Chapter 15 Dynamic Characteristic Identification Clay Jordan and Tommy Hazelwood Abstract This paper introduces a dynamic system parameter extraction approach using experimental data and a known characteristic equation for a single degree of freedom mass-spring-damper system. The efficacy of curve fitting to determine mass, damping, and stiffness for simulated underdamped, critically damped, and overdamped systems is explored. Two methods are investigated to obtain these characteristics for simulated systems; a step response approach in the time domain and a transfer function and dynamic stiffness approach in the frequency domain. Commonly available software, MATLAB, is used for curve fitting. An examination of the effect of inaccurate seeds, or starting values, for mass, damping, and stiffness is included. Keywords Dynamic stiffness · Step response · Curve fitting · MATLAB · System analysis 15.1 Introduction This paper investigates a method to identify the mass (m), damping (c), and stiffness (k) of a system by curve fitting a modeled single degree of freedom mass-spring-damper system. Data is computer generated with MATLAB using known values for mass, damping, and stiffness to simulate empirical measurement data that is layered with noise to emulate real data. A step response approach in the time domain and a dynamic stiffness approach in the frequency domain are used to curve fit this data. The step response of the system to an input is curve fit using a MATLAB error minimization algorithm resulting in the identification of the values for the mass, damping, and stiffness coefficients. These parameters are compared to the same values determined using the dynamic stiffness of the modeled system utilizing the same error minimization algorithm. The mass, damping, and stiffness coefficients generated through these two methodologies are compared to the original known values. 15.2 Background Attempting to understand and control motion in a system—be it a machine tool’s linear stage, scientific equipment, or other piece of machinery— is simplified by knowing the basic dynamic characteristics of that system. If the basic dynamic characteristics of mass (m), damping (c), and stiffness (k) are not known, for instance, due to the age of the equipment, an inability to directly access the equipment, or some other gap in knowledge, it is possible to identify these values using minimization/optimization tools. This is accomplished by characterizing the responses of the system to an input or by creating a simple model of the system and using an error minimization function to determine values for the mass, damping, and stiffness coefficients given a reasonable seed. 15.3 Analysis The efficacy of determining the mass, damping, and stiffness coefficients of a single degree of freedom mass-spring-damper system using MATLAB’s fminsearch function is investigated by first simulating a system and then separately evaluating the C. Jordan ( ) · T. Hazelwood Oak Ridge National Laboratory, Dynamic Systems Analysis Group, Electrical and Electronics Systems Research Division, Oak Ridge, TN, USA e-mail: jordanca@ornl.gov; hazelwoodtj@ornl.gov © Society for Experimental Mechanics, Inc. 2020 N. Dervilis (ed.), Special Topics in Structural Dynamics & Experimental Techniques, Volume 5, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-12243-0_15 101
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