The objective of this lab is to design, simulate, and implement a state feedback compensator for a 2DOF mass-spring system. The controller will be designed and implemented in LabVIEW using the Simulation Module and Control Design Toolkit.
State feedback compensation of a2dof rectilinear
system
Objectives
Design, simulate, and implement a state feedback compensator
for a 2DOF mass-spring system.
Pre-lab
Derive the equations of motion for the 2DOF rectilinear
mass-spring. The plant configuration is shown below. The first andsecond mass carriages are free and the third is clamped. The medium
stiffness spring is connecting the first and second carriages, andthe low stiffness spring is connecting the second and third.
2DOF Spring-Mass System
Find a state-space realization of the system.
Design and simulate a full state feedback compensator to
control the position of the second mass carriage. Design yourcompensator to meet the following performance specifications:
Percent overshoot
Settling time
Zero steady-state error to a step input.
Lab procedure
Configure the plant as shown in Fig. 1 above.
Code your state feedback compensator into the control loop
VI.
Perform a 3000 count step input and determine if you have met
the performance specifications.
Once you have achieved the desired performance, save your
plot and turn it in with the rest of your work.
Post-lab
Explain how the state feedback gains affect the system's
response in terms of its characteristic equation.
What effect does the compensator have on the zero(s) of the
system? If a system has an undesirable zero, how can its effect bereduced using only a state feedback compensator?
Why is full state feedback compensation often unfeasible
especially with higher-order systems?
