1. Eigenvalues: p1=-4.526, p2,3=-0.4993±2.7883i, p4=-0.4753
2.1 Step Input Response:
Roots([ ])
Eigenvalues: p1=-4.526, p2,3= ±2.7883i, p4=
Steady-state response
Laplace transform of unit step input
Final value theorem:
Stability: If the step response reaches to a constant value, the system is said to be stable.
Steady State Error: ess=1-css ess=0
[r,p,k]=residue(nh,[dh,0])
r = i i
1.0000
z=r(3);a2=2*abs(z),fi2=angle(z)

2. Step Response of a Second Order System:
ωn : Undamped natural frequency
ξ: Damping Ratio
clc,clear
wn=1;ksi=0.2;
tp=2*pi/wn;dt=tp/20;ts=tp/ksi;
t=0:dt:ts;w=wn*sqrt(1-ksi^2);
a=wn/w;sigma=ksi*wn;fi=-acos(ksi)-pi/2;
c=a*exp(-sigma*t).*cos(w*t-fi)+1;
plot(t,c)

3. tr : Rise Time
td : Delay Time
ts : Settling time (%5)
cmax : Peak value, tmax: Peak time, cmax-css:Maksimum overshoot
css : Steady State Response, 1-css : Steady State Error Re
- σ 

4. Design Criteria of Control Systems:
Stability
Steady State Error ess=1-css → 0
Sensitivity to a disturbance [css]d → 0
Overshoot , typical value % 5, damping ratio ξ=0.7
Settling time : tss (Depends on the application)
Transfer Function of a PID Controller
Sensitivity to disturbance
At the first stage apply P control: observe the stability ess, [css]d
If necessary apply PI control, it eliminates/reduces the steady state error
If necessary apply PD kontrol, it reduces the overshoot
Apply PID control, useful for all criteria