wolf optimization algorithm (CGWO) combining chaotic initialization and chaotic search to obtain optimal parameters of attitude and position controllers. Aiming at the problems that ADRC parameters are many, coupling is strong, and the parameters are difficult to determine, an ADRC parameter self-learning algorithm CARLA-ADRC is provided by combining a Continuous Action Reinforcement Learning (CARLA) of Wuli, Bao hong, Dujing and the like (an ADRC parameter learning algorithm [ J ]. automated report).
However, the above mentioned methods have the disadvantages of not wide optimization search range, not high solution accuracy, too long solution time and easy trapping in local optimal values.
Disclosure of Invention
The invention aims to provide an ADRC parameter optimization method for an unmanned aerial vehicle, which solves the problem that controller parameters are difficult to adjust in an ADRC-based unmanned aerial vehicle control system.
The technical scheme adopted by the invention is that the method for optimizing the ADRC parameters of the unmanned aerial vehicle is implemented by adding fuzzy logic on the basis of the traditional PSO algorithm according to the following steps:
step 1: initializing a population; the method mainly comprises the group dimension, the group scale, the maximum iteration times of the group, and the position and the speed of initial particles. Wherein, the population dimension is 7 dimensions, corresponds 7 parameters of ADRC respectively: beta is a01，β02，β03，r，c，h1，b0(ii) a Adjusting the population scale and the maximum population iteration times according to the actual needs of the project; the position and velocity of the initial particle is randomly generated based on the upper and lower limits of the position and velocity of the particle.
Step 2: judging whether the maximum iteration times is reached; if so, recording the global optimal particles, wherein the position values of the particles are the optimized optimal parameters of the controller; if not, go to step 3.
And step 3: calculating a fitness value for each particle according to a fitness function, wherein the fitness function is defined as follows:
because the rising stage of the ADRC is mainly influenced by the TD part, the invention takes the absolute error product criterion (IAE) as the basis, the designed fitness function is defined as the sum of the accumulated value of the system response value and the expected value error in the period from the rising time to the end of the sampling period of the system step response, compared with fitness functions of other modes, the designed fitness function can ensure that a controller has better performance, and the mathematical expression of the fitness function is as follows:
wherein, the fitness value of J particles, trAnd (e) the difference value between the response of the controller and the expected input of the controller at the time T.
And 4, step 4: calculating the particles with the minimum fitness value according to the fitness of all the particles in the iteration, and recording the optimal value of the particles in the iteration; and simultaneously comparing the current iteration with the global optimum value, if the current iteration optimum value is smaller than the global optimum value, updating the global optimum value, and otherwise, not updating.
And 5: and calculating a population iteration process, population diversity and population error.
The calculation method of the population iteration process comprises the following steps:
expressed in percentage, the degree of PSO iteration is expressed in normalized form, and the normalized number of iterations is:
wherein, ni (k) is the population iteration degree in the kth iteration, k is the algebra of the current iteration, and M is the maximum population iteration algebra.
The method for calculating the population diversity comprises the following steps:
the diversity of the population is expressed by the degree of dispersion between the particles, obtained by measuring the average of the euclidean distances between each particle and the best particle, and the population diversity d (k) is specified as follows:
wherein,
is the globally optimal particle before the kth iteration. Population diversity is expressed using a normalized form, defined for normalized population diversity as:
the error of the population is defined as the average value of the sum of the differences between the fitness of each particle and the fitness of the best particle; population error E (k) is defined as:
the population error is expressed in a normalized form, and the normalized population error is defined as:
wherein k is the kth iteration of PSO, M is the population size, Fitness (x)i) Is the fitness value of the particle i.
Step 6: solving for c according to a fuzzy logic system1、c2。
Wherein, c1、c2The learning factors are PSO learning factors and respectively represent weights of social cognition and self cognition; c is defined as1、c2The value range is 0.5-2.5.
Wherein, the structure of the fuzzy logic system is a three-input two-output system; it should be noted that before fuzzy inference, fuzzy rules need to be defined according to the requirements of actual projects.
Wherein, for the fuzzy logic system, the iterative process, the population diversity and the population error obtained in the step 5 are used as the input of the fuzzy logic system, and the factor c is learned1、c2As an output of the fuzzy system.
And 7: the velocity and position of the particles are updated.
Wherein, the velocity updating formula of the particles is as follows:
wherein alpha is an adjustable parameter and the value range is 0.6-0.8.
Wherein the position of the particle is updated as follows:
xi(k+1)＝xi(k)+vi(k+1) (8)
wherein k is the number of iterations; v. ofi(k) Is the velocity, x, of particle i at the kth iterationi(k +1) is the position of particle i at the (k +1) th iteration, piThe historical optimum value of the particle i and the historical optimum value of all the particles g.
And 8: and returning to the step 2 for judgment.
The invention provides a parameter optimization method for an active disturbance rejection controller of an unmanned aerial vehicle, which has the following advantages: on the basis of a traditional Particle Swarm Optimization (PSO), fuzzy logic is added, and the method has the advantages of high convergence speed, high solving precision and difficulty in falling into a local optimum value.
The parameter optimization method for the active disturbance rejection controller of the unmanned aerial vehicle solves the difficulties that the ADRC has more parameters needing to be adjusted compared with a PID controller, the parameters are mutually influenced, manual adjustment is difficult and optimal adjustment is difficult to achieve, the parameter optimization method can be widely applied to parameter adjustment of the ADRC of the unmanned aerial vehicle, and compared with a controller without parameter optimization, the unmanned aerial vehicle control system with high stability and strong robustness can be realized after the controller parameters are optimized through the method.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a quad-rotor unmanned aerial vehicle attitude control system designed by the present invention;
fig. 2 is an implementation flow of the method for optimizing the ADRC parameters of the unmanned aerial vehicle according to the present invention;
FIG. 3 is a framework of a fuzzy logic system designed by the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments.
Taking a quad-rotor unmanned aerial vehicle as an example, aiming at the system characteristics of the quad-rotor unmanned aerial vehicle, a mathematical model of the quad-rotor unmanned aerial vehicle is analyzed; wherein, four rotor unmanned aerial vehicle's mathematical model is as follows:
wherein JrIs the moment of inertia of the rotor, omegaiThe rotating speed of the corresponding motor; phi, theta, psi are the angles of rotation of the body about the x, y, z axes, respectively (counterclockwise);
acceleration of the fuselage along the x-axis, y-axis, and z-axis, respectively; j. the design is a squarex,Jy,JzThe moment of inertia of the fuselage in three directions is respectively; g is the acceleration (value 9.81) and m is the mass of the fuselage.
Wherein, U1、U2、U3、U4Is defined as follows:
wherein d is the arm length from the motor to the center of the unmanned aerial vehicle; c. CTIs the coefficient of tension of the propeller; c. CMIs the torque coefficient.
The attitude control system based on the ADRC quad-rotor unmanned aerial vehicle, which is designed for the quad-rotor unmanned aerial vehicle, is shown in FIG. 1;
wherein the translational motion of the quad-rotor unmanned aerial vehicle in the 3-dimensional space can be realized by changing the attitude angle, so the expected input of the control system comprises three control quantities, namely the expected roll angle phidDesired pitch angle θdAnd a desired yaw angle psid。
Wherein, quad-rotor unmanned aerial vehicle's attitude control loop includes attitude control ware and controlled variable conversion based on ADRC.
The ADRC mainly comprises a Tracking Differentiator (TD), an Extended State Observer (ESO) and a nonlinear state error feedback control rate (NLSEF).
The TD arranges a transition process for the input signal, and solves the contradiction between the overshoot and the rapidity of the system. The tracking differentiator mathematical expression for a second order system is as follows:
wherein, fhan (-) is the fastest synthesis function, T is the sampling period of the control system, vd、v1、v2The desired input signal, the desired input tracking signal, and the differential of the tracking signal, respectively. r and h are two adjustable parameters of the tracking differentiator; wherein r is0For the velocity factor, increase r0Increase response speed, decrease transition course, but over-large r0The closer the tracking signal is to the desired input signal, the less meaningful the transition will be; h is0For the filter factor, increase h0Can improve the filtering effect and simultaneouslyGreater phase delay is also introduced.
The ESO is the core of the ADRC, which does not depend on an accurate mathematical model of a control object, estimates and compensates the total disturbance of the system (the uncertainty inside the system and the disturbance outside the system) according to the input and the output of the system to the controller, and the mathematical expression of the ESO is as follows:
wherein fal (-) is a non-linear function α1，α2The interval length of the linear segment of the nonlinear function is determined for variable parameters, and the value is generally alpha1＝0.5，α2＝0.25。β01、β02、β03Is determined by the sampling step size of the system.
The NLSEF generates a system tracking error signal by using a TD stage and an ESO stage, and generates a control quantity by a series of nonlinear combination, and the mathematical expression of the NLSEF is as follows:
by compensating the expanded state variable observed by the ESO, the control quantity can be derived:
wherein r is the gain of the control quantity, generally takes a larger value, c is the damping factor, h1Is a precision factor, b0Is a compensation factor.
In summary, the parameters that need to be adjusted for ADRC are: beta is a01，β02，β03，r，c，h1，b0。
The specific implementation flow of the unmanned aerial vehicle ADRC parameter optimization method is as follows, and the flow chart is shown in FIG. 2:
step 1: population initializationMelting; the method mainly comprises the group dimension, the group scale, the maximum iteration times of the group, and the position and the speed of initial particles. Wherein, the population dimension is 7 dimensions, corresponds 7 parameters of ADRC respectively: beta is a01，β02，β03，r，c，h1，b0(ii) a Adjusting the population scale and the maximum population iteration times according to the actual needs of the project; the position and velocity of the initial particle is randomly generated based on the upper and lower limits of the position and velocity of the particle.
TABLE 1 particle range
| Parameter(s) | Value range | Parameter(s) | Value range |
| r | [0，400] | β01 | [0，500] |
| c | [0，400] | β02 | [0，4000] |
| h1 | [0，400] | β03 | [0，8000] |
| b0 | [0，100] |
Step 2: judging whether the maximum iteration times is reached; if so, recording the global optimal particles, wherein the position values of the particles are the optimized optimal parameters of the controller; if not, go to step 3.
With the present embodiment, the maximum number of iterations is set to 100.
And step 3: calculating a fitness value for each particle according to a fitness function, wherein the fitness function is defined as follows:
because the rising stage of the ADRC is mainly influenced by the TD part of the ADRC, the invention takes absolute error product criterion (IAE) as a basis, the designed fitness function is defined as the sum of the accumulated value of the system response value and the expected value error in the period from the rising time of the system step response to the end of the sampling period, compared with fitness functions of other modes, the designed fitness function can enable the controller to have better performance, and the mathematical expression of the fitness function is as follows:
wherein, the fitness value of J particles, trAnd (e) the difference value between the response of the controller and the expected input of the controller at the time T.
And 4, step 4: calculating the particles with the minimum fitness value according to the fitness of all the particles in the iteration, and recording the optimal value of the particles in the iteration; and simultaneously comparing the current iteration with the global optimum value, if the current iteration optimum value is smaller than the global optimum value, updating the global optimum value, and otherwise, not updating.
And 5: and calculating a population iteration process, population diversity and population error.
The calculation method of the population iteration process comprises the following steps:
expressed in percentage, the degree of PSO iteration is expressed in normalized form, and the normalized number of iterations is:
wherein, ni (k) is the population iteration degree in the kth iteration, k is the algebra of the current iteration, and M is the maximum population iteration algebra.
The method for calculating the population diversity comprises the following steps:
the diversity of the population is expressed by the degree of dispersion between the particles, obtained by measuring the average of the euclidean distances between each particle and the best particle, and the population diversity d (k) is specified as follows:
wherein,
is the globally optimal particle before the kth iteration. Population diversity is expressed using a normalized form, defined for normalized population diversity as:
the error of the population is defined as the average value of the sum of the differences between the fitness of each particle and the fitness of the best particle; population error E (k) is defined as:
the population error is expressed in a normalized form, and the normalized population error is defined as:
wherein k is the kth iteration of PSO, M is the population size, Fitness (x)i) Is the fitness value of the particle i.
Step 6: solving for c according to a fuzzy logic system1、c2。
Wherein, c1、c2The learning factors are PSO learning factors and respectively represent weights of social cognition and self cognition; c is defined as1、c2The value range is 0.5-2.5.
The structure of the fuzzy logic system is shown in fig. 3.
Wherein, for the fuzzy logic system, the iterative process, the population diversity and the population error obtained in the step 5 are used as the input of the fuzzy logic system, and the factor c is learned1、c2As an output of the fuzzy system.
And 7: the velocity and position of the particles are updated.
Wherein, the velocity updating formula of the particles is as follows:
wherein alpha is a parameter and the value range is 0.6-0.8.
Wherein the position of the particle is updated as follows:
xi(k+1)＝xi(k)+vi(k+1) (22)
wherein k is the number of iterations; v. ofi(k) Is the velocity, x, of particle i at the kth iterationi(k +1) is the position of particle i at the (k +1) th iteration, piThe historical optimum value of the particle i and the historical optimum value of all the particles g.
And 8: and returning to the step 2 for judgment.
And (3) respectively corresponding to 7 controller parameters of the ADRC through the optimization result obtained in the step (2), namely the optimal controller parameter.
The above is a theoretical analysis part of the invention, and finally, simulation analysis needs to be performed on Matlab and Simulink platforms, and experimental results are verified and compared.
And finally, deploying the optimized optimal controller parameters to an actual unmanned aerial vehicle hardware platform, and observing whether the actual flight effect of the unmanned aerial vehicle reaches the expectation.
While the invention has been described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (5)
1. The parameter optimization method for the active disturbance rejection controller of the unmanned aerial vehicle is characterized in that a particle swarm algorithm combined with fuzzy logic is adopted to optimize parameters of the active disturbance rejection controller, and the method is implemented according to the following steps:
step 1: initializing a population;
step 2: judging whether the maximum iteration times is reached; if so, recording the global optimal particle, wherein the position value of the particle is the optimized optimal parameter of the controller; if not, turning to step 3;
and step 3: calculating the fitness value of each particle according to the fitness function;
and 4, step 4: calculating the particle with the minimum fitness value according to the fitness of all the particles in the current iteration, and recording the optimal value of the particle in the current iteration; meanwhile, the iteration is compared with the global optimum value, if the optimum value of the iteration is smaller than the global optimum value, the global optimum value is updated, otherwise, the iteration is not updated;
and 5: calculating a population iteration process, population diversity and population errors;
step 6: solving for c according to a fuzzy logic system1、c2；
And 7: updating the speed and position of the particles;
and 8: and returning to the step 2 for judgment.
2. The method according to claim 1, wherein the population dimension in step 1 is 7 dimensions, and corresponds to 7 parameters of the active disturbance rejection controller: beta is a01，β02，β03，r，c，h1，b0(ii) a Adjusting the population scale and the maximum population iteration times according to the actual needs of the project; the position and velocity of the initial particle is randomly generated based on the upper and lower limits of the position and velocity of the particle.
3. The method for optimizing parameters of the active disturbance rejection controller of the unmanned aerial vehicle according to claim 1, wherein the designed fitness function enables the controller to have better performance than fitness functions of other modes, and a mathematical expression of the fitness function is as follows:
wherein, the fitness value of J particles, trAnd (e) the difference value between the response of the controller and the expected input of the controller at the time T.
4. The method for optimizing parameters of the active disturbance rejection controller of the unmanned aerial vehicle according to claim 1, wherein the method for calculating the population iteration process, the population diversity and the population error comprises the following steps:
the calculation method of the population iteration process comprises the following steps:
the percentage is used for expressing the iteration degree of the particle swarm algorithm, the normalization mode is used for expressing, and the iteration times after normalization are as follows:
wherein, NI (k) is the population iteration degree in the k iteration, k is the algebra of the current iteration, and M is the maximum population iteration algebra; the method for calculating the population diversity comprises the following steps:
the diversity of the population is expressed by the degree of dispersion between the particles, obtained by measuring the average of the euclidean distances between each particle and the best particle, and the population diversity d (k) is specified as follows:
wherein,
is the global optimal particle before the k iteration; population diversity is expressed using a normalized form, defined for normalized population diversity as:
the error of the population is defined as the average value of the sum of the differences between the fitness of each particle and the fitness of the best particle; population error E (k) is defined as:
the population error is expressed in a normalized form, and the normalized population error is defined as:
wherein k is the kth iteration of the particle swarm algorithm, M is the population size, Fitness (x)i) Is the fitness value of particle i.
5. The method of claim 1, wherein the fuzzy logic system is configured as a three-input two-output system; for the fuzzy logic system, the iterative process, the population diversity and the population error obtained in the step 5 are used as the input of the fuzzy logic system, and a factor c is learned1、c2As an output of the fuzzy system.
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| CN114415519A (en) * | 2022-01-25 | 2022-04-29 | 佛山智能装备技术研究院 | Real-time optimization method for parameter rapid convergence of ADRC extended observer |
| US20230213948A1 (en) * | 2021-12-30 | 2023-07-06 | Aerospace Information Research Institute, Chinese Academy Of Sciences | Stability control method and device based on particle active disturbance rejection |
| CN118364528A (en) * | 2024-06-19 | 2024-07-19 | 中国石油大学(华东) | Deep water polyester cable mooring system layout optimization method and system |
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