├── static └── scenario.png ├── docs └── 水箱液位的模糊控制系统设计.pdf ├── README.md ├── src ├── main.m └── test.m └── LICENSE /static/scenario.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/SAKURA-CAT/water-tank/HEAD/static/scenario.png -------------------------------------------------------------------------------- /docs/水箱液位的模糊控制系统设计.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/SAKURA-CAT/water-tank/HEAD/docs/水箱液位的模糊控制系统设计.pdf -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # water-tank: 单水箱液位模糊控制系统设计 2 | 3 | 《基于Matlab的单水箱液位的模糊控制系统设计》是本人的一次课堂作业，由于网上的资源不是很多，所以这边分享一个我对我们的"祖传代码"稍加修改的版本。 4 | 5 | ## 1. 情景说明 6 | 7 | ![scenario](./static/scenario.png) 8 | 9 | 如上图所示，有一个倒锥形容器盛放水，有一个出水口`V_2`，一个入水口`V_1`，现在可以通过测量装置得到当前容器中的水位`h`，现在需要设计一个模糊控制系统，使得水位`h`能够稳定在某个目标值。 10 | 11 | 因此有如下关系： 12 | 13 | * 控制目标：倒锥形容器的液位高度h=h0 14 | * 检测装置：通过测量容器底部压力来间接测量液位 15 | * 执行机构：控制进水电磁阀V1的开启度（[0,90°]）。 16 | * 为简单起见，假设电磁阀V1的开启度与进水量间呈线性关系（即上水箱的液位恒定）。 17 | * 注意：受控对象是倒锥形容器，其液位高度h和进水量Q间的关系不是线性关系。电磁阀V2的开度固定，但出水量与倒锥形容器的液位高度成正比。 18 | 19 | ## 2. 仓库说明 20 | 21 | > 本仓库只供学习使用，并且因为本人也比较🥦，所以有不妥之处欢迎指正~ 22 | 23 | 一般情况下，如果要“抄作业”，应该先跑代码（校验一下可行性，一般情况下应该跑得通），然后再看笔者与小组成员上交的文档，这样可以更好地理解。 24 | 25 | ### 2.1 文档说明 26 | 27 | 为了观看体验和上传的方便，我将代码和文档分开了，文档在`./docs`文件夹下，代码在`./src`文件夹下。并且为了观看格式的统一，我将文档转为了PDF格式。 28 | 29 | ### 2.2 代码说明 30 | 31 | 由于文档中对模糊控制规则进行了对照试验，分为[25规则](./src/main.m)与[5规则](./src/test.m)，所以代码也分为了两个版本。 32 | 33 | 另一方面，笔者在使用使用的matlab的时候，会有警告说相关的api即将被弃用（但是偷懒所以笔者没改），所以如果来者在跑代码的时候发现跑不通，可以提交[issue](https://github.com/SAKURA-CAT/water-tank/issues)，我看到会尽快修复。 34 | 35 | > 或者提交[PR](https://github.com/SAKURA-CAT/water-tank/pulls)也行~ 36 | 37 | ## 3. 代码运行 38 | 39 | 导入matlab后直接运行即可。两份代码实际上只有在模糊规则定义的部分会有不同，但是为了单个文件的可执行性，会有一些重复的部分。 40 | 41 | ## 4. 其他 42 | 43 | 也没啥了，如果来者能够采纳我们小组的代码——或者我们的工作对你有所帮助，将是我们的荣幸。 44 | -------------------------------------------------------------------------------- /src/main.m: -------------------------------------------------------------------------------- 1 | % 水箱的数学模型函数： 2 | function y=func( h,u ) 3 | ki = 0.306; 4 | ko = 0.212; 5 | y = (-ko*sqrt(h)+ki*u)/(3.1415926*(1+2*sqrt(3)*h/3+(h^2)/3)); 6 | end 7 | % 主程序： 8 | %定义模糊控制器 9 | a=newfis('Water Tank'); 10 | %定义高度误差e的隶属度函数 11 | a=addvar(a,'input','e',[-1 1]); 12 | a=addmf(a,'input',1,'N','trapmf',[-1,-1,-0.8,0]); 13 | a=addmf(a,'input',1,'ZR','trimf' ,[-0.8,0,0.8]); 14 | a=addmf(a,'input',1,'P','trapmf',[0,0.8,1,1]); 15 | %定义高度误差变化率de的隶属度函数 16 | a=addvar(a,'input','de',[-1 1]); 17 | a=addmf(a,'input',2,'N','trapmf' ,[-1,-1,-0.8,0]); 18 | a=addmf(a,'input',2,'ZR','trimf' ,[-0.8,0,0.8]); 19 | a=addmf(a,'input',2,'B','trapmf' ,[0,0.8,1,1]); 20 | %定义输出变量（入水阀门开关度）u的隶属度函数 21 | a=addvar(a,'output','u',[-5 5]); 22 | a=addmf(a,'output',1,'NB','trapmf',[-5,-5,-4,-2]); 23 | a=addmf(a,'output',1,'NS','trimf',[-4,-2,0]); 24 | a=addmf(a,'output',1,'ZR','trimf',[-2,0,2]); 25 | a=addmf(a,'output',1,'PS','trimf',[0,2,4]); 26 | a=addmf(a,'output',1,'PB','trapmf',[2,4,5,5]); 27 | 28 | % 绘制定义的隶属度函数 29 | figure(1); 30 | 31 | % 绘制水位差e的隶属度函数 32 | subplot(2,1,1); 33 | plotmf(wt, 'input', 1); % 绘制水位差e的隶属度函数 34 | 35 | % 设置图标题和坐标轴标签 36 | title('水位差e的隶属度函数'); 37 | xlabel('水位差e'); 38 | ylabel('隶属度'); 39 | 40 | % 绘制水位变化率de的隶属度函数 41 | subplot(2,1,2); 42 | plotmf(wt, 'input', 2); % 绘制水位变化率de的隶属度函数 43 | 44 | % 设置图标题和坐标轴标签 45 | title('水位变化率de的隶属度函数'); 46 | xlabel('水位变化率de'); 47 | ylabel('隶属度'); 48 | 49 | 50 | %定义模糊规则 51 | rulelist = [1 0 5 1 2;2 1 4 1 1;2 2 3 1 1;2 3 2 1 1;3 0 1 1 2]; 52 | a=addrule(a,rulelist); 53 | 54 | %定义采样时间间隔 55 | T=1; 56 | %定义总采样点数 57 | N=2500; 58 | 59 | % 初始高度 60 | h = 10; 61 | %预想达到的液面高度 62 | hd1 = 5; 63 | 64 | e = h - hd1; %计算初始时刻的液面误差 65 | de = 0; %设定初始时刻液面误差变化率为0 66 | %误差变化率的系数，以求得模糊推理中论域内的误差变化率 67 | %针对de，其余两个参数设置为1 68 | kd = 5.9; 69 | %定义水箱进水口阀门的绝对开关量 70 | u1 = 0; 71 | 72 | % 保存采样集合 73 | hd = zeros(1, N); % 理想页面高度 74 | yy = zeros(1, N); % 实际高度 75 | ed = zeros(1, N); % 高度差e 76 | dd = zeros(1, N); % 高度差变化率de 77 | uu = zeros(1, N); % 阀门开启度 78 | 79 | 80 | % 开始采样 81 | for k = 1:N 82 | hd(1,k) = hd1; 83 | 84 | %求得论域内的误差变化率 85 | de1 = kd*de; 86 | if e>=1 87 | e=1; 88 | elseif e<=-1 89 | e=-1; 90 | end 91 | if de1>=1 92 | de1=1; 93 | end 94 | %输入模糊控制器的参数 95 | in = [e de1]; 96 | ed(1, k) = e; 97 | dd(1, k) = de1; 98 | 99 | %得出模糊控制器的输出结果（进水阀门开启或关闭的变化量 100 | u = evalfis(in,a); 101 | u1 = u1+u; %得到阀门此时的绝对开启量 102 | %判断此时阀门绝对开启量与最大开启量的关系 103 | if u1>=5 104 | u1=5; 105 | elseif u1<=0 106 | u1=0; 107 | end 108 | 109 | uu(1,k)=u1; %将每一采样点时刻的绝对开启量存入一数组uu 110 | %阀门绝对开启度作用于控制对象 111 | k1 = func(h,u1); 112 | k2 = func(h+T*k1/2,u1); 113 | k3 = func(h+T*k2/2,u1); 114 | k4 = func(h+T*k3,u1); 115 | h = h+(k1+2*k2+2*k3+k4)*T/6; %用龙格库塔法求出每一采样时刻的液面高度 116 | yy(1,k)=h; %将每一采样时刻液面高度存入数组yy 117 | e1 = e; %将误差赋给新变量e1 118 | e = h-hd(1,k); %求得新的误差 119 | de = (e-e1)/T; %得出新的误差变化率 120 | end 121 | 122 | % 页面高度变化 123 | figure(2); 124 | plot(1:N,hd,'k',1:N, yy,'r'); 125 | grid on 126 | xlabel('时间（秒）'); 127 | ylabel('液面高度'); 128 | 129 | % 阀门开启量变化 130 | figure(3); 131 | plot(1:N,uu,'b'); 132 | grid on 133 | xlabel('时间（秒）'); 134 | ylabel('输入阀门开关度'); 135 | 136 | % 创建一个新的图形窗口，并设置两个子图的位置 137 | figure(4); 138 | 139 | % 绘制输入e的变化曲线 140 | subplot(2,1,1); 141 | plot(1:N, ed, 'b'); 142 | xlabel('时间（秒）'); 143 | ylabel('e输入变化曲线'); 144 | 145 | % 绘制输入de的变化曲线 146 | subplot(2,1,2); 147 | plot(1:N, dd, 'b'); 148 | xlabel('时间（秒）'); 149 | ylabel('de输入变化曲线'); 150 | -------------------------------------------------------------------------------- /src/test.m: -------------------------------------------------------------------------------- 1 | function y = fu(h, u) 2 | ko = 0.5; 3 | ki = 0.067; 4 | y = (-ko*h + ki*u) / (3.1415926*(1 + 2*sqrt(3)*h/3 + (h^2)/3)); 5 | end 6 | 7 | 8 | %定义模糊控制器 9 | a = newfis('Water Tank'); 10 | %定义高度误差e的隶属度函数 11 | a=addvar(a,'input','e',[-2 2]); 12 | a = addmf(a, 'input', 1, 'N', 'trimf', [-3, -2, 0]); 13 | a = addmf(a, 'input', 1, 'ZO', 'trimf', [-1.5, 0, 1.5]); 14 | a = addmf(a, 'input', 1, 'P', 'trimf', [0, 2, 3]); 15 | %定义高度误差变化率de的隶属度函数 16 | a=addvar(a,'input','de',[-2 2]); 17 | a = addmf(a, 'input', 2, 'N', 'trimf', [-3, -2, 0]); 18 | a = addmf(a, 'input', 2, 'ZO', 'trimf', [-1.5, 0, 1.5]); 19 | a = addmf(a, 'input', 2, 'P', 'trimf', [0, 2, 3]); 20 | %定义输出变量（入水阀门开关度）u的隶属度函数 21 | a = addvar(a, 'output', 'u', [-2 2]); 22 | a = addmf(a, 'output', 1, 'NB', 'trimf', [-3, -2,-1]); 23 | a = addmf(a, 'output', 1, 'NS', 'trimf', [-2, -1, 0]); 24 | a = addmf(a, 'output', 1, 'ZO', 'trimf', [-1, 0, 1]); 25 | a = addmf(a, 'output', 1, 'PS', 'trimf', [0, 1, 2]); 26 | a = addmf(a, 'output', 1, 'PB', 'trimf', [1, 2, 3]); 27 | 28 | %定义模糊规则 29 | rulelist = [ 30 | 1 0 5 1 2; 31 | 2 1 4 1 1; 32 | 2 2 3 1 1; 33 | 2 3 2 1 1; 34 | 3 0 1 1 2 35 | ]; 36 | a=addrule(a,rulelist); 37 | showrule(a) 38 | 39 | 40 | % 绘制定义的隶属度函数 41 | figure(1); 42 | 43 | % 绘制水位差e的隶属度函数 44 | subplot(3, 1, 1); 45 | plotmf(a, 'input', 1); 46 | ylabel('隶属度函数'); 47 | xlabel('水位差e'); 48 | 49 | % 绘制水位变化率de的隶属度函数 50 | subplot(3, 1, 2); 51 | plotmf(a, 'input', 2); 52 | ylabel('隶属度函数'); 53 | xlabel('水位变化率de'); 54 | 55 | % 绘制阀门变量u的隶属度函数 56 | subplot(3, 1, 3); 57 | plotmf(a, 'output', 1); 58 | ylabel('隶属度函数'); 59 | xlabel('阀门开度u'); 60 | 61 | 62 | 63 | T = 1; %定义采样时间间隔 64 | N = 1000; %定义总采样点数 65 | h0 = 5; %预计达到的高度 66 | h = 10; %初始高度 67 | e = h - h0; %计算初始时刻的液面误差 68 | de = 0; %设定初始时刻液面误差变化率为0 69 | u1 = 0; %定义水箱进水口阀门的绝对开关量 70 | % 映射系数 71 | ke = 0.1; 72 | kd = 1.2; 73 | 74 | % 将u从论域中映射回真实角度 75 | ku = 45; 76 | 77 | % 保存采样集合 78 | h00 = zeros(1, N); %理想高度 79 | hh = zeros(1, N); %实际高度 80 | ee = zeros(1, N); %高度差e 81 | dee = zeros(1, N); %高度差变化率de 82 | uu = zeros(1, N); %阀门开启度变化率 83 | u11 = zeros(1, N); %阀门绝对开启度[0,90] 84 | 85 | %将模糊控制器作用于被控对象 86 | for k = 1:N 87 | %理想液面高度 88 | h00(1, k) = h0; 89 | 90 | e1 = ke*e; 91 | de1 = kd*de; 92 | if e1 >= 2 93 | e1 = 2; 94 | elseif e1 <=-2 95 | e1 = -2; 96 | end 97 | % 记录到集合 98 | ee(1, k) = e1; 99 | dee(1, k) = de1; 100 | 101 | in = [e1 de1]; 102 | u = evalfis(in, a); %得出模糊控制器的输出结果（进水阀门开启或关闭的变化量） 103 | if u >= 2 104 | u = 2; 105 | elseif u <= -2 106 | u = -2; 107 | end 108 | 109 | uu(1, k) = u; 110 | %阀门绝对开启量，题目限制为0到90度 111 | u1 = ku * u + u1; 112 | 113 | if u1 >=90 114 | u1=90; 115 | elseif u1<=0 116 | u1=0; 117 | end 118 | 119 | u11(1, k) = u1; 120 | 121 | %用龙格库塔法求出每一采样时刻的液面高度 122 | k1 = fu(h, u1); 123 | k2 = fu(h + T*k1/2, u1); 124 | k3 = fu(h + T*k2/2, u1); 125 | k4 = fu(h + T*k3, u1); 126 | h = h + (k1 + 2*k2 + 2*k3 + k4) * T/6; 127 | hh(1, k) = h; %将每一采样时刻液面高度存入数组hh 128 | 129 | e2 = e; %将误差赋给e2 130 | e = h - h0; %求得新的误差 131 | de = (e - e2) / T; %得出新的误差变化率 132 | end 133 | 134 | %将每一采样时刻构成的时间序列作为一时间轴 135 | kk = 1:N; 136 | 137 | %画出预想的液面高度，以及实际液面高度随时间的变化 138 | figure(2); 139 | plot(kk, hh, 'k', kk, h00, 'r'); 140 | grid on 141 | xlabel('时间（秒）'); 142 | ylabel('液面高度'); 143 | legend('实际高度', '预期高度') 144 | 145 | %画出进水阀门的绝对开启量随时间的变化 146 | figure(3); 147 | plot(kk, uu, 'b'); 148 | grid on 149 | xlabel('时间（秒）'); 150 | ylabel('模糊控制器输出曲线'); 151 | 152 | % 创建一个新的图形窗口，并设置两个子图的位置 153 | figure(4); 154 | % 绘制输入e的变化曲线 155 | subplot(2, 1, 1); 156 | plot(kk, ee, 'b'); 157 | xlabel('时间（秒）'); 158 | ylabel('e输入变化曲线'); 159 | 160 | % 绘制输入de的变化曲线 161 | subplot(2, 1, 2); 162 | plot(kk, dee, 'b'); 163 | xlabel('时间（秒）'); 164 | ylabel('de输入变化曲线'); 165 | 166 | %画出进水阀门的绝对开启量随时间的变化 167 | figure(5); 168 | plot(kk, u11, 'b'); 169 | grid on 170 | xlabel('时间（秒）'); 171 | ylabel('输入阀门绝对开关度'); 172 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | Apache License 2 | Version 2.0, January 2004 3 | http://www.apache.org/licenses/ 4 | 5 | TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 6 | 7 | 1. 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