Example 2-2: Multi-DOF mechanical systems k2 c2 k1 c1 f1: Control Force f2: Disturbance (External force) DEU-MEE 5017 Advanced Automatic Control

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)

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

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