Abstract
The conventional harmonic balance principle is a convenient tool for finding periodic solutions in variable-structure systems, which may occur as chattering in sliding mode control or as a normal operating mode in relay systems, limit cycling tests aimed at controller tuning through variable-structure algorithms, etc. In the present book chapter, the conventional harmonic balance principle is extended to transient oscillatory processes in systems. This principle is termed the dynamic harmonic balance principle. It is formulated for the system having one single-valued oddsymmetric nonlinearity and linear plant without zeros in the transfer function. Based on the dynamic harmonic balance, the equations for the amplitude, frequency rate of change, and amplitude rate of change are derived. This principle is then illustrated by analysis of transient motions in a variable-structure system and the decaying motions of a rocking block.
| Original language | British English |
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| Title of host publication | Recent Trends in Sliding Mode Control |
| Publisher | Institution of Engineering and Technology |
| Pages | 155-174 |
| Number of pages | 20 |
| ISBN (Electronic) | 9781785610776 |
| ISBN (Print) | 9781785610769 |
| DOIs | |
| State | Published - 1 Jan 2016 |