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State Feedback Compensation of a 2DOF Rectilinear System

Module by: Robert Bishop. E-mail the author

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Summary: 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.

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State Feedback Compensation of a2DOF Rectilinear System

Objectives

  1. Design, simulate, and implement a state feedback compensator for a 2DOF mass-spring system.

Pre-Lab

  1. Derive the equations of motion for the 2DOF rectilinear mass-spring. The plant configuration is shown below. The first and second mass carriages are free and the third is clamped. The medium stiffness spring is connecting the first and second carriages, and the low stiffness spring is connecting the second and third.
    Figure 1: 2DOF Spring-Mass System
    Figure 1 (Graphic1)
  2. Find a state-space realization of the system.
  3. Design and simulate a full state feedback compensator to control the position of the second mass carriage. Design your compensator to meet the following performance specifications:
    1. Percent overshoot ≤ 10 % ≤10%
    2. Settling time ≤ 1 sec ≤1sec
    3. Zero steady-state error to a step input.

Lab Procedure

  1. Configure the plant as shown in Fig. 1 above.
  2. Code your state feedback compensator into the control loop VI.
  3. Perform a 3000 count step input and determine if you have met the performance specifications.
  4. Once you have achieved the desired performance, save your plot and turn it in with the rest of your work.

Post-Lab

  1. Explain how the state feedback gains affect the system's response in terms of its characteristic equation.
  2. What effect does the compensator have on the zero(s) of the system? If a system has an undesirable zero, how can its effect be reduced using only a state feedback compensator?
  3. Why is full state feedback compensation often unfeasible especially with higher-order systems?

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