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<P>则有</P>
<P><IMG height=57 src="19.files/7.21.h12.gif" width=225
border=0> (4.84)</P>
<P><IMG height=46 src="19.files/7.21.h13.gif" width=126
border=0>
(4.85)</P>
<P><IMG height=44 src="19.files/7.21.h14.gif" width=211
border=0> (4.86)</P>
<P><IMG height=50 src="19.files/7.21.h15.gif" width=206
border=0> (4.87)</P>
<P>其中：Sj是第j条规则的语言变量，r是语言变量值。</P>
<P>显然．采用式(4．84)—(4．87)，可求<SUP>a</SUP>F／<SUP>a</SUP>P。</P>
<P>对于第2层而言，如果要求<SUP>a</SUP>F／<SUP>a</SUP>P，则应考虑：</P>
<P><IMG height=47 src="19.files/7.21.h33.gif" width=129
border=0> (4.88)</P>
<P>其中：U<SUB>ri</SUB>是第2层的输出</P>
<P>由于</P>
<P><IMG height=48 src="19.files/7.21.h34.gif" width=171
border=0> (4.89)</P>
<P>其中：Ak是第k条规则的前件语言变量</P>
<P><IMG height=61 src="19.files/7.21.h35.gif" width=294 border=0></P>
<P><IMG height=91 src="19.files/7.21.h36.gif" width=246 border=0></P>
<P>其中：U<SUB>r</SUB><SUP>-1</SUP>(Z<SUB>r</SUB>)是U<SUB>r</SUB><SUP>-1</SUP>(Z<SUB>r</SUB>)的导数。</P>
<P>同时，根据式(4．75)、(4．76)则<SUP>a</SUP>U<SUB>ri</SUB>／<SUP>a</SUP>P很容易求取。</P>
<P>这样则对于第2层；<SUP>a</SUP>F／<SUP>a</SUP>P可以求出。</P>
<P>在式(4．82)中，由于<SUP>a</SUP>Q／<SUP>a</SUP>F，<SUP>a</SUP>F／<SUP>a</SUP>P都在第2，4层可以求出，故而能对这两层的隶属函数进行学习。一般<SUP>a</SUP>Q／<SUP>a</SUP>F不取实际值．只取其符号，即有：</P>
<P><IMG height=47 src="19.files/7.21.h37.gif" width=179 border=0></P>
<P>最后有：</P>
<P><IMG height=46 src="19.files/7.21.h38.gif" width=282 border=0></P>
<P>4．ULR模糊控制器对倒立摆的控制</P>
<P>对倒立摆的控制采用下列9条由条件语句组成的控制规则实现．如表4—2所示。</P>
<TABLE height=100 cellSpacing=1 cellPadding=0 width="90%" align=center
bgColor=#666666 border=0>
<TBODY>
<TR>
<TD width="40%" bgColor=#ffffff colSpan=2 height=39 rowSpan=2>
<P align=center>控 制</P></TD>
<TD width="60%" bgColor=#ffffff colSpan=3 height=19>
<P align=center>角度变化率<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">Δθ</SPAN></P></TD></TR>
<TR>
<TD align=middle width="20%" bgColor=#ffffff height=18>PO2</TD>
<TD align=middle width="20%" bgColor=#ffffff height=18>ZE2</TD>
<TD align=middle width="20%" bgColor=#ffffff height=18>NE2</TD></TR>
<TR>
<TD width="20%" bgColor=#ffffff height=57 rowSpan=3>
<P align=center>角 度<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">θ</SPAN></P></TD>
<TD align=middle width="20%" bgColor=#ffffff height=12>PO1</TD>
<TD align=middle width="20%" bgColor=#ffffff height=12>PL</TD>
<TD align=middle width="20%" bgColor=#ffffff height=12>PM</TD>
<TD align=middle width="20%" bgColor=#ffffff height=12>ZE</TD></TR>
<TR>
<TD align=middle width="20%" bgColor=#ffffff height=18>ZE1</TD>
<TD align=middle width="20%" bgColor=#ffffff height=18>PS</TD>
<TD align=middle width="20%" bgColor=#ffffff height=18>ZE</TD>
<TD align=middle width="20%" bgColor=#ffffff height=18>NS</TD></TR>
<TR>
<TD align=middle width="20%" bgColor=#ffffff height=18>NE1</TD>
<TD align=middle width="20%" bgColor=#ffffff height=18>ZE</TD>
<TD align=middle width="20%" bgColor=#ffffff height=18>NM</TD>
<TD align=middle width="20%" bgColor=#ffffff
height=18>NL</TD></TR></TBODY></TABLE></TD></TR>
<TR>
<TD width="100%" height=207>
<P>角度<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">θ</SPAN>是倒立摆和平衡位置的夹角，它的范围取-12<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">°</SPAN>—+12<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">°</SPAN>。角度变化率<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">Δθ</SPAN>的范围取每秒-12<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">°</SPAN>，即-12<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">°</SPAN>／S，到每秒+12<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">°</SPAN>，即+12<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">°</SPAN>／S。
</P>
<P>倒立摆安装在一个小车上，为了使倒立摆能处于平衡状态，故而要对小车进行控制。</P>
<P>角度<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">θ</SPAN>，角度变化率<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">Δθ</SPAN>以及控制的模糊量都是取三角隶属函数，它们的参数分别如表4—3中所示。</P>
<P align=center>表4-1 隶属函数</P>
<DIV align=center>
<TABLE cellSpacing=1 cellPadding=0 width="60%" bgColor=#666666 border=0>
<TBODY>
<TR>
<TD align=middle width="25%" bgColor=#ffffff>
<P align=center>模糊量</P></TD>
<CENTER>
<TD align=middle width="26%" bgColor=#ffffff>C</TD>
<TD align=middle width="19%" bgColor=#ffffff>L</TD>
<TD align=middle width="30%" bgColor=#ffffff>R</TD></CENTER></TR>
<TR>
<TD align=middle width="25%" bgColor=#ffffff>PO1
<P>ZE1</P>
<P>NE1</P></TD>
<TD align=middle width="26%" bgColor=#ffffff>0.3
<P>0.0</P>
<P>-0.3</P></TD>
<TD align=middle width="19%" bgColor=#ffffff>0.3
<P>0.3</P>
<P>5000</P></TD>
<TD align=middle width="30%" bgColor=#ffffff>5000
<P>0.3</P>
<P>0.3</P></TD></TR>
<TR>
<TD align=middle width="25%" bgColor=#ffffff>PO2
<P>ZE2</P>
<P>NE2</P></TD>
<TD align=middle width="26%" bgColor=#ffffff>1.0
<P>0.0</P>
<P>-1.0</P></TD>
<TD align=middle width="19%" bgColor=#ffffff>1.0
<P>1.0</P>
<P>5000</P></TD>
<TD align=middle width="30%" bgColor=#ffffff>5000
<P>1.0</P>
<P>1.0</P></TD></TR>
<TR>
<TD align=middle width="25%" bgColor=#ffffff>PL
<P>PM</P>
<P>PS</P>
<P>ZE</P>
<P>NS</P>
<P>NM</P>
<P>NL</P></TD>
<TD align=middle width="26%" bgColor=#ffffff>20.0
<P>10.0</P>
<P>5.0</P>
<P>0.0</P>
<P>-5.0</P>
<P>-10.0</P>
<P>-20.0</P></TD>
<TD align=middle width="19%" bgColor=#ffffff>5.0
<P>5.0</P>
<P>4.0</P>
<P>1.0</P>
<P>5.0</P>
<P>6.0</P>
<P>0.0</P></TD>
<TD align=middle width="30%" bgColor=#ffffff>0.0
<P>6.0</P>
<P>5.0</P>
<P>1.0</P>
<P>4.0</P>
<P>5.0</P>
<P>5.0</P></TD></TR></TBODY></TABLE></DIV></TD></TR>
<TR>
<TD width="100%" height=200>
<P>模糊控制器的输入有角度和角度变化率，它们都归一化到[-1，1]区间。实际控制的结果如图4—23中所示。从图中可知，在执行了大约500步左右工作，则可以达到平衡状态，图中给出的是初始角度不同时的工作过程状态。
</P>
<TABLE cellPadding=0 width="100%" border=0>
<TBODY>
<TR>
<TD align=middle width="50%" height=182><IMG height=271
src="19.files/7.21.h39.gif" width=352 border=0>
<P align=center>(a)</P></TD>
<TD align=middle width="50%" height=182><IMG height=273
src="19.files/7.21.h40.gif" width=352 border=0>
<P align=center>(b)</P></TD></TR>
<TR>
<TD width="100%" colSpan=2>
<P align=center>图4-23 倒立摆平衡仿真结果</P></TD></TR>
<TR>
<TD width="100%" colSpan=2>
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