WSEAS Transactions on Systems and Control
Print ISSN: 1991-8763, E-ISSN: 2224-2856
Volume 20, 2025
A Novel Approach to Modelling Overdamped Second and Higher-Order Systems using Linearized Derived Equations
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Abstract: A second-order system is widely recognized in control systems, as many practical systems are modeled using it. The system's response to a step input is well-defined, with mathematical expressions available for key parameters like rise time, settling time, and others. However, most of these equations apply specifically to an underdamped second-order system, where an explicit solution is relatively straightforward, except for the delay time equation, which is derived from a linear equation involving the damping factor, ϛ. This paper develops mathematical equations for both delay time and rise time-based on linear equations, allowing the extraction of a mathematical model from the system's output response for both low and high damping factor values. Additionally, the proposed equations can be applied to model higher-order systems by using an equivalent second-order system, with results showing that this model accurately represents the higher-order system. Further analysis investigates the effect of the damping factor on natural frequency ratio $$(ϛ/w_{n})$$ at high ϛ values, demonstrating that the system's response depends on $$ϛ/w_{n}$$ rather than the individual values of ϛ or wn. This implies that the system response remains consistent for a fixed ϛ/wn ratio.
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Keywords: over damped second order system, delay time, rise time, natural frequency ratio, damping ratio, mathematical model, higher order system
Pages: 100-108
DOI: 10.37394/23203.2025.20.12