CN113253603A - Design method of unmanned aerial vehicle active disturbance rejection controller based on FOPSO algorithm - Google Patents
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Abstract
The invention discloses an unmanned aerial vehicle active disturbance rejection controller design method based on an FOPSO algorithm, aiming at the characteristics that the traditional active disturbance rejection controller has various adjustable parameters and is difficult to set, the FOPSO algorithm is adopted to set the parameters of the active disturbance rejection controller, the optimal parameters are obtained through continuous iterative evolution of particles, the system response speed is improved, the interference resistance and the adaptability of the quad-rotor unmanned aerial vehicle to unknown interference and parameter uncertainty are improved, the FOPSO algorithm introduces fractional order differential terms on the basis of the traditional PSO algorithm, and the inherent memory characteristic can effectively improve the defect that the PSO algorithm is easy to fall into the local optimal solution along with the increase of the iteration times; the invention solves the technical problems of various parameters and difficult manual setting of the active disturbance rejection controller in the prior art.
Description
Technical Field
The invention relates to the technical field of nonlinear control of an aviation aircraft, in particular to a design method of an unmanned aerial vehicle active disturbance rejection controller based on an FOPSO algorithm.
Background
Active Disturbance Rejection Control (ADRC) does not depend on a mathematical model, has a good inhibiting effect on uncertainty of a controlled object and external interference, and has the core idea that the unmodeled dynamic and external Disturbance part is regarded as the 'sum Disturbance' of a system, and an extended state observer is adopted to estimate the sum Disturbance so as to compensate the Control system. The ADRC algorithm is simple to implement, strong in anti-interference capability and natural in decoupling performance. However, the traditional ADRC controller has more parameters and complicated parameter setting, and the adjustable parameters of the controller are generally selected according to experience, so that the method has great uncertainty, more conservative control effect and certain defects in control performance.
Disclosure of Invention
The invention aims to provide a design method of an active disturbance rejection controller of an unmanned aerial vehicle based on an FOPSO algorithm, and aims to solve the technical problems that in the prior art, the active disturbance rejection controller has various parameters and is difficult to manually set.
In order to achieve the purpose, the invention adopts a design method of an unmanned aerial vehicle active disturbance rejection controller based on an FOPSO algorithm, which comprises the following steps:
establishing a four-rotor unmanned aerial vehicle dynamic model;
designing an active disturbance rejection controller according to the four-rotor unmanned aerial vehicle dynamic model;
improved PSO algorithm with addition of fractional order differential operatorObtaining an FOPSO algorithm;
and setting the adjustable parameters of the active disturbance rejection controller by using the FOPSO algorithm.
The design method of the unmanned aerial vehicle active disturbance rejection controller based on the FOPSO algorithm adopts a cascade controller, the cascade controller comprises a PD (passive disturbance rejection) controller and an active disturbance rejection controller, the PD controller is responsible for outer ring position control, and the active disturbance rejection controller is responsible for inner ring attitude control.
The active disturbance rejection controller consists of a tracking differentiator, an extended state observer and a nonlinear state error feedback law.
In the process of designing the active disturbance rejection controller according to the four-rotor unmanned aerial vehicle dynamic model, firstly, the reference values of the pitch angle and the roll angle are solved reversely according to the PD controller of the horizontal position, then the expected pitch angle is input into the tracking differentiator, meanwhile, the extended state observer of the pitch angle is established, and the final control quantity of the active disturbance rejection controller is obtained through the nonlinear state error feedback law.
Wherein, a fractional order differential operator is added in the improved PSO algorithmIn the process of obtaining the FOPSO algorithm, the original velocity equation of the PSO algorithm needs to be rearranged, and the order of velocity differentiation is generalized to be a real number alpha belonging to [0,1]]。
In the process of setting the adjustable parameters of the active disturbance rejection controller by using the FOPSO algorithm, a fitness function in a preset range is selected as a speed and position updating basis of the FOPSO algorithm, and the set parameters are input into the active disturbance rejection controller after the operation of the FOPSO algorithm is finished.
According to the design method of the unmanned aerial vehicle active disturbance rejection controller based on the FOPSO algorithm, aiming at the characteristics that the traditional active disturbance rejection controller has various adjustable parameters and is difficult to set, the FOPSO algorithm is adopted to set the parameters of the active disturbance rejection controller, the optimal parameters are obtained through continuous iterative evolution of particles, the response speed of a system is improved, the interference resistance and the adaptability of the quad-rotor unmanned aerial vehicle to unknown interference and parameter uncertainty are improved, the FOPSO algorithm introduces fractional order differential terms on the basis of the traditional PSO algorithm, and the inherent memory characteristic can effectively improve the defect that the PSO algorithm is easy to fall into a local optimal solution along with the increase of iteration times; the invention solves the technical problems of various parameters and difficult manual setting of the active disturbance rejection controller in the prior art.
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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 schematic flow chart of a design method of an active disturbance rejection controller of an unmanned aerial vehicle based on an FOPSO algorithm according to the present invention.
Fig. 2 is a block diagram of the configuration of the cascade controller of the present invention.
Fig. 3 is a block diagram of the active disturbance rejection controller of the present invention.
FIG. 4 is a flow chart of the fractional particle swarm algorithm of the present invention.
FIG. 5 is an iterative graph of fitness values for the fractional particle swarm algorithm of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
Particle Swarm Optimization (PSO) is commonly used to optimize continuous nonlinear, constrained and unconstrained, indistinguishable polymorphic mode functions. The method has the advantages of simple algorithm, high efficiency and high convergence speed, but is easy to fall into local optimum along with the increase of iteration times. In Order to effectively improve the convergence speed of the traditional PSO algorithm and avoid the traditional PSO algorithm from falling into a local optimal solution, a Fractional Order differential term is introduced on the basis of the traditional PSO algorithm, the improved Fractional Order Particle Swarm algorithm (FOPSO) has inherent memory characteristics of a Fractional Order, and meanwhile, the adjustable range of the parameters of the controller is enlarged and more flexible. In the present invention, the subsequent corresponding terms are expressed using english abbreviation.
Referring to fig. 1 to 5, the present invention provides a design method of an active disturbance rejection controller of an unmanned aerial vehicle based on an FOPSO algorithm, including the following steps:
s1: establishing a four-rotor unmanned aerial vehicle dynamic model;
s2: designing an active disturbance rejection controller according to the four-rotor unmanned aerial vehicle dynamic model;
s3: improved PSO algorithm with addition of fractional order differential operatorObtaining an FOPSO algorithm;
s4: and setting the adjustable parameters of the active disturbance rejection controller by using the FOPSO algorithm.
The design method of the unmanned aerial vehicle active disturbance rejection controller based on the FOPSO algorithm adopts a cascade controller, the cascade controller comprises a PD controller and an active disturbance rejection controller, the PD controller is responsible for outer ring position control, and the active disturbance rejection controller is responsible for inner ring attitude control.
The active disturbance rejection controller consists of a tracking differentiator, an extended state observer and a nonlinear state error feedback law.
In the process of designing the active disturbance rejection controller according to the four-rotor unmanned aerial vehicle dynamic model, firstly, the reference values of the pitch angle and the roll angle are solved reversely according to the PD controller of the horizontal position, then the expected pitch angle is input into the tracking differentiator, meanwhile, the extended state observer of the pitch angle is established, and the final control quantity of the active disturbance rejection controller is obtained through the nonlinear state error feedback law.
Adding fractional order differential operator in improved PSO algorithmIn the process of obtaining the FOPSO algorithm, the original velocity equation of the PSO algorithm needs to be rearranged, and the order of velocity differentiation is generalized to be a real number alpha belonging to [0,1]]。
In the process of setting the adjustable parameters of the active disturbance rejection controller by using the FOPSO algorithm, a fitness function in a preset range is selected as a speed and position updating basis of the FOPSO algorithm, and the set parameters are input into the active disturbance rejection controller after the operation of the FOPSO algorithm is finished.
The design method of the unmanned aerial vehicle active disturbance rejection controller based on the FOPSO algorithm further comprises a cascade controller, wherein an outer ring is a PD controller, and an inner ring is an active disturbance rejection controller. The active disturbance rejection controller consists of a Tracking Differentiator (TD), an Extended State Observer (ESO) and nonlinear state error feedback (NLSEF). Selecting beta in ESO1,β2,β3And NK in LSEF1,k2As the input particles of the FOPSO algorithm provided by the invention, a fitness function in a preset range is selected as a speed and position updating basis of the FOPSO algorithm, and after the iterative operation is finished, the parameter setting result of the active disturbance rejection controller is obtained to complete the design of the active disturbance rejection controller, wherein the specific technical scheme comprises the following implementation steps:
step 1: the four-rotor unmanned aerial vehicle is subjected to dynamics modeling, and the dynamics model can be simplified into a linear form as follows:
wherein the content of the first and second substances,
where phi, theta, psi denote roll, pitch and yaw angles, respectively, in an inertial coordinate system, the point marks on the symbols denote the derivative of the variable, and two points denote the second derivative, e.g.Representing roll angular acceleration; m is the total mass of the unmanned plane, JiRepresenting the moment of inertia of each axis; u shape1For height control, U2~U4Is an attitude angle control amount. KpIs the lift coefficient of the rotor, KdFor the back-twist coefficient, l represents the distance from the motor rotor to the center of mass of the unmanned aerial vehicle, omegaiRepresenting the rotor speed squared.
Step 2: and (3) designing an active disturbance rejection controller of the quad-rotor unmanned aerial vehicle according to the scalar model of the attitude loop in the step (1) to provide necessary instructions for the FOPSO algorithm to set the parameters of the controller.
Transforming the rotational motion equation in step1 into:
wherein the content of the first and second substances,
in the formula fiIs a disturbance inside the system, xiiFor external disturbances, niTo control the gain.
Taking pitch angle θ as an example, the pitch system state equation can be expressed as:
in the formula y1=θ,y3=f(y1,y2And ξ (t)) ═ g (t) is the total perturbation of the system.
In addition, the PD controller according to the horizontal position reversely solves the reference values of the pitch angle and the roll angle, and inputs the reference values into the attitude ring control system. The PD control method is selected to adjust the control of the level and the height of the four rotors, and comprises the following steps:
wherein e isx,ey,ezRespectively, the tracking error of the system position, Kpx,Kpy,Kpz,Kdx,Kdy,KdzRespectively, the controller parameters for the corresponding channel. According to the high and horizontal motion equations in the built four-rotor dynamic model, the following equations can be obtained:
reference values for pitch angle θ and roll angle φ:
will have a desired pitch angle thetadInputting into TD to obtain tracking signal theta of pitch angled1And a differential signal thetad2。
The ESO to establish pitch angle is:
then according to the NLSEF principle, the state error of the pitching channel is as follows:
the final control quantity is obtained as follows:
and step 3: improving PSO algorithm, adding fractional order differential operatorThe speed update formula of the PSO algorithm is improved.
The fractional differential of Gr nwald-Letniko for the unary function x (t) is defined as:
where a, t are the upper and lower bounds of the calculus operator, and a ∈ R, α ∈ (0,1], Γ (—) is the gamma function the approximate expression of equation (13) is:
where T is the sampling period and r is the truncation order.
In order to modify the order of the velocity derivative, the original velocity equations of the particle swarm algorithm need to be rearranged:
in the formulaFor random learning factors, influencing the optimization result pbestAnd gbest;pbestFor the individual optimal solution, gbestRepresenting a globally optimal solution. V on the left side of formula (15)t+1-VtIs a discrete form of differentiation at an order α of 1 (assuming T is 1), so:
considering the characteristic of fractional calculus, the order of speed differentiation can be generalized to real number alpha epsilon [0,1], so that smoother change and longer memory effect can be obtained. Considering the first r of the given differential definitional equation as 4, the velocity update equation is rewritten as:
the location update formula is unchanged, and still:
Xt+1=Xt+Vt+1 (18)
and 4, step 4: the FOPSO algorithm sets adjustable parameters of the active disturbance rejection controller.
Selecting beta in ESO1,β2,β3And k in NLSEF1,k2As input particles for the FOPSO algorithm. Selecting a proper fitness function as the speed and position updating basis of the FOPSO algorithm, wherein the fitness of the algorithmThe function takes the ITAE criterion, the basic form is as follows:
where m is the algorithm running time and e (t) is the system real-time error.
Inputting the set parameters into the active disturbance rejection attitude controller after the operation of the algorithm is finished, wherein the algorithm comprises the following steps:
step1 initialization, determining particle swarm size N and learning factor c1And c2Problem dimension d, maximum number of iterations IMThe position of the particle and the upper and lower limits of the velocity, and randomly generating N initial velocities.
Step2, constructing a new fitness function according to ADRC debugging experience, and calculating the fitness value F of each particles。
Step3 for each particle, determining the fitness value F of the particlesIndividual optimal position P over historyiThe current fitness value is set as the individual extreme value PbestAnd the current position is the individual optimal position.
Step4 for each particle, determining the fitness value F of the particlesGlobal optimum position P over historygThen the current fitness value is set as a global extreme value GbestAnd the current position is a global optimal position.
Step5, updating the speed and position of the particle according to the updating formula of the group speed and position of the particle, and limiting the speed and position to VmaxAnd [ X ]min,Xmax]And (4) the following steps.
Step6 outputs the solution of each particle if the termination condition is reached, otherwise, the iteration number is updated, and the process goes to Step 2.
Furthermore, the invention can build a Simulink simulation example, comprehensively compare various optimization algorithms and analyze results.
Building a simulation model through an S function, and assuming that an initial attitude angle and an initial height are both 0, giving an instruction of a position channel as xd=cost,yd=sint,zdAnd setting the expected yaw angle to be 30 degrees, and using a PSO algorithm, a Genetic Algorithm (GA), a Grey wolf optimization algorithm (GWO) and an Adaptive Particle Swarm Optimization (APSO) to optimize parameters of the ADRC controller, and verifying whether overshoot, adjusting time, stability and steady-state error reach 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 (6)
1. A design method of an unmanned aerial vehicle active disturbance rejection controller based on an FOPSO algorithm is characterized by comprising the following steps:
establishing a four-rotor unmanned aerial vehicle dynamic model;
designing an active disturbance rejection controller according to the four-rotor unmanned aerial vehicle dynamic model;
improved PSO algorithm with addition of fractional order differential operatorObtaining an FOPSO algorithm;
and setting the adjustable parameters of the active disturbance rejection controller by using the FOPSO algorithm.
2. The design method of the FOPSO algorithm-based drone active-disturbance-rejection controller of claim 1, wherein the design method of the FOPSO algorithm-based drone active-disturbance-rejection controller adopts a cascade controller, the cascade controller comprises a PD controller and an active-disturbance-rejection controller, the PD controller is responsible for outer-loop position control, and the active-disturbance-rejection controller is responsible for inner-loop attitude control.
3. The design method of the unmanned aerial vehicle active disturbance rejection controller based on the FOPSO algorithm, according to claim 2, wherein the active disturbance rejection controller is composed of a tracking differentiator, an extended state observer and a nonlinear state error feedback law.
4. The design method of the unmanned aerial vehicle active disturbance rejection controller based on the FOPSO algorithm as claimed in claim 3, wherein in the design process of the active disturbance rejection controller according to the dynamical model of the quad-rotor unmanned aerial vehicle, the PD controller according to the horizontal position is used to solve the reference values of the pitch angle and the roll angle, and then the expected pitch angle is input to the tracking differentiator, and simultaneously the extended state observer of the pitch angle is established, and the final control quantity of the active disturbance rejection controller is obtained from the nonlinear state error feedback law.
5. The design method of the unmanned aerial vehicle active disturbance rejection controller based on the FOPSO algorithm as claimed in claim 4, wherein a fractional order differential operator is added in the improved PSO algorithmIn the process of obtaining the FOPSO algorithm, the original velocity equation of the PSO algorithm needs to be rearranged, and the order of velocity differentiation is generalized to be a real number alpha belonging to [0,1]]。
6. The design method of the unmanned aerial vehicle active disturbance rejection controller based on the FOPSO algorithm, according to claim 5, wherein in the process of setting the adjustable parameters of the active disturbance rejection controller by using the FOPSO algorithm, a fitness function in a preset range is selected as a speed and position updating basis of the FOPSO algorithm, and the set parameters are input into the active disturbance rejection controller after the operation of the FOPSO algorithm is finished.
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CN113985740A (en) * | 2021-12-30 | 2022-01-28 | 中国科学院空天信息创新研究院 | Stability control method and device based on particle active disturbance rejection |
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CN115657703A (en) * | 2022-12-27 | 2023-01-31 | 南京理工大学 | Fire-fighting unmanned aerial vehicle attitude control method based on improved active disturbance rejection controller |
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Cited By (6)
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CN113759722A (en) * | 2021-09-13 | 2021-12-07 | 桂林电子科技大学 | Parameter optimization method for active disturbance rejection controller of unmanned aerial vehicle |
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CN113985740A (en) * | 2021-12-30 | 2022-01-28 | 中国科学院空天信息创新研究院 | Stability control method and device based on particle active disturbance rejection |
CN114879502A (en) * | 2022-05-23 | 2022-08-09 | 中国科学院光电技术研究所 | Parameter self-tuning method for position ring active disturbance rejection controller |
CN114879502B (en) * | 2022-05-23 | 2023-06-30 | 中国科学院光电技术研究所 | Parameter self-tuning method for position loop active disturbance rejection controller |
CN115657703A (en) * | 2022-12-27 | 2023-01-31 | 南京理工大学 | Fire-fighting unmanned aerial vehicle attitude control method based on improved active disturbance rejection controller |
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