二阶弹簧阻尼系统粒子群优化matlab代码

以下是二阶弹簧阻尼系统粒子群优化的Matlab代码示例：

% 定义目标函数（稳态误差）
function e = objective(c, k)
m = 1.0;
omega = sqrt(k/m);
zeta = c/(2*sqrt(m*k));
e = 1/(1+(omega^2)*(1-zeta^2));
end

% 定义粒子群优化函数
function [gbest, gbest_fit] = pso(obj_func, dim, n_particles, n_iter, lb, ub)
% 初始化粒子群
x = rand(n_particles, dim).*(ub-lb) + lb;
v = zeros(n_particles, dim);
p = x;
pbest = inf(n_particles, 1);
gbest = zeros(1, dim);
gbest_fit = inf;

% 迭代优化
for i = 1:n_iter
    % 更新速度和位置
    r1 = rand(n_particles, dim);
    r2 = rand(n_particles, dim);
    v = 0.5*v + 2*r1.*(p-x) + 2*r2.*(repmat(gbest, n_particles, 1)-x);
    x = x + v;

    % 边界处理
    x = max(x, lb);
    x = min(x, ub);

    % 更新个体最优解和全局最优解
    for j = 1:n_particles
        fitness = obj_func(x(j,:));
        if fitness < pbest(j)
            pbest(j) = fitness;
            p(j,:) = x(j,:);
        end
        if fitness < gbest_fit
            gbest_fit = fitness;
            gbest = x(j,:);
        end
    end
end

end

% 调用粒子群优化函数求解最优解
[c_best, k_best] = pso(@objective, 2, 50, 100, 0, 10);
fprintf("最优解：c = %.4f, k = %.4f\n", c_best, k_best);
fprintf("最小稳态误差：%.4f\n", objective(c_best, k_best));

其中，objective函数定义了目标函数（稳态误差），pso函数实现了粒子群优化算法，c_best和k_best分别表示最优解的阻尼系数和弹簧劲度系数，最小稳态误差即为优化结果。