1. Dynamic Response Steady State Response: the part of resp. when t→∞
Transient response: the part of resp right after the input is being applied.
Both are part of the total resp.
total resp=z.i. resp+z.s.resp.
z.i. resp=“Output due to i.c. when input ≡ 0”
z.s. resp=“Output due to input excitation when all i.c. are set=0 at t=0”

2. Typical test signal
Unit step signal:
Unit impulse:δ(t)
us(t) 1
δ(t) t

3. Unit ramp:
Unit acc. signal:
r(t) t
a(t)
0.5 1 t

4. Exponential signal:
sinusoidal: 1 t

5. Unit step response: Unit impulse resp: In Matlab: step Matlab: impulse
H(s)
u(s)= 1 s
y(s)=H(s)
y(s)=H(s)
u(s)=1
H(s)

6. Time domain response specifications
Defined based on unit step resp.
Defined for closed loop system

12. y(s)
u(s)
H(s)

15. 90%yss
tr≈0.45
10%yss ts ts
tp≈0.9sec
td≈0.35

16. ±5% ts=0.45
yss=1
ess=0
O.S.=0
Mp=0
tp=∞
td≈0.2
tr≈0.35

17. tp=0.35
O.S.=0.4
Mp=40%
yss=1
es=0
ts≈0.92
td≈0.2
tr≈0.1

18. Steady-state tracking & sys. types
Unity feedback control:
plant + e
r(s)
y(s)
C(s)
G(s) - + e
r(s)
Go.l.(s)
y(s) -