Servo with Spring mass damper system

[jonnybgood]

I need to investigate some tight control on an open loop modelling of a servo motor linked with a spring mass damper system.
The linkage with spring mass damper is stable with a counterbalance on the other side. The aim is to shift the mass of the s-m-d
system and eliminate oscillations as much as possible. Diagram is attached.

I need some similar example so I can follow it to derive the state space equations. Obviously the transfer functions of each separate
system is not a problem but I have some trouble deriving the state space equation of the cascaded systems.

Later I need to simulate with simulink and impliment a PID to obtain a certain over shoot and settling time.



I would really appreciate your help. thanks

 

[albert22]

Once converting the torque to the linear displacement on the shock absorver and the spring. The eq should not be complicated.
But I think that this system is nonlinear (because of sin theta) and you will have to linearize the resulting model for small variations in angle theta.