On Averaging and Vibrational Control of Mechanical Systems with Multi-Frequency Inputs

[+] Author and Article Information
Sevak Tahmasian

Department of Biomedical Engineering and Mechanics, Virginia Tech, Blacksburg, VA 24061

1Corresponding author.

ASME doi:10.1115/1.4040296 History: Received March 19, 2017; Revised May 08, 2018


This paper discusses the averaging, control authority, and vibrational control of mechanical control-affine systems with high-frequency, high-amplitude inputs. The inputs have different frequencies of the same order. This work is the extension of the existing averaging method for high-frequency mechanical systems with single-frequency inputs. The control authority of mechanical systems with multi-frequency inputs, and the effects of inputs' waveform and frequency on control authority are investigated. The results show that, in general, using multi-frequency inputs may result in lower control authority of mechanical systems compared to single-frequency inputs, especially when using harmonic inputs. The results on control authority of the systems with multi-frequency inputs is demonstrated using vibrational control of a horizontal pendulum with two inputs. This paper also discusses the averaging of multiple-time-scale control systems.

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