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Prévia do material em texto

Problem 3.15PP
For the system in Fig., compute the transfer function from the motor voltage to position 02. 
Figure Motor with a flexible load 
i.
S tep -by-s tep s o lu tio n
step 1 of 4
Step 1 of 4
Consider the electrical system in Figure 2.54 from the text book. 
Apply KirchhofTs voltage law.
Apply Laplace transform on both sides.
The mechanical equation describing the system is,
J ,0 ,+ b (e ,-0 ,)+ k (e ,-0 ,)+ B $ ,= K ,i,
Apply Laplace transform on both sides.
[ V + ( B + i ) j + * ] « l ( i ) - [ f a + * ] « , ( i ) = A : , / , (» ) ...... (2)
Step 2 of 4
The mechanical equation describing the load is,
Apply Laplace transform on both sides.
J2S^$2 (^ ) ^^502 (k)s+RJc‘ 
bKs+kK,
(y,»’ + fts+ * )-
V / + [ V i + ( f i + * ) i . ] » ’ +
[ (B + 4 ) J ^ ,+ * t .+ X ,4 : , ] j+ * ) ^ 
i . 4 V *[LJc' *2RJbk)s*RJ^
Therefore, the transfer function form the motor voltage to position 0 l(s ) i:
« , ( j ) bK,s+kK,
K i ‘ ) 1 V i*’ + [ V i + ( f i+ 4 ) i . ] * ’ + 
|[ ( 5 + 4 ) « . +kL. + K,K,']s+kR, 
LJ>W +{2LJ>k+RJ^)s‘ + (LJ :‘
( j ^ + b s + k ) -
t-2R,bk)s+RJ[^