PendCon Research: Uncertain Double Pendulum Part I
Uncertain Double Pendulum Part I
Double Pendulum with Additional Dynamics
The double pendulum with additional weights which are mounted on a horizontal bar. One of them hangs on a spring. By this way it is possible to generate an oscillatory disturbance. The challenge is that the double pendulum and the additional spring-mass system are coupled. Consequently, the controller must not only be able to reject this strong oscillatory disturbance, he must also be designed in such a way that the closed-loop system is not destabilized by these additional dynamics.Short Introduction into Hinf Controller Design
- Basic idea of Hinf controller design
- Internal stability
- Characterization of Hinf suboptimal controllers by Riccati equations
- Characterization of Hinf suboptimal controllers by LMIs (linear matrix inequalities)
- Weighting schemes for the design of Hinf controllers
- Choice of the weights
- Important properties of Hinf optimal controllers
- MATLAB tools for the design of Hinf controllers
Hinf Controller Design for the Double Pendulum
- Choice of the weights
- Controller design for the hanging pendulum (the plant has two pole pairs on the imaginary axis)
- Controller design for the inverted pendulum (the plant has two positive real poles)
- Tracking of a large command (design of a two-degrees-of-freedom Hinf controller)
- Analysis of the closed-loop system
Hinf controller design where an oscillatory disturbance has to be rejected
- Plant model for the double pendulum with the additional spring-mass-system
- Simulation and measurement of step responses
- Choice of a suitable weighting scheme for high performance rejection of a constant disturbance
- Hinf controller design for the pendulum with the additional spring-mass-system
- Comparison with LQ and H2 controllers
- Analysis of the closed-loop system
Mackenroth, U.: Robust High-Performance Disturbance Rejection for an Uncertain Inverted Double Pendulum, ACC'09, Seattle, June 2008