Research indexBook chapter
Analysis Methods
Stefani, Wolovich
15 Jan 2019
NobleIDark:/48914/w1/20260524/E575C580DOI10.1201/9781315214030-8
Analysis Methods
Stefani, Wolovich · 2019 · Subscription
NobleIDark:/48914/w1/20260524/E575C580DOI10.1201/9781315214030-8
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Abstract
The division of the total response into zero-state and zero input components is a rather natural and logical division because these zero-input responses can easily be obtained empirically by setting either the initial conditions or the input to zero and then obtaining each response. The forced response cannot be obtained separately in most cases, so the division into forced and natural components is more mathematical than practical. Many systems are describable by a second-order linear differential equation with constant coefficients while many other higherorder systems have complex conjugate dominant roots that cause the response to be nearly second order. Thus, the study of second- order response characteristics is important in understanding system behavior. Most physical systems are designed so that the control input does affect the complete system and, as a consequence, an appropriate controller does exist. The ultimate objective of any control system is to improve and often to optimize the performance of a given dynamical system.