B.1 模糊PID控制器MATLAB仿真代码
% 极地船舶新风口模糊PID防冰控制系统仿真
% 物理模型说明：
% 热平衡：C_s * dT_s/dt = P_input - K_loss*(T_s - T_a)
% K_loss = h + m_dot*c_w （对流换热 + 过冷水滴升温热损失）
% P_input = P_ff + P_pid （前馈稳态功率 + PID动态修正）
% P_ff = K_loss*(T_target - T_a) （精确补偿稳态热损失）
%
% 传统PID参数整定（Z-N临界比例度法）：
% 工况1稳态：K_loss≈62.5，C_s=250，时间常数τ=C_s/K_loss=4s
% 一阶系统临界增益Ku→∞，改用经验法：
% 取τ=4s，纯比例控制稳态误差5%时 Kp_u = 1/(K_loss*0.05/C_s) ≈ 20
% Z-N推荐：Kp=0.6*Ku=12，Ti=0.5*Tu，Td=0.125*Tu
% 简化取：Kp_t=8, Ki_t=0.8, Kd_t=2.0（对应τ=4s系统的合理整定值）
%
% 模糊PID初始参数（论文3.4.5节）：Kp0=2.5, Ki0=1.0, Kd0=0.5
% 注意：这里参数是归一化值，通过Gc=K_loss放大到功率量纲
% 等效实际Kp = Kp0*K_loss ≈ 2.5*62.5 = 156，与传统PID量级一致
clear; clc; close all;
%% 1. 工况设置（论文3.5.2节，3种动态工况）
t_step = 0.05;
t_total = 150; % 工况3延长至150s，有足够稳定时间
t = 0:t_step:t_total;
N = length(t);
T_a = zeros(1,N); v_wind = zeros(1,N); RH = zeros(1,N);
for i = 1:N
if t(i) < 30
% 工况1：常规（-8℃，8m/s，75%）
T_a(i)=-8; v_wind(i)=8; RH(i)=75;
elseif t(i) < 60
% 工况2：极端低温高速（线性恶化）
r = (t(i)-30)/30;
T_a(i)=-8-14*r; v_wind(i)=8+14*r; RH(i)=75+20*r;
else
% 工况3：突变后稳定
T_a(i)=-5; v_wind(i)=5; RH(i)=65;
end
end
%% 2. 结冰速率（论文式3-2：m_dot = Ec × n × M_total，M_total=1.12×M_wind）
% 碰撞效率（论文3.1.1节）
Ec = 0.85 + 0.05*(v_wind > 15);
% 结冰系数（论文表2.2，取各区间中点值）
n_ice = zeros(1,N);
for i = 1:N
if T_a(i) >= 0, n_ice(i) = 0;
elseif T_a(i) > -10, n_ice(i) = 0.42; % -5~-10℃中点
elseif T_a(i) > -18, n_ice(i) = 0.60; % -11~-18℃中点
else, n_ice(i) = 0.76; % -19~-25℃中点
end
end
% 风飞沫量（论文表2-1，取各区间中点值）
M_wind = zeros(1,N);
for i = 1:N
if T_a(i) > -10 && v_wind(i) <= 5, M_wind(i) = 0.00015;
elseif T_a(i) > -10 && v_wind(i) <= 15, M_wind(i) = 0.00024;
elseif T_a(i) > -10, M_wind(i) = 0.000355;
elseif T_a(i) > -18 && v_wind(i) <= 5, M_wind(i) = 0.000185;
elseif T_a(i) > -18 && v_wind(i) <= 15, M_wind(i) = 0.00029;
elseif T_a(i) > -18, M_wind(i) = 0.000405;
elseif v_wind(i) <= 5, M_wind(i) = 0.000215;
elseif v_wind(i) <= 15, M_wind(i) = 0.00033;
else, M_wind(i) = 0.000465;
end
end
% 式3-2：M_total = 1.12*M_wind（含12%海浪飞沫折算）
m_dot = Ec .* n_ice .* (1.12 * M_wind);
%% 3. 对流换热系数h（论文表2.3，取各区间中点值）
h = zeros(1,N);
for i = 1:N
if T_a(i) > -10 && v_wind(i) <= 5, h(i) = 35;
elseif T_a(i) > -10 && v_wind(i) <= 15, h(i) = 62;
elseif T_a(i) > -10, h(i) = 99;
elseif T_a(i) > -18 && v_wind(i) <= 5, h(i) = 36;
elseif T_a(i) > -18 && v_wind(i) <= 15, h(i) = 63;
elseif T_a(i) > -18, h(i) = 100;
elseif v_wind(i) <= 5, h(i) = 37;
elseif v_wind(i) <= 15, h(i) = 64;
else, h(i) = 102;
end
end
%% 4. 热力学参数
T_s_target = 2; % 控制目标：2℃（0℃以上2℃安全裕量，论文2.4.1节）
c_w = 4200; % 水的定压比热容（J/(kg·℃)）
r = 335000; % 水的熔解热（J/kg）
% 综合热损失系数（W/(m²·℃)）
K_loss = h + m_dot * c_w;
% 前馈稳态功率（精确补偿稳态热损失，使系统能到达目标温度）
% 式3-3修正版：以T_s_target=2℃为目标
P_ff = K_loss .* (T_s_target - T_a);
% 论文式3-4参考值（用于结果对比展示）
P_dyn_ref = h.*(0-T_a) + m_dot.*c_w.*(0-T_a) + m_dot.*r;
% 等效热容：C_s * dT/dt = P_input - K_loss*(T_s-T_a)
% 取C_s=250，工况1时间常数τ=250/62≈4s，响应合理
C_s = 250;
P_max = 4500; % 最大功率限制（W/m²）
%% 5. 模糊控制器（论文3.4节）
fis = mamfis('Name','fuzzy_pid_anti_icing');
% 输入1：温度偏差 e = T_s - T_target（℃），论域[-25,5]
fis = addInput(fis,[-25,5],'Name','e');
fis = addMF(fis,'e','trimf',[-25,-25,-19],'Name','NVB');
fis = addMF(fis,'e','trimf',[-25,-19,-12],'Name','NB');
fis = addMF(fis,'e','trimf',[-19,-12, -5],'Name','NS');
fis = addMF(fis,'e','trimf',[-12, -5, 1],'Name','ZO');
fis = addMF(fis,'e','trimf',[ -5, 1, 5],'Name','PS');
% 输入2：湿度RH（%），论域[60,100]
fis = addInput(fis,[60,100],'Name','RH');
fis = addMF(fis,'RH','trimf',[60,60,70],'Name','PD');
fis = addMF(fis,'RH','trimf',[60,70,80],'Name','ZPD');
fis = addMF(fis,'RH','trimf',[70,80,90],'Name','ZD');
fis = addMF(fis,'RH','trimf',[80,90,95],'Name','ZPG');
fis = addMF(fis,'RH','trimf',[90,100,100],'Name','PG');
% 输入3：结冰速率（kg/(m²·s)），论域[0,0.0004]
fis = addInput(fis,[0,0.0004],'Name','m_dot');
fis = addMF(fis,'m_dot','trapmf',[0,0,0,0.00005], 'Name','不结冰');
fis = addMF(fis,'m_dot','trimf', [0,0.00005,0.00011], 'Name','低速');
fis = addMF(fis,'m_dot','trimf', [0.00005,0.00011,0.00027], 'Name','中速');
fis = addMF(fis,'m_dot','trimf', [0.00011,0.00027,0.0004], 'Name','高速');
% 输出：ΔKp∈[0,5]，ΔKi∈[0,2]，ΔKd∈[0,1]
fis = addOutput(fis,[0,5],'Name','delta_Kp');
fis = addMF(fis,'delta_Kp','trimf',[0,0,2.5],'Name','S');
fis = addMF(fis,'delta_Kp','trimf',[0,2.5,5],'Name','M');
fis = addMF(fis,'delta_Kp','trimf',[2.5,5,5],'Name','L');
fis = addOutput(fis,[0,2],'Name','delta_Ki');
fis = addMF(fis,'delta_Ki','trimf',[0,0,1],'Name','S');
fis = addMF(fis,'delta_Ki','trimf',[0,1,2],'Name','M');
fis = addMF(fis,'delta_Ki','trimf',[1,2,2],'Name','L');
fis = addOutput(fis,[0,1],'Name','delta_Kd');
fis = addMF(fis,'delta_Kd','trimf',[0,0,0.5],'Name','S');
fis = addMF(fis,'delta_Kd','trimf',[0,0.5,1],'Name','M');
fis = addMF(fis,'delta_Kd','trimf',[0.5,1,1],'Name','L');
fis.DefuzzificationMethod = 'centroid';
rules = double([
1 1 1 1 1 1 1 1; 1 2 1 1 1 1 1 1; 1 3 1 1 1 1 1 1; 1 4 1 1 1 1 1 1; 1 5 1 1 1 1 1 1;
2 1 1 1 1 1 1 1; 2 2 1 1 1 1 1 1; 2 3 1 1 1 1 1 1; 2 4 1 1 1 1 1 1; 2 5 1 2 1 1 1 1;
3 1 1 1 1 1 1 1; 3 2 1 1 1 1 1 1; 3 3 1 1 1 1 1 1; 3 4 1 1 1 1 1 1; 3 5 1 2 1 1 1 1;
4 1 1 1 1 1 1 1; 4 2 1 1 1 1 1 1; 4 3 1 1 1 1 1 1; 4 4 1 1 1 1 1 1; 4 5 1 2 1 1 1 1;
5 1 1 1 1 1 1 1; 5 2 1 1 1 1 1 1; 5 3 1 1 1 1 1 1; 5 4 1 1 1 1 1 1; 5 5 1 1 1 1 1 1;
1 1 2 2 2 1 1 1; 1 2 2 2 1 1 1 1; 1 3 2 2 1 1 1 1; 1 4 2 2 1 1 1 1; 1 5 2 3 2 2 1 1;
2 1 2 2 1 1 1 1; 2 2 2 2 1 1 1 1; 2 3 2 1 1 1 1 1; 2 4 2 1 1 1 1 1; 2 5 2 2 2 2 1 1;
3 1 2 2 1 1 1 1; 3 2 2 1 1 1 1 1; 3 3 2 1 1 1 1 1; 3 4 2 1 1 1 1 1; 3 5 2 2 1 1 1 1;
4 1 2 1 1 1 1 1; 4 2 2 1 1 1 1 1; 4 3 2 1 1 1 1 1; 4 4 2 1 1 1 1 1; 4 5 2 1 1 1 1 1;
5 1 2 1 1 1 1 1; 5 2 2 1 1 1 1 1; 5 3 2 1 1 1 1 1; 5 4 2 1 1 1 1 1; 5 5 2 1 1 1 1 1;
1 1 3 3 3 2 1 1; 1 2 3 3 2 2 1 1; 1 3 3 2 2 2 1 1; 1 4 3 2 2 1 1 1; 1 5 3 3 3 3 1 1;
2 1 3 3 2 2 1 1; 2 2 3 2 2 2 1 1; 2 3 3 2 1 1 1 1; 2 4 3 2 1 1 1 1; 2 5 3 3 2 2 1 1;
3 1 3 2 2 2 1 1; 3 2 3 2 1 1 1 1; 3 3 3 1 1 1 1 1; 3 4 3 1 1 1 1 1; 3 5 3 2 1 1 1 1;
4 1 3 2 1 1 1 1; 4 2 3 1 1 1 1 1; 4 3 3 1 1 1 1 1; 4 4 3 1 1 1 1 1; 4 5 3 2 1 1 1 1;
5 1 3 1 1 1 1 1; 5 2 3 1 1 1 1 1; 5 3 3 1 1 1 1 1; 5 4 3 1 1 1 1 1; 5 5 3 1 1 1 1 1;
1 1 4 3 3 3 1 1; 1 2 4 3 3 2 1 1; 1 3 4 3 2 2 1 1; 1 4 4 3 2 2 1 1; 1 5 4 3 3 3 1 1;
2 1 4 3 3 2 1 1; 2 2 4 3 2 2 1 1; 2 3 4 2 2 2 1 1; 2 4 4 2 2 1 1 1; 2 5 4 3 3 2 1 1;
3 1 4 3 2 2 1 1; 3 2 4 2 2 2 1 1; 3 3 4 2 1 1 1 1; 3 4 4 2 1 1 1 1; 3 5 4 3 2 2 1 1;
4 1 4 2 2 2 1 1; 4 2 4 2 1 1 1 1; 4 3 4 1 1 1 1 1; 4 4 4 1 1 1 1 1; 4 5 4 2 1 1 1 1;
5 1 4 2 1 1 1 1; 5 2 4 1 1 1 1 1; 5 3 4 1 1 1 1 1; 5 4 4 1 1 1 1 1; 5 5 4 1 1 1 1 1]);
fis = addRule(fis, rules);
writefis(fis,'fuzzy_pid_anti_icing.fis');
%% 6. 仿真循环
% ---------------------------------------------------------------
% PID参数说明：
% 控制律：P_pid = Gc*(Kp*e + Ki*∫e + Kd*de/dt)
% 其中 Gc = K_loss（控制增益，使Kp/Ki/Kd保持论文量级）
%
% 传统PID（Z-N经验整定，工况1稳态模型）：
% 系统：一阶 G(s) = 1/(C_s*s + K_loss)，τ=C_s/K_loss≈4s，K=1/K_loss
% Z-N推荐PID：Kp=1.2*τ/K/Td，取Td=τ/4=1s
% 简化：Kp_t=8, Ki_t=1.5, Kd_t=2.5（工况1整定，工况2/3参数固定→劣势）
%
% 模糊PID（论文3.4.5节初始参数）：
% Kp0=2.5, Ki0=1.0, Kd0=0.5（归一化基础值）
% 实际等效：Kp_eff=Kp0*Gc≈156，与传统PID量级一致
% 工况恶化时模糊推理增大ΔKp/ΔKi/ΔKd，自适应响应
% ---------------------------------------------------------------
% 模糊PID基础参数（论文3.4.5节）
Kp0=2.5; Ki0=1.0; Kd0=0.5;
% 传统PID（工况1整定，固定参数）
Kp_t=8.0; Ki_t=1.5; Kd_t=2.5;
% 初始化
T_s_f=zeros(1,N); T_s_t=zeros(1,N);
P_f=zeros(1,N); P_t=zeros(1,N);
Kp_log=zeros(1,N); Ki_log=zeros(1,N); Kd_log=zeros(1,N);
T_s_f(1)=T_a(1); T_s_t(1)=T_a(1);
ef_prev=0; int_ef=0;
et_prev=0; int_et=0;
int_lim=150; % 积分限幅（归一化，对应功率修正约±300W）
fprintf('仿真运行中...\n');
for i = 2:N
Gc = K_loss(i); % 控制增益
%--- 模糊PID ---
ef = T_s_target - T_s_f(i-1); % 误差（正=需加热）
% 软抗积分饱和：过零时积分衰减
if ef * ef_prev < 0, int_ef = int_ef * 0.2; end
int_ef = int_ef + ef*t_step;
int_ef = max(-int_lim, min(int_lim, int_ef));
def = (ef - ef_prev)/t_step;
% 模糊推理（输入：e=T_s-T_target，RH，m_dot）
e_in = max(-25, min(5, T_s_f(i-1)-T_s_target));
rh_in = max(60, min(100, RH(i)));
md_in = max(0, min(4e-4, m_dot(i)));
fo = evalfis(fis,[e_in,rh_in,md_in]);
Kp_f = Kp0 + fo(1);
Ki_f = Ki0 + fo(2);
Kd_f = Kd0 + fo(3);
Kp_log(i)=Kp_f; Ki_log(i)=Ki_f; Kd_log(i)=Kd_f;
u_f = Gc * (Kp_f*ef + Ki_f*int_ef + Kd_f*def);
P_f(i) = max(0, min(P_max, P_ff(i) + u_f));
Ploss_f = K_loss(i)*(T_s_f(i-1)-T_a(i));
T_s_f(i) = T_s_f(i-1) + (t_step/C_s)*(P_f(i)-Ploss_f);
ef_prev = ef;
%--- 传统PID（固定参数，无抗饱和）---
et = T_s_target - T_s_t(i-1);
int_et = int_et + et*t_step;
int_et = max(-int_lim*1.5, min(int_lim*1.5, int_et));
det = (et - et_prev)/t_step;
u_t = Gc * (Kp_t*et + Ki_t*int_et + Kd_t*det);
P_t(i) = max(0, min(P_max, P_ff(i) + u_t));
Ploss_t = K_loss(i)*(T_s_t(i-1)-T_a(i));
T_s_t(i) = T_s_t(i-1) + (t_step/C_s)*(P_t(i)-Ploss_t);
et_prev = et;
if t(i)>=30 && t(i)<30+t_step, fprintf(' 工况2：极端低温高速工况开始\n'); end
if t(i)>=60 && t(i)<60+t_step, fprintf(' 工况3：突变工况开始\n'); end
end
fprintf('仿真完成！\n\n');
%% 7. 绘图
lw=1.8; fs=10;
idx_c1=t>=0&t<=30; idx_c2=t>=30&t<=60; idx_c3=t>=60&t<=150;
figure(1); clf;
plot(t(idx_c1),T_s_f(idx_c1),'r-','LineWidth',lw,'DisplayName','模糊PID'); hold on;
plot(t(idx_c1),T_s_t(idx_c1),'b--','LineWidth',lw,'DisplayName','传统PID');
yline(T_s_target,'k:','LineWidth',1.5,'DisplayName','目标 2℃');
yline(0,'g--','LineWidth',1.0,'DisplayName','防冰临界 0℃');
xlabel('时间 t (s)','FontSize',fs); ylabel('表面温度 (℃)','FontSize',fs);
title('工况1（常规）：T_a=-8℃，v=8m/s，RH=75%','FontSize',fs);
legend('Location','southeast','FontSize',fs); grid on; xlim([0 30]);
set(gcf,'Position',[50,550,750,360]);
figure(2); clf;
plot(t(idx_c2),T_s_f(idx_c2),'r-','LineWidth',lw,'DisplayName','模糊PID'); hold on;
plot(t(idx_c2),T_s_t(idx_c2),'b--','LineWidth',lw,'DisplayName','传统PID');
yline(T_s_target,'k:','LineWidth',1.5,'DisplayName','目标 2℃');
yline(0,'g--','LineWidth',1.0,'DisplayName','防冰临界 0℃');
xlabel('时间 t (s)','FontSize',fs); ylabel('表面温度 (℃)','FontSize',fs);
title('工况2（极端）：T_a: -8→-22℃，v: 8→22m/s，RH: 75→95%','FontSize',fs);
legend('Location','best','FontSize',fs); grid on; xlim([30 60]);
set(gcf,'Position',[50,130,750,360]);
figure(3); clf;
plot(t(idx_c3),T_s_f(idx_c3),'r-','LineWidth',lw,'DisplayName','模糊PID'); hold on;
plot(t(idx_c3),T_s_t(idx_c3),'b--','LineWidth',lw,'DisplayName','传统PID');
yline(T_s_target,'k:','LineWidth',1.5,'DisplayName','目标 2℃');
yline(0,'g--','LineWidth',1.0,'DisplayName','防冰临界 0℃');
xlabel('时间 t (s)','FontSize',fs); ylabel('表面温度 (℃)','FontSize',fs);
title('工况3（突变）：T_a骤升至-5℃，v骤降至5m/s，RH降至65%','FontSize',fs);
legend('Location','best','FontSize',fs); grid on; xlim([60 150]);
set(gcf,'Position',[850,550,750,360]);
figure(4); clf;
plot(t,Kp_log,'r-','LineWidth',lw,'DisplayName','Kp'); hold on;
plot(t,Ki_log,'g-','LineWidth',lw,'DisplayName','Ki');
plot(t,Kd_log,'b-','LineWidth',lw,'DisplayName','Kd');
xline(30,'m--','LineWidth',1,'HandleVisibility','off');
xline(60,'m--','LineWidth',1,'HandleVisibility','off');
text(15,max(Kp_log)*0.9,'工况1','HorizontalAlignment','center','FontSize',9,'Color',[0.5 0.5 0.5]);
text(45,max(Kp_log)*0.9,'工况2','HorizontalAlignment','center','FontSize',9,'Color',[0.5 0.5 0.5]);
text(105,max(Kp_log)*0.9,'工况3','HorizontalAlignment','center','FontSize',9,'Color',[0.5 0.5 0.5]);
xlabel('时间 t (s)','FontSize',fs); ylabel('PID参数值','FontSize',fs);
title('模糊PID参数自整定曲线（全程）','FontSize',fs);
legend('Location','northeast','FontSize',fs); grid on;
set(gcf,'Position',[850,130,750,360]);
figure(5); clf;
plot(t,m_dot*1e4,'k-','LineWidth',lw);
xline(30,'m--','LineWidth',1); xline(60,'m--','LineWidth',1);
text(15,max(m_dot*1e4)*0.85,'工况1','HorizontalAlignment','center','FontSize',9,'Color',[0.5 0.5 0.5]);
text(45,max(m_dot*1e4)*0.85,'工况2','HorizontalAlignment','center','FontSize',9,'Color',[0.5 0.5 0.5]);
text(105,max(m_dot*1e4)*0.85,'工况3','HorizontalAlignment','center','FontSize',9,'Color',[0.5 0.5 0.5]);
xlabel('时间 t (s)','FontSize',fs);
ylabel('结冰速率 (×10⁻⁴ kg/(m²·s))','FontSize',fs);
title('结冰速率变化曲线（全程）','FontSize',fs);
grid on; set(gcf,'Position',[450,340,750,360]);
%% 8. 量化数据输出
fprintf('==================== 仿真量化数据 ====================\n');
% 工况1：上升时间（首次到达0℃/2℃）
T1f=T_s_f(idx_c1); T1t=T_s_t(idx_c1); t1=t(idx_c1);
tmp=find(T1f>=0,1,'first'); f_r0=ifv(isempty(tmp),NaN,(tmp-1)*t_step);
tmp=find(T1t>=0,1,'first'); t_r0=ifv(isempty(tmp),NaN,(tmp-1)*t_step);
tmp=find(T1f>=T_s_target,1,'first'); f_r2=ifv(isempty(tmp),NaN,(tmp-1)*t_step);
tmp=find(T1t>=T_s_target,1,'first'); t_r2=ifv(isempty(tmp),NaN,(tmp-1)*t_step);
idx1s=t>=20&t<30;
fprintf('工况1（常规）\n');
fprintf(' 首次到达0℃：模糊PID=%.1fs，传统PID=%.1fs\n',f_r0,t_r0);
fprintf(' 首次到达2℃：模糊PID=%.1fs，传统PID=%.1fs\n',f_r2,t_r2);
fprintf(' 稳态均值(20~30s)：模糊PID=%.3f℃，传统PID=%.3f℃\n',...
mean(T_s_f(idx1s)),mean(T_s_t(idx1s)));
fprintf(' 稳态偏差RMS：模糊PID=%.3f℃，传统PID=%.3f℃\n',...
rms(T_s_f(idx1s)-T_s_target),rms(T_s_t(idx1s)-T_s_target));
% 工况2：温度最低点 + 恢复时间
T2f=T_s_f(idx_c2); T2t=T_s_t(idx_c2); t2=t(idx_c2);
[mn_f,mi_f]=min(T2f); [mn_t,mi_t]=min(T2t);
fprintf('工况2（极端）\n');
fprintf(' 温度最低点：模糊PID=%.2f℃(t=%.1fs)，传统PID=%.2f℃(t=%.1fs)\n',...
mn_f,t2(mi_f),mn_t,t2(mi_t));
tmp=find(T2f(mi_f:end)>=T_s_target-0.5,1,'first');
f_rec=ifv(isempty(tmp),NaN,tmp*t_step);
tmp=find(T2t(mi_t:end)>=T_s_target-0.5,1,'first');
t_rec=ifv(isempty(tmp),NaN,tmp*t_step);
fprintf(' 从最低点恢复至1.5℃：模糊PID=%.1fs，传统PID=%.1fs\n',f_rec,t_rec);
% 工况3：超调 + 稳态
T3f=T_s_f(idx_c3); T3t=T_s_t(idx_c3);
idx3s=t>=130&t<=150;
fprintf('工况3（突变）\n');
fprintf(' 最大超调：模糊PID=%.2f℃，传统PID=%.2f℃\n',max(T3f),max(T3t));
fprintf(' 稳态均值(130~150s)：模糊PID=%.3f℃，传统PID=%.3f℃\n',...
mean(T_s_f(idx3s)),mean(T_s_t(idx3s)));
fprintf(' 稳态波动峰峰值：模糊PID=%.3f℃，传统PID=%.3f℃\n',...
max(T_s_f(idx3s))-min(T_s_f(idx3s)),...
max(T_s_t(idx3s))-min(T_s_t(idx3s)));
% 节能
fprintf('节能性（全程平均功率）\n');
fp=mean(P_f(2:end)); tp=mean(P_t(2:end));
fprintf(' 模糊PID=%.1fW/m²，传统PID=%.1fW/m²，节能=%.1f%%\n',...
fp,tp,(tp-fp)/tp*100);
fprintf('\n典型时刻（t=30/60/100/150s）：\n');
for tk=[30,60,100,150]
idx=find(t>=tk,1,'first');
fprintf(' t=%3ds：m_dot=%.5f kg/(m²·s)，P_ref=%.0fW/m²，模糊PID=%.2f℃，传统PID=%.2f℃\n',...
tk,m_dot(idx),P_dyn_ref(idx),T_s_f(idx),T_s_t(idx));
end
fprintf('=======================================================\n');
function v=ifv(c,a,b); if c,v=a; else,v=b; end; end
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