# 0.10 Inverted pendulum on a translating base

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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.

## Objectives

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

## Pre-lab

• Derive the equations of motion for an inverted pendulum with a translating base shown in the figure below
• Find a state-space realization of the system.
• Design and simulate a full state-feedback compensator that stabilizes the system and satisfies the following performancespecifications:
• Percent overshoot $\le 10%$
• Setting time $\le 2\mathrm{sec}$

## Lab procedure

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

## Post-lab

• How did the response of the system with no dither compare to your simulation? Can you explain the discrepancy?
• What effect did dither have on the response of the system? Was this response trajectory closer to what you hadsimulated?

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