Robust high-performance disturbance rejection for an uncertain inverted double pendulum

This paper deals with some new aspects of the well-known double pendulum experiment (sometimes also denoted as pendubot). It becomes challenging if it is made uncertain by adding suitable mechanic and electronic devices and if additionally the performance requirements are taken to the limit. It will be proposed how this can be achieved. The performance for the upward directed double pendulum is measured in terms of disturbance rejection properties. Several controllers are designed: pole placement, LQ, H₂, H_infin and mu. They are compared with respect to their performance and robustness properties. The main performance limitation comes from additional high-frequency dynamics of the plant which are found by identification. Additionally, the dynamics of the actuator are made uncertain by adding a suitable electronic circuit at the input of the pwm amplifier. To handle this challenging situation, a mu controller will be designed which has remarkable robustness and performance properties. In a further part of the experiment, a weight with a spring is mounted at the double pendulum. This leads to an oscillatory disturbance and moreover to a change of the dynamics of the plant so that excellent robustness properties of the controller are required.