PendCon Advanced: The Double Pendulum Experiment
The Double Pendulum Experiment
The double pendulum experiment resembles the rotary pendulum but is harder to control. In the inverted position, the rotary pendulum has a double pole at the origin and a negative and a positive pole, whereas the double pendulum has two negative and two positive poles. This matter of fact makes this experiment more exiting. Despite of this, stabilization is possible by elementary methods taught in an advanced course like pole placement with two differentiators as observers to estimate the rates.
Comparison of the design methods
There are a lot of design methods for linear controllers and the students may ask why not he should not use the simplest one. It will be shown that there are big differences with respect to robustness and performance.
High-Frequency Dynamics
The amplifier-motor-encoder section of the plant has a high-frequency resonance peak at approximately 2900 rad/sec. If this dynamics is not included into the model, the real closed-loop system may become unstable whereas the simulated is stable. It an interesting experience for the students to see how unmodeled high-frequency dynamics can destabilized a plant. It will be shown how these dynamics can be taken into account and an analysis shows that it is really the reason for the instability.
Uncertainty set
It is a unique feature of the PendCon double pendulum experiment that it includes mechanical and electrical devices which change the dynamics substantially and make it much harder to control. This requires a resign of the controllers and highlights very clearly the differences between the different design methods.
Videos
- Stabilization of a Double Pendulum at its Stability Boundary
- Hanging Double Pendulum
- Inverted Double Pendulum
- Tracking of a large command
- Upper hanging and Lower Inverted Double Pendulum