# c# 实现模糊PID控制算法

```using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Text;

namespace FuzzyPID
{
class FuzzyPID
{
public const int N = 7;

double target; //系统的控制目标
double actual; //采样获得的实际值
double e; //误差
double e_pre_1; //上一次的误差
double e_pre_2; //上上次的误差
double de;   //误差的变化率
double emax;  //误差基本论域上限
double demax;  //误差辩化率基本论域的上限
double delta_Kp_max;  //delta_kp输出的上限
double delta_Ki_max;  //delta_ki输出上限
double delta_Kd_max;  //delta_kd输出上限
double Ke;   //Ke=n/emax,量化论域为[-3,-2,-1,0,1,2,3]
double Kde;   //Kde=n/demax,量化论域为[-3,-2,-1,0,1,2,3]
double Ku_p;  //Ku_p=Kpmax/n,量化论域为[-3,-2,-1,0,1,2,3]
double Ku_i;  //Ku_i=Kimax/n,量化论域为[-3,-2,-1,0,1,2,3]
double Ku_d;  //Ku_d=Kdmax/n,量化论域为[-3,-2,-1,0,1,2,3]
int[,] Kp_rule_matrix = new int[N, N];//Kp模糊规则矩阵
int[,] Ki_rule_matrix = new int[N, N];//Ki模糊规则矩阵
int[,] Kd_rule_matrix = new int[N, N];//Kd模糊规则矩阵
string mf_t_e;    //e的隶属度函数类型
string mf_t_de;   //de的隶属度函数类型
string mf_t_Kp;   //kp的隶属度函数类型
string mf_t_Ki;   //ki的隶属度函数类型
string mf_t_Kd;   //kd的隶属度函数类型
double[] e_mf_paras; //误差的隶属度函数的参数
double[] de_mf_paras;//误差的偏差隶属度函数的参数
double[] Kp_mf_paras; //kp的隶属度函数的参数
double[] Ki_mf_paras; //ki的隶属度函数的参数
double[] Kd_mf_paras; //kd的隶属度函数的参数
double Kp;
double Ki;
double Kd;
double A;
double B;
double C;

public FuzzyPID(double e_max, double de_max, double kp_max, double ki_max, double kd_max, double Kp0, double Ki0, double Kd0)
{
emax = e_max;
demax = de_max;
delta_Kp_max = kp_max;
delta_Ki_max = ki_max;
delta_Kd_max = kd_max;
e = target - actual;
de = e - e_pre_1;
Ke = (N / 2) / emax;
Kde = (N / 2) / demax;
Ku_p = delta_Kp_max / (N / 2);
Ku_i = delta_Ki_max / (N / 2);
Ku_d = delta_Kd_max / (N / 2);
Kp = Kp0;
Ki = Ki0;
Kd = Kd0;
A = Kp + Ki + Kd;
B = -2 * Kd - Kp;
C = Kd;
}

//三角隶属度函数
double trimf(double x, double a, double b, double c)
{
double u;
if (x >= a && x <= b)
u = (x - a) / (b - a);
else if (x > b && x <= c)
u = (c - x) / (c - b);
else
u = 0;
return u;
}

//正态隶属度函数
double gaussmf(double x, double ave, double sigma)
{
double u;
if (sigma < 0)
{
throw new Exception("In gaussmf, sigma must larger than 0");
}
u = Math.Exp(-Math.Pow(((x - ave) / sigma), 2));
return u;
}

//梯形隶属度函数
double trapmf(double x, double a, double b, double c, double d)
{
double u;
if (x >= a && x < b)
u = (x - a) / (b - a);
else if (x >= b && x < c)
u = 1;
else if (x >= c && x <= d)
u = (d - x) / (d - c);
else
u = 0;
return u;
}

//设置模糊规则Matrix
public void setRuleMatrix(int[,] kp_m, int[,] ki_m, int[,] kd_m)
{
for (int i = 0; i < N; i++)
for (int j = 0; j < N; j++)
{
Kp_rule_matrix[i, j] = kp_m[i, j];
Ki_rule_matrix[i, j] = ki_m[i, j];
Kd_rule_matrix[i, j] = kd_m[i, j];
}

}

//设置模糊隶属度函数的子函数
void setMf_sub(string type, double[] paras, int n)
{
int N_mf_e = 0, N_mf_de = 0, N_mf_Kp = 0, N_mf_Ki = 0, N_mf_Kd = 0;
switch (n)
{
case 0:
if (type == "trimf" || type == "gaussmf" || type == "trapmf")
mf_t_e = type;
else
throw new Exception("Type of membership function must be \"trimf\" or \"gaussmf\" or \"trapmf\"");
if (mf_t_e == "trimf")
N_mf_e = 3;
else if (mf_t_e == "gaussmf")
N_mf_e = 2;
else if (mf_t_e == "trapmf")
N_mf_e = 4;

e_mf_paras = new double[N * N_mf_e];
for (int i = 0; i < N * N_mf_e; i++)
e_mf_paras[i] = paras[i];
break;

case 1:
if (type == "trimf" || type == "gaussmf" || type == "trapmf")
mf_t_de = type;
else
throw new Exception("Type of membership function must be \"trimf\" or \"gaussmf\" or \"trapmf\"");
if (mf_t_de == "trimf")
N_mf_de = 3;
else if (mf_t_de == "gaussmf")
N_mf_de = 2;
else if (mf_t_de == "trapmf")
N_mf_de = 4;
de_mf_paras = new double[N * N_mf_de];
for (int i = 0; i < N * N_mf_de; i++)
de_mf_paras[i] = paras[i];
break;

case 2:
if (type == "trimf" || type == "gaussmf" || type == "trapmf")
mf_t_Kp = type;
else
throw new Exception("Type of membership function must be \"trimf\" or \"gaussmf\" or \"trapmf\"");
if (mf_t_Kp == "trimf")
N_mf_Kp = 3;
else if (mf_t_Kp == "gaussmf")
N_mf_Kp = 2;
else if (mf_t_Kp == "trapmf")
N_mf_Kp = 4;
Kp_mf_paras = new double[N * N_mf_Kp];
for (int i = 0; i < N * N_mf_Kp; i++)
Kp_mf_paras[i] = paras[i];
break;

case 3:
if (type == "trimf" || type == "gaussmf" || type == "trapmf")
mf_t_Ki = type;
else
throw new Exception("Type of membership function must be \"trimf\" or \"gaussmf\" or \"trapmf\"");
if (mf_t_Ki == "trimf")
N_mf_Ki = 3;
else if (mf_t_Ki == "gaussmf")
N_mf_Ki = 2;
else if (mf_t_Ki == "trapmf")
N_mf_Ki = 4;
Ki_mf_paras = new double[N * N_mf_Ki];
for (int i = 0; i < N * N_mf_Ki; i++)
Ki_mf_paras[i] = paras[i];
break;

case 4:
if (type == "trimf" || type == "gaussmf" || type == "trapmf")
mf_t_Kd = type;
else
throw new Exception("Type of membership function must be \"trimf\" or \"gaussmf\" or \"trapmf\"");
if (mf_t_Kd == "trimf")
N_mf_Kd = 3;
else if (mf_t_Kd == "gaussmf")
N_mf_Kd = 2;
else if (mf_t_Kd == "trapmf")
N_mf_Kd = 4;
Kd_mf_paras = new double[N * N_mf_Kd];
for (int i = 0; i < N * N_mf_Kd; i++)
Kd_mf_paras[i] = paras[i];
break;

default: break;
}
}

//设置模糊隶属度函数的类型和参数
public void setMf(string mf_type_e, double[] e_mf,
string mf_type_de, double[] de_mf,
string mf_type_Kp, double[] Kp_mf,
string mf_type_Ki, double[] Ki_mf,
string mf_type_Kd, double[] Kd_mf)
{
setMf_sub(mf_type_e, e_mf, 0);
setMf_sub(mf_type_de, de_mf, 1);
setMf_sub(mf_type_Kp, Kp_mf, 2);
setMf_sub(mf_type_Ki, Ki_mf, 3);
setMf_sub(mf_type_Kd, Kd_mf, 4);
}

//实现模糊控制
public double realize(double t, double a)
{
double[] u_e = new double[N],
u_de = new double[N],
u_u = new double[N];
int[] u_e_index = new int[3], u_de_index = new int[3];//假设一个输入最多激活3个模糊子集
double delta_Kp, delta_Ki, delta_Kd;
double delta_u;
target = t;
actual = a;
e = target - actual;
de = e - e_pre_1;
e = Ke * e;
de = Kde * de;
/* 将误差e模糊化*/
int j = 0;
for (int i = 0; i < N; i++)
{
if (mf_t_e == "trimf")
u_e[i] = trimf(e, e_mf_paras[i * 3], e_mf_paras[i * 3 + 1], e_mf_paras[i * 3 + 2]);//e模糊化，计算它的隶属度
else if (mf_t_e == "gaussmf")
u_e[i] = gaussmf(e, e_mf_paras[i * 2], e_mf_paras[i * 2 + 1]);//e模糊化，计算它的隶属度
else if (mf_t_e == "trapmf")
u_e[i] = trapmf(e, e_mf_paras[i * 4], e_mf_paras[i * 4 + 1], e_mf_paras[i * 4 + 2], e_mf_paras[i * 4 + 3]);//e模糊化，计算它的隶属度

if (u_e[i] != 0)
u_e_index[j++] = i;        //存储被激活的模糊子集的下标，可以减小计算量
}
for (; j < 3; j++) u_e_index[j] = 0;       //富余的空间填0

/*将误差变化率de模糊化*/
j = 0;
for (int i = 0; i < N; i++)
{
if (mf_t_de == "trimf")
u_de[i] = trimf(de, de_mf_paras[i * 3], de_mf_paras[i * 3 + 1], de_mf_paras[i * 3 + 2]);//de模糊化，计算它的隶属度
else if (mf_t_de == "gaussmf")
u_de[i] = gaussmf(de, de_mf_paras[i * 2], de_mf_paras[i * 2 + 1]);//de模糊化，计算它的隶属度
else if (mf_t_de == "trapmf")
u_de[i] = trapmf(de, de_mf_paras[i * 4], de_mf_paras[i * 4 + 1], de_mf_paras[i * 4 + 2], de_mf_paras[i * 4 + 3]);//de模糊化，计算它的隶属度

if (u_de[i] != 0)
u_de_index[j++] = i;      //存储被激活的模糊子集的下标，可以减小计算量
}
for (; j < 3; j++) u_de_index[j] = 0;     //富余的空间填0

double den = 0, num = 0;
/*计算delta_Kp和Kp*/
for (int m = 0; m < 3; m++)
for (int n = 0; n < 3; n++)
{
num += u_e[u_e_index[m]] * u_de[u_de_index[n]] * Kp_rule_matrix[u_e_index[m], u_de_index[n]];
den += u_e[u_e_index[m]] * u_de[u_de_index[n]];
}
delta_Kp = num / den;
delta_Kp = Ku_p * delta_Kp;
if (delta_Kp >= delta_Kp_max) delta_Kp = delta_Kp_max;
else if (delta_Kp <= -delta_Kp_max) delta_Kp = -delta_Kp_max;
Kp += delta_Kp;
if (Kp < 0) Kp = 0;
/*计算delta_Ki和Ki*/
den = 0; num = 0;
for (int m = 0; m < 3; m++)
for (int n = 0; n < 3; n++)
{
num += u_e[u_e_index[m]] * u_de[u_de_index[n]] * Ki_rule_matrix[u_e_index[m], u_de_index[n]];
den += u_e[u_e_index[m]] * u_de[u_de_index[n]];
}

delta_Ki = num / den;
delta_Ki = Ku_i * delta_Ki;
if (delta_Ki >= delta_Ki_max) delta_Ki = delta_Ki_max;
else if (delta_Ki <= -delta_Ki_max) delta_Ki = -delta_Ki_max;
Ki += delta_Ki;
if (Ki < 0) Ki = 0;
/*计算delta_Kd和Kd*/
den = 0; num = 0;
for (int m = 0; m < 3; m++)
for (int n = 0; n < 3; n++)
{
num += u_e[u_e_index[m]] * u_de[u_de_index[n]] * Kd_rule_matrix[u_e_index[m], u_de_index[n]];
den += u_e[u_e_index[m]] * u_de[u_de_index[n]];
}
delta_Kd = num / den;
delta_Kd = Ku_d * delta_Kd;
if (delta_Kd >= delta_Kd_max) delta_Kd = delta_Kd_max;
else if (delta_Kd <= -delta_Kd_max) delta_Kd = -delta_Kd_max;
Kd += delta_Kd;
if (Kd < 0) Kd = 0;

A = Kp + Ki + Kd;
B = -2 * Kd - Kp;
C = Kd;
delta_u = A * e + B * e_pre_1 + C * e_pre_2;

delta_u = delta_u / Ke;

if (delta_u >= 0.95 * target) delta_u = 0.95 * target;
else if (delta_u <= -0.95 * target) delta_u = -0.95 * target;

e_pre_2 = e_pre_1;
e_pre_1 = e;

return delta_u;
}

void showMf(string type, double[] mf_paras)
{
int tab = 0;
if (type == "trimf")
tab = 2;
else if (type == "gaussmf")
tab = 1;
else if (type == "trapmf")
tab = 3;
this.WriteLine(\$"函数类型：{mf_t_e}");
this.WriteLine("函数参数列表：");
double[] p = mf_paras;
for (int i = 0; i < N * (tab + 1); i++)
{
this.Write(p[i] + " ");
if (i % (tab + 1) == tab)
this.Write("\r\n");
}
}

public void showInfo()
{
this.WriteLine("Info of this fuzzy controller is as following:");
this.WriteLine(\$"基本论域e：[{-emax},{emax}]");
this.WriteLine(\$"基本论域de：[{-demax},{demax}]");
this.WriteLine(\$"基本论域delta_Kp：[{-delta_Kp_max},{delta_Kp_max}]");
this.WriteLine(\$"基本论域delta_Ki：[{-delta_Ki_max},{delta_Ki_max}]");
this.WriteLine(\$"基本论域delta_Kd：[{-delta_Kd_max},{delta_Kd_max}]");
this.WriteLine("误差e的模糊隶属度函数参数：");
showMf(mf_t_e, e_mf_paras);
this.WriteLine("误差变化率de的模糊隶属度函数参数：");
showMf(mf_t_de, de_mf_paras);
this.WriteLine("delta_Kp的模糊隶属度函数参数：");
showMf(mf_t_Kp, Kp_mf_paras);
this.WriteLine("delta_Ki的模糊隶属度函数参数：");
showMf(mf_t_Ki, Ki_mf_paras);
this.WriteLine("delta_Kd的模糊隶属度函数参数：");
showMf(mf_t_Kd, Kd_mf_paras);
this.WriteLine("模糊规则表：");
this.WriteLine("delta_Kp的模糊规则矩阵");
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
this.Write(Kp_rule_matrix[i, j]);
}
this.Write("\r\n");
}
this.WriteLine("delta_Ki的模糊规则矩阵"); ;
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
this.WriteLine(Ki_rule_matrix[i, j]);
}
WriteEnd();
}
this.WriteLine("delta_Kd的模糊规则矩阵"); ;
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
this.WriteLine(Kd_rule_matrix[i, j]);
}
WriteEnd();
}
this.WriteLine(\$"误差的量化比例因子Ke={Ke}");
this.WriteLine(\$"误差变化率的量化比例因子Kde={Kde}");
this.WriteLine(\$"输出的量化比例因子Ku_p={Ku_p}");
this.WriteLine(\$"输出的量化比例因子Ku_i={Ku_i}");
this.WriteLine(\$"输出的量化比例因子Ku_d={Ku_d}");
this.WriteLine(\$"设定目标target={target}");
this.WriteLine(\$"误差e={e}");
this.WriteLine(\$"Kp={Kp}");
this.WriteLine(\$"Ki={Ki}");
this.WriteLine(\$"Kd={Kd}");
WriteEnd();
}

public void Write(object str)
{
Console.Write(str);
}
public void WriteLine(object str)
{
Console.WriteLine(str);
}
public void WriteEnd()
{
Console.Write("\r\n");
}

public static void test()
{
int NB = -3;
int NM = -2;
int NS = -1;
int ZO = 0;
int PS = 1;
int PM = 2;
int PB = 3;

double target = 300;
double actual = 400;
double u = 0;

int[,] deltaKpMatrix = new int[7, 7] {{PB,PB,PM,PM,PS,ZO,ZO
},
{PB,PB,PM,PS,PS,ZO,NS
},
{PM,PM,PM,PS,ZO,NS,NS},
{PM,PM,PS,ZO,NS,NM,NM},
{PS,PS,ZO,NS,NS,NM,NM},
{PS,ZO,NS,NM,NM,NM,NB},
{ZO,ZO,NM,NM,NM,NB,NB}};
int[,] deltaKiMatrix = new int[7, 7]{{NB,NB,NM,NM,NS,ZO,ZO},
{NB,NB,NM,NS,NS,ZO,ZO},
{NB,NM,NS,NS,ZO,PS,PS},
{NM,NM,NS,ZO,PS,PM,PM},
{NM,NS,ZO,PS,PS,PM,PB},
{ZO,ZO,PS,PS,PM,PB,PB},
{ZO,ZO,PS,PM,PM,PB,PB}};
int[,] deltaKdMatrix = new int[7, 7]{{PS,NS,NB,NB,NB,NM,PS},
{PS,NS,NB,NM,NM,NS,ZO},
{ZO,NS,NM,NM,NS,NS,ZO},
{ZO,NS,NS,NS,NS,NS,ZO},
{ZO,ZO,ZO,ZO,ZO,ZO,ZO},
{PB,NS,PS,PS,PS,PS,PB},
{PB,PM,PM,PM,PS,PS,PB}};
double[] e_mf_paras = { -3, -3, -2, -3, -2, -1, -2, -1, 0, -1, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 3 };
double[] de_mf_paras = { -3, -3, -2, -3, -2, -1, -2, -1, 0, -1, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 3 };
double[] Kp_mf_paras = { -3, -3, -2, -3, -2, -1, -2, -1, 0, -1, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 3 };
double[] Ki_mf_paras = { -3, -3, -2, -3, -2, -1, -2, -1, 0, -1, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 3 };
double[] Kd_mf_paras = { -3, -3, -2, -3, -2, -1, -2, -1, 0, -1, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 3 };

var fuzzypid = new FuzzyPID(1500, 1000, 0.3, 0.9, 0.6, 0.01, 0.04, 0.01);
fuzzypid.setMf("trimf", e_mf_paras, "trimf", de_mf_paras, "trimf", Kp_mf_paras, "trimf", Ki_mf_paras, "trimf", Kd_mf_paras);
fuzzypid.setRuleMatrix(deltaKpMatrix, deltaKiMatrix, deltaKdMatrix);

for (int i = 0; i < 50; i++)
{
u = fuzzypid.realize(target, actual);
actual += u;
Console.WriteLine(\$"{i}  {target} {u} {actual}");

//if (i>19)
//{
//  target = 300;
//}
}
//fuzzypid.showInfo();

}

}
}```