Stabilization of an Inverse Pendulum

The "inverted pendulum" is a classic example of an unstable system.

In this experiment, the inverted pendulum is stabilized so that the pendulum arm remains vertical. To achieve this, the pendulum carriage is moved back and forth by an electric motor.

To achieve stabilization, linear controllers with state feedback are designed for the linearized model of the inverted pendulum with different pole configurations.

This controller is then tested on the “PC60” track in Amira.

Each group consists of 3–5 participants. During the lab experiment, each participant keeps a lab report describing all the steps taken and the results obtained.

The experiment lasts 3 1/2 hours.

Experiment steps:

1. Linearization of the “Inverse Pendulum” section
2. Plotting the pole-zero diagrams for the linearized system
3. Controller selection and root locus plot
4. Design of a state feedback control system prior to the lab experiment using Octave (
   provided) or MATLAB, and simulation with both the linearized and nonlinear systems
5. Testing the controllers on the nonlinear system using the “Amira PC60” experimental setup
6. Comparison of simulation and experiment
7. Comparison of the results for the linearized and nonlinear plant
8. Discussion of the results

The section of the experimental setup to be controlled is the Amira inverted pendulum.

The system is considered a linear multi-variable system (SIMO system):

Experiment instructions and Octave and MATLAB scripts available for download as a ZIP archive:

https://mrt-pc1.mrt.maschinenbau.uni-kassel.de/MRT/Lehre/Praktika/Versuche/InvPendel

The username and password for access will be provided in the course.

J. ACKERMANN: Design by Pole Specification. Online http://elib.dlr.de/96051/1/Ackermann_Entwurf%20durch%20Polvorgabe_Regelungstechnik_Sonderdruck_1977.pdf

Handouts for the lecture “State Space Methods and Multi-Variable Systems”