Periodic Control in a Stick Balancing Problem

Understanding the human balancing is a fundamental question. Investigation of simple tasks can help in this challenging problem. In order to describe the nature of the underlying control mechanism, first of all, the balancing force has to be determined. As a second step one can identify the behaviour of the controller. There are two main problems in the model of the whole control process of balancing, time-delay is unknown and the exact mathematical definition of the control goal is also not known. The explanation for this latter issue the classical inverted pendulum model has 2DoF but only one control forces exists, thus it can be handled as a typical underactuated mechanical system. In under-actuated systems the task of inverse dynamics is not well defined. Some degrees-of-freedom cannot directly be controlled, and the corresponding generalized coordinates depend on the system dynamics only. In this study we model the control mechanism as a time periodically (i.e. clock-driven) switched controller. We investigate the stability properties of the closed-loop system. We show a periodically switched controlled which can be a possible model of human balancing.