Abstract
This paper presents and compares two practical implementation schemes based on parametric and coordinate control. The parametric feedback control idea employs a parametric resonance phenomenon. An approximate frequency domain stationarization approach yields the setting for a very simple controller scheme. The application and numerical analysis of the results are given for the pendulum control example, which length varies in a parametric control case. The coordinate and parametric control demonstrate similar damping properties. The study also provides an inventive idea for passive parametric control combined with coordinate control that shows better damping.
Highlights
M ODERN control theory provides a number of standardized solutions when an engineer is challenged by a situation that falls into the classical framework of oscillation control
It is notable that even the simplest case of the passive parametric control system, realized by using a spring in the suspension of the pendulum, shows the decay time 55.3% less than the decay time of the reference uncontrolled pendulum
We demonstrate how the conceptual design of the control for the same physical object can be assisted by the ability to observe it from different perspectives, or, in other words, to describe it by different mathematical models
Summary
M ODERN control theory provides a number of standardized solutions when an engineer is challenged by a situation that falls into the classical framework of oscillation control. Having been an unquestionable advantage, the out-of-shelf feedback control schemes often prevent the practitioners from investigating the inventive ways to reach the desired, and sometimes even better result. The latter requires the understanding of the physics of oscillations: the mathematical model that describes the object and in turn advises the way to control it. A certain physical system is never given a chance to be observed (and controlled) from different perspectives, unlike being considered through different mathematical models. If the output of the oscillatory system has to be stabilized, the linear time-invariant model would be the ground for most engineering solutions, out of which classical proportional-integrative (PI) feedback controller will dominate. What other concepts can be invented if the model is different, for example, when parameters are seen as timevarying?
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