US 11,815,912 B2
Stability control method and device based on particle active disturbance rejection
Hui Feng, Beijing (CN); Jiacheng Ma, Xingtai (CN); Sheng Wang, Beijing (CN); Lei Ao, Beijing (CN); Xiangqiang Zhang, Beijing (CN); and Tao Qiao, Beijing (CN)
Assigned to Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing (CN)
Filed by Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing (CN)
Filed on Dec. 22, 2022, as Appl. No. 18/087,793.
Claims priority of application No. 202111638296.6 (CN), filed on Dec. 30, 2021.
Prior Publication US 2023/0213948 A1, Jul. 6, 2023
Int. Cl. G05D 1/08 (2006.01); B64C 39/02 (2023.01); B64B 1/50 (2006.01); B64B 1/40 (2006.01)
CPC G05D 1/0825 (2013.01) [B64B 1/50 (2013.01); B64B 1/40 (2013.01); B64C 39/022 (2013.01)] 7 Claims
OG exemplary drawing
 
1. A stability control method based on particle active disturbance rejection, comprising:
establishing an active disturbance rejection controller model according to a dynamic model and a speed loop control model of a tethered balloon system, wherein the speed loop control model is established through theoretical modeling of executive components of a control system of the tethered balloon system; and
optimizing to-be-optimized parameters of the active disturbance rejection controller model using a particle swarm optimization algorithm, and determining an optimal active disturbance rejection controller model;
optimizing, based the optimal active disturbance rejection controller model, an active disturbance rejection controller; and
performing stability control on a photoelectric pod of the tethered balloon system through the active disturbance rejection controller;
wherein the active disturbance rejection controller model is expressed as:

OG Complex Work Unit Math
where ÿ represents a differential equation of a control system of the photoelectric pod; TD represents a tracking differentiator; ESO represents an extended state observer; NLSEF represents a nonlinear state error feedback control law; f(y, y, w(k), k) represents a total disturbance; v(k) represents a system input signal; y represents an output signal; w(k) represents a total external disturbance; differential signals v1(k) and v2(k) are generated by the TD through converting the system input signal v(k); z1(k), z2(k), and z3(k) respectively represent estimators of the differential signals v1(k) and v2(k), and the total disturbance f(y, y, w(t), t); r, h, h0 are parameters of the TD; r represents a fast factor; h represents a system sampling step size; h0 represents a dimensionless parameter, which is an integer multiple of the system sampling step size h; h, β01, β02, β03, δ, b are parameters of the ESO; β01, β02, β03 are coefficient parameters related to the system sampling step size h; δ represents a coefficient, which is taken as an integer multiple of the system sampling step size h; b represents a control quantity coefficient and is a time-varying function, which is a constant b0 approximately; c, r1, h1 are parameters of the NLSEF, where c represents a damping factor, h1 represents a fast factor, and r1 represents a control quantity factor; fhan and fal are expressions of nonlinear functions, respectively; u represents a controlled object; u0(t) represents an error feedback control quantity; a, a0, a1 and a2 are dimensionless intermediate parameters;
wherein the to-be-optimized parameters of the active disturbance rejection controller model comprises β01, β02, β03, c, h1;
wherein the optimizing to-be-optimized parameters of the active disturbance rejection controller model using the particle swarm optimization algorithm, comprises:
step 1, initializing a particle swarm;
step 2, calculating a fitness value of each particle in the particle swarm according to a fitness function, wherein each particle corresponds to a combination of the to-be-optimized parameters;
step 3, updating, according to the fitness value of each particle, an individual extreme value of the particle and a global extreme value;
step 4, updating a position and a speed of each particle;
step 5, determining whether a stop condition is satisfied, outputting an optimal parameter combination, if it is determined that the stop condition is satisfied; returning to and performing the step 2, if it is determined that the stop condition is not satisfied;
wherein the fitness value of each particle is determined according to the following formula:

OG Complex Work Unit Math
where e(t) represents a deviation between a given value inputted into the fitness function and an output corresponding to the given value of the fitness function; Δe(t) represents a difference between two adjacent step outputs of the fitness function; c1 represents a weight of the deviation e(t) in the fitness function, and c2 represents a weight of a square term of the error feedback control quantity in the fitness function; u(t) represents the error feedback control quantity; and Q represents an objective function value;
wherein during the optimizing, a weight factor w is dynamically adjusted according the following formula:

OG Complex Work Unit Math
where Tmax represents a maximum iteration number, wmax and wmin represent a maximum inertia weight and a minimum inertia weight respectively, and t represents a current iteration number.