模型参考自适应控制的卡尔曼滤波Matlab代码

下面是一个基于自适应控制的卡尔曼滤波的 Matlab 代码示例。这个示例主要是用于对一个双自由度系统进行状态观测和控制。

clear all;
clc;

% 系统参数
m1 = 1;
m2 = 1;
k1 = 1;
k2 = 1;
b1 = 0.1;
b2 = 0.1;

% 系统状态向量初始化
x = zeros(4, 1);
x_hat = zeros(4, 1);
x_hat_dot = zeros(4, 1);
x_ref = zeros(4, 1);

% 控制器参数
Kp = 1;
Ki = 1;
Kd = 1;
Kp_hat = 1;
Ki_hat = 1;
Kd_hat = 1;
delta_t = 0.01;

% 卡尔曼滤波器参数初始化
Q = diag([1, 1, 1, 1]);
R = diag([0.1, 0.1, 0.1, 0.1]);
P = diag([1, 1, 1, 1]);

% 系统输入
u = 0.1;

% 系统仿真循环
for i = 1:1000
    
    % 参考信号更新
    x_ref(1) = sin(i*0.01);
    x_ref(2) = cos(i*0.01);
    
    % 状态估计
    x_hat_dot = x_hat_dot + (Kp_hat * (x_ref - x_hat) + Ki_hat * (x_ref - x_hat_dot)) * delta_t;
    x_hat = x_hat + x_hat_dot * delta_t;
    
    % 卡尔曼滤波器更新
    [x_hat, P] = adaptive_kalman_filter(x, u, x_hat, P, Q, R, delta_t);
    
    % 控制器输出
    F = Kp * (x_ref - x_hat) + Ki * (x_ref - x_hat_dot) + Kd * (x_ref - x);
    
    % 系统动力学模拟
    x_dot = [x(3:4); (-k1*x(1) - k2*(x(1) - x(2)) - b1*x(3) - b2*(x(3) - x(4)) + F)/m1; (k2*(x(1) - x(2)) - b2*(x(3) - x(4)))/m2];
    x = x + x_dot * delta_t;
    
    % 输出
    disp(x_hat);
end

function [x_hat_new, P_new] = adaptive_kalman_filter(x, u, x_hat_old, P_old, Q, R, delta_t)

F = [0, 0, delta_t, 0;
     0, 0, 0, delta_t;
     -u/m1, 0, -b1/m1, -b2/m1;
     u/m2, -k2/m2, b2/m2, -b2/m2-k2/m2];
H = [1, 0, 0, 0;
     0, 1, 0, 0];

x_hat_priori = F * x_hat_old;
P_priori = F * P_old * F' + Q;
K = P_priori * H' * inv(H * P_priori * H' + R);
x_hat_new = x_hat_priori + K * (x - H * x_hat_priori);
P_new = (eye(4) - K * H) * P_priori;

end

注意：这个示例代码仅用于参考，请根据实际系统需求进行修改。