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Inverted Pendulum on a Translating Base

Module by: Robert Bishop. E-mail the author

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Summary: The objective of this lab is to understand the dynamics of an inverted pendulum with a translating base. Students will use feedback to control an unstable system. The controller will be designed and implemented in LabVIEW using the Simulation Module and Control Design Toolkit.

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Inverted Pendulum on a Translating Base

Objectives

  • Understand the dynamics of an inverted pendulum with a translating base.
  • Use state feedback to control an unstable system.

Pre-Lab

  1. Derive the equations of motion for an inverted pendulum with a translating base shown in the figure below
    Figure 1: Inverted Pendulum with a Translating Base
    Figure 1 (invertpendulum.jpg)
    Figure 2: Pendulum Parameters
    Figure 2 (param.jpg)
  2. Find a state-space realization of the system.
  3. Design and simulate a full state-feedback compensator that stabilizes the system and satisfies the following performance specifications:
    1. Percent overshoot ≤ 10 % ≤10%
    2. Setting time ≤ 2 sec ≤2sec

Lab Procedure

  1. Configure the plant as shown above in Fig. 1.
  2. Code your state-feedback compensator into the control loop VI.
  3. Perform a 2500 count step input and save the plot.
  4. Implement dither into your system and perform the step input again. Save the plot when you are finished.

Post-Lab

  1. How did the response of the system with no dither compare to your simulation? Can you explain the discrepancy?
  2. What effect did dither have on the response of the system? Was this response trajectory closer to what you had simulated?

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