模糊控制（三）一个例程——模糊推理控制小车速度

梦里梦外; 2023-07-18 03:16 114阅读 0赞

## 模糊控制（三）一个例程——模糊推理控制小车速度 ##

飞思卡尔智能车大赛中，智能小车的速度控制算法采用模糊控制。  
比赛中的控制算法大多采用PID控制算法，PID可以对速度迅速响应，但拥有相应迅速对小车 速度的控制是不够的，还需要根据赛道实际情况设置不同的车速，以达到最快通过不同路况，以下采用模糊推理实现对小车的速度控制。  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQzOTA3NTM3_size_16_color_FFFFFF_t_70]

## 1.变量模糊化 ##

在模糊控制中，输入输出变量大小用语言形式进行描述。常选用的7个语言值为\{负大，负中，负小，零，正小，正中，正大\}，即\{NB，NM，NS，O，PS，PM，PB\}。

对小车当前行驶方向和赛道方向形成的偏差e及其变化率ec作为模糊控制器的输入，小车的目标车速为模糊控制器的输出。设偏差值的模糊量为E，偏差变化率模糊量为EC，U为目标车速。为了让速度切换更加细腻流畅，设置偏差e、偏差变化ec和控制量u的基本论域为\[-6,6\]，并划分为13个等级，即\{-6，-5，-4，-3，-2，-1，0，1，2，3，4，5，6\}。

E、EC和U均使用三角形隶属函数进行模糊化  
![在这里插入图片描述][20200323230339292.png]

/** * 列坐标：NB,NM,NS,O,PS,PM,PB * 横坐标：-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6 * @param 建立输入、输出隶属度函数,进行微调调整模糊量的范围 */
    /***************************************误差隶属度函数***************************************/
    float Input1_Terms_Membership[7][13] =
    {  1,0.15,0,0,0,0,0,0,0,0,0,0,0,
    0,0.2,1,0.2,0,0,0,0,0,0,0,0,0,
    0,0,0,0.2,1,0.2,0,0,0,0,0,0,0,
    0,0,0,0,0,0.1,1,0.1,0,0,0,0,0,
    0,0,0,0,0,0,0,0.1,1,0.1,0,0,0,
    0,0,0,0,0,0,0,0,0,0.2,1,0.2,0,
    0,0,0,0,0,0,0,0,0,0,0,0.2,1
    };
    /***************************************误差变化率隶属度函数***************************************/
    float Input2_Terms_Membership[7][13] =
    {  1,0.15,0,0,0,0,0,0,0,0,0,0,0,
    0,0.2,1,0.2,0,0,0,0,0,0,0,0,0,
    0,0,0,0.2,1,0.2,0,0,0,0,0,0,0,
    0,0,0,0,0,0.1,1,0.1,0,0,0,0,0,
    0,0,0,0,0,0,0,0.1,1,0.1,0,0,0,
    0,0,0,0,0,0,0,0,0,0.2,1,0.2,0,
    0,0,0,0,0,0,0,0,0,0,0,0.2,1
    };
    /***************************************输出（速度）***************************************/
    float Output_Terms_Membership[7][13] =
    {  1,0.15,0,0,0,0,0,0,0,0,0,0,0,
    0,0.2,1,0.2,0,0,0,0,0,0,0,0,0,
    0,0,0,0.2,1,0.2,0,0,0,0,0,0,0,
    0,0,0,0,0,0.1,1,0.1,0,0,0,0,0,
    0,0,0,0,0,0,0,0.1,1,0.1,0,0,0,
    0,0,0,0,0,0,0,0,0,0.2,1,0.2,0,
    0,0,0,0,0,0,0,0,0,0,0,0.2,1
    };

## 2.模糊查询表的计算 ##

对模糊量EC、E和U设置相关的模糊控制规则表  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQzOTA3NTM3_size_16_color_FFFFFF_t_70 1]

/** * 纵轴为E(error)，横轴为EC(error_delta)，值为速度七档NB(0),NM(1),NS(2),Z(3),PS(4),PM(5),PB(6)速度由小变大再变小 * 列坐标：E（NB,NM,NS,O,PS,PM,PB） * 横坐标：EC（NB,NM,NS,O,PS,PM,PB） * 值：U（1：NB:2,NM,3:NS,4:O,5:PS,6:PM,7:PB） * @param 模糊控制规则表，调整速度变化趋势 */
    int Rule[7][7] =
    {  1,1,2,2,6,7,7,
     1,1,2,2,6,6,6,
     1,2,3,4,5,6,6,
     1,3,4,4,4,5,7,
     2,2,3,4,5,6,7,
     2,2,2,2,6,7,7,
     1,1,2,2,6,7,7
    };//调试参数

规则库蕴含的模糊关系：  
![在这里插入图片描述][20200323230754266.png]  
其中，模糊运算×表示“取小”。

计算出模糊规则蕴含的模糊关系R后，通过遍历E和EC所有的论域对模糊值进行选取并计算模糊输出值：  
![在这里插入图片描述][20200323230819826.png]  
其中，o表示模糊矩阵的合成，类似于普通矩阵的乘积运算，将乘积运算换成“取小”，将加法运算换成“取大”。

在遍历过程中，对E和EC所有论域对应的模糊输出值一一采取加权平均法去模糊化，得到最终的模糊控制器查询表。

float  R[169][13] = {  0 };
    float R1[13][13] = {  0 };
    float AdBd1[13][13] = {  0 };
    float R2[169] = {  0 };
    float AdBd2[169] = {  0 };
    float R3[169][13] = {  0 };
    float  Cd[13] = {  0 };
    float Fuzzy_Table[13][13] = {  0 };
    float SPEED[13] = {  200,220,230,240,250,270,300,270,250,240,230,220,200 };//调试参数
    int Max_Input1_value = 0, Max_Input2_value = 0;
    
    /** * @param 模糊化过程实现论域内不同值对应隶属度最大的语言值 */
    int  E_MAX(int e)
    { 
    	int i = 0, max = 0;
    	for (i = 0; i < 7; i++)
    		if (Input1_Terms_Membership[i][e] > Input1_Terms_Membership[max][e])
    			max = i;
    	return max;
    }
    
    int  EC_MAX(int ex)
    { 
    	int i = 0, max = 0;
    	for (i = 0; i < 7; i++)
    		if (Input2_Terms_Membership[i][ex] > Input1_Terms_Membership[max][ex])
    			max = i;
    	return max;
    }
    
    void calculate()
    { 
    	/***************************************计算所有规则模糊关系的并集Rule***************************************/
    	int i = 0, j = 0, k = 0;
    	int Input1_value_index = 0, Input2_value_index = 0;
    
    	//计算Rule(初始化），计算Rij，并对所有的R取并集，R=(EXEC)XU
    	for (Input1_Terms_Index = 0; Input1_Terms_Index < 7; Input1_Terms_Index++)
    		for (Input2_Terms_Index = 0; Input2_Terms_Index < 7; Input2_Terms_Index++)
    		{ 
    			// E和EC的语言值两两组合及其输出计算Rule
    			Output_Terms_Index = Rule[Input1_Terms_Index][Input2_Terms_Index] - 1;
    			k = 0;
    			for (i = 0; i < 13; i++)
    				for (j = 0; j < 13; j++)
    				{ 
    					// E和EC进行取小运算
    					if (Input1_Terms_Membership[Input1_Terms_Index][i] < Input2_Terms_Membership[Input2_Terms_Index][j])
    						R1[i][j] = Input1_Terms_Membership[Input1_Terms_Index][i];
    					else
    						R1[i][j] = Input2_Terms_Membership[Input2_Terms_Index][j];
    					// 转换R1矩阵为R2一维向量
    					R2[k] = R1[i][j];
    					k++;
    				}
    			///<A=Input1_Terms_Membership[Input1_Terms_Index],B=Input2_Terms_Membership[Input2_Terms_Index]
    			///<R1=AXB建立13x13的矩阵,R2=R1'把矩阵转成169x1的列向量
    			for (i = 0; i < 169; i++)
    				for (j = 0; j < 13; j++)
    				{ 
    					// R1(E, EC)与U进行取小运算
    					if (R2[i] < Output_Terms_Membership[Output_Terms_Index][j])
    						R3[i][j] = R2[i];
    					else
    						R3[i][j] = Output_Terms_Membership[Output_Terms_Index][j];
    					// R进行取大运算，为所有规则模糊关系的并集
    					if (R3[i][j] > R[i][j])
    						R[i][j] = R3[i][j];
    				}
    		}
    
    
    	/*************************对于每种可能的E、EC的精确取值模糊化后进行推理得到模糊输出Cd，Cd=(AdxBd)oR*************************/
    	for (Input1_value_index = 0; Input1_value_index < 13; Input1_value_index++) { 
    		for (Input2_value_index = 0; Input2_value_index < 13; Input2_value_index++)
    		{ 
    			for (j = 0; j < 13; j++)
    				Cd[j] = 0;
    			int kd = 0;
    			float temp = 0;
    			Max_Input1_value = E_MAX(Input1_value_index);	///<找出误差隶属度最大的语言值
    			Max_Input2_value = EC_MAX(Input2_value_index);	///<找出误差变化率隶属度最大的语言值
    			for (i = 0; i < 13; i++)
    				for (j = 0; j < 13; j++)
    				{ 
    					// E(Ad)和EC(Bd)进行取小运算
    					if (Input1_Terms_Membership[Max_Input1_value][i] < Input2_Terms_Membership[Max_Input2_value][j])
    						AdBd1[i][j] = Input1_Terms_Membership[Max_Input1_value][i];
    					else
    						AdBd1[i][j] = Input2_Terms_Membership[Max_Input2_value][j];
    					AdBd2[kd] = AdBd1[i][j];
    					kd++;
    				}
    			for (i = 0; i < 169; i++)
    				for (j = 0; j < 13; j++)
    				{ 
    					// 模糊矩阵的合成，将乘积运算换成“取小”，将加法运算换成“取大”
    					if (AdBd2[i] < R[i][j])
    						temp = AdBd2[i];
    					else
    						temp = R[i][j];
    					if (temp > Cd[j])
    						Cd[j] = temp;
    				}
    
    
    			/*************************去模糊化（加权平均法），计算实际输出*************************/
    			float sum1 = 0, sum2 = 0;
    			float OUT;
    			for (i = 0; i < 13; i++)
    			{ 
    				sum1 = sum1 + Cd[i];
    				sum2 = sum2 + Cd[i] * SPEED[i];
    			}
    			OUT = (int)(sum2 / sum1 + 0.5);///<四舍五入
    			Fuzzy_Table[Input1_value_index][Input2_value_index] = OUT;
    			cout << OUT << ",";
    		}
    		cout << endl;
    	}
    }

## 3.模糊查询表设置车速 ##

将模糊查询表复制进入代码程序，将实际的e和ec映射到论域中后，在模糊查询表中查询结果并设置目标车速。

int_16 Fuzzy_Table[13][13]= 
    {  
    203,211,211,211,226,226,230,230,228,210,210,210,210,
    209,221,221,221,238,238,241,241,237,231,231,231,227,
    209,221,221,221,238,238,241,241,237,231,231,231,227,
    209,221,221,221,238,238,241,241,237,231,231,231,227,
    215,238,238,238,245,245,266,266,246,237,237,237,232,
    215,238,238,238,245,245,266,266,246,237,237,237,232,
    218,250,250,250,276,276,283,283,280,245,245,245,216,
    218,250,250,250,276,276,283,283,280,245,245,245,216,
    232,240,240,240,250,250,271,271,246,236,236,236,217,
    226,230,230,230,236,236,239,239,236,214,214,214,208,
    226,230,230,230,236,236,239,239,236,214,214,214,208,
    226,230,230,230,236,236,239,239,236,214,214,214,208,
    211,211,211,211,226,226,230,230,228,208,208,208,203
    }  ;
    
    int_16 get_speed_set(void) { 
    	int_16 E = 0, EC = 0;
    	int_16 speed_target;
    	static int_16 re_pos = 0, ek = 0, eck = 0;
    	float ke = 400, kec = 10;
    	ek = 2500 - row;
    	eck = 2500 - row - re_pos;
    	re_pos = ek;
    
    	if (ek > 0) { 
    
    		E = (int_32)(ek / ke + 0.5);
    	}
    	else { 
    
    		E = (int_32)(ek / ke - 0.5);
    	}
    	//将E的论域转换到模糊控制器的论域
    	if (E > 6)
    		E = 6;
    	else if (E < -6)
    		E = -6;
    	if (eck > 0) { 
    
    		EC = (int_16)(eck / kec + 0.5);
    	}
    	else { 
    
    		EC = (int_16)(eck / kec - 0.5);
    	}//将EC的论域转换到模糊控制器的论域
    	if (EC > 6)
    		EC = 6;
    	else if (EC < -6)
    		EC = -6;
    
    	speed_target = (int_16)(Fuzzy_Table[E + 6][EC + 6]);
    	return speed_target ;
    }

调好参数，完胜PID  
大功告成~

————————————————  
版权声明：本文为CSDN博主「博途慧算」的原创文章，遵循 CC 4.0 BY-SA 版权协议，转载请附上原文出处链接及本声明。  
原文链接：https://blog.csdn.net/lygeneral/article/details/105010950

上文：[模糊控制（二）模糊控制——模糊推理][Link 1]

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[Link 1]: https://editor.csdn.net/md/?articleId=105060313