1. Example 2-2: Multi-DOF mechanical systemsk2 c2 k1 c1
f1: Control Force
f2: Disturbance (External force)
DEU-MEE 5017 Advanced Automatic Control

2. clc,clear
m1=1.2;m2=1;k1=350;k2=300;c1=4;c2=3;
m=[m1,0;0,m2];
c=[c1+c2,-c2;-c2,c2];
k=[k1+k2,-k2;-k2,k2];
syms s;
a=[s^2*m+s*c+k];
h=inv(a);pretty(h)

3. Block diagram of closed loop system:
P, PI, PD, PID control
Study the PID control with MATLAB/Simulink
Block diagram of open loop system:

4. Simulation with MATLAB/Simulink:
Kp=250, Ki=150 Kd=10
Kp=1, Ki=400 Kd=15
Kp=250, Ki=300 Kd=10