Page 60 - MATLAB an introduction with applications

MATLAB Basics ——— 45

Residue Function: The residue function converts the polynomial transfer function
n
bs + b s n− 1 + + +
... b s b
() =
Hs 0 1 n− 1 n
+
as + a s m− 1 + + m− 1 s a m
m
... a
1
0
to the partial fraction transfer function
r 1 r 2 r n
() =
Hs s − p 1 + s − p 2 + ... + s − p n + k ( ) s
[r, p, k] = residue(B, A) Determine the vectors r, p and k, which contain the residue values, the poles and
the direct terms from the partial-fraction expansion. The inputs are the polynomial
coefficients B and A from the numerator and denominator of the transfer function,
respectively.
ss2tf Function: The ss2tf function converts the continuous-time, state-space equations
x′ = Ax + Bu
y = Cx + Du
to the polynomial transfer function
bs + b s n− 1 + + +
n
... b s b
() =
Hs 0 m 1 m− 1 n− 1 n
as + a s + + m− 1 s a m
+
... a
0
1
The function has two output matrices:
[num, den] = ss2tf(A, B, C, D,iu) Computes vectors num and den containing the coefficients, in descending
powers of s, of the numerator and denominator of the polynomial transfer
function for the iu input. The input arguments A, B, C and D are the
th
th
matrices of the state-space equations corresponding to the iu input, where
iu is the number of the input for a multi-input system. In the case of a single-
input system, iu is 1.
ss2zp Function: The ss2zp function converts the continuous-time, state-space equations
x′ = Ax + Bu
y = Cx + Du
to the zero-pole-gain transfer function
−
(s − z )(s z )...(s − z )
() =
Hs k 1 2 n
(s − p 1 )(s − p 2 )...(s − p m )
The function has three output matrices:
[z, p, k] = ss2zp(A, B, C, D, iu) Determines the zeros (z) and poles (p) of the zero-pole-gain transfer function
th
for the iu input, along with the associated gain (k). The input matrices A,
th
B, C and D of the state-space equations correspond to the iu input, where
iu is the number of the input for a multi-input system. In the case of a single-
input system, iu is 1.
tf2ss Function: The ts2ss function converts the polynomial transfer function

n
bs + b s n− 1 + + +
... b s b
() =
Hs 0 1 n− 1 n
m
+
as + a s m− 1 + + m− 1 s a m
... a
1
0
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