Project - Position control of mass spring damper system
Dear Assessor,
Thank you for your time.
The simulink file, Matlab file and output screenshot are attached for your reference.
Please find the calculation of fixing parameters value and optimising PID gains below.
The nominal parameters of the spring-mass system are given in the project problem statement.
m= 3.6 (mass of the spring-mass system in kg)
k= 400 (stiffness constant of the spring-mass system in N/m)
c= 100 (damper coefficient of the spring-mass system in Ns/m)
Calculation of other parameters from given information
Km= 1/m (constant)
wn= sqrt(k/m) (Natural frequency of spring-mass system)
zeta= c/(2*wn*m); (Damping ratio);
Checking poles for stability
P1 = -zeta*wn-wn*sqrt(zeta^2-1) (Pole 1)
P2 = -zeta*wn+wn*sqrt(zeta^2-1) (Pole 2)
P = [P1; P2]
Both poles are on the left side of the imaginary axis hence the system is stable
After multiple iterations, PID gains are optimised and they are as follows
Kp= 800, Kd= 0.5 and Ki= 3600
Please refer to the screenshot for the output signal profile.
Submitted for review and your kind approval.
Regards,
Bilal