ELE 809 Study Guide - Fall 2018, Comprehensive Midterm Notes - Transfer Function, Polynomial, Volkswagen Beetle
12 Oct 2018
School
Department
Course
Professor
ELE 809
MIDTERM EXAM
STUDY GUIDE
Fall 2018
ELE809
Chapter 1 Stability
Introduction (section 6.1)
• ControlDesignRequirements:
- Transient Response
- Stability (in this chapter)
- Steady-state Errors (next chapter)
• TransientresponseandSteady-stateErrorare meaningless for an
unstable system.
• This chapter investigates stability for linear time- invariant (LTI)
systems.
4
Introduction
• Whatisstability?
• Systemtotalresponse:
c(t) cforced (t) cnatural (t)
• If t results in cnatural (t) then the LTI system is
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unstable.
• If t results incnatural (t) 0 then the LTI system is stable.
t c (t)
results in natural remaining constant or
• If
oscillating, then the LTI system is marginally stable.
5
Introduction
• Iftheinputisunbounded,forcedresponsecouldbe unbounded as well.
(Hard to determine the stability)
• Bounded-InputBounded-Output(BIBO)Stability: - A system is stable if
every bounded input yields a
bounded output. (stable systems)
- A system is unstable if every bounded input yields a unbounded
output. (marginally stable and unstable systems)
6
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Document Summary
Steady-state errors (next chapter: transientresponseandsteady-stateerrorare meaningless for an, this chapter investigates stability for linear time- invariant (lti) unstable system. systems. Introduction: whatisstability, systemtotalresponse, if t cforced (t) results in cnatural (t) c(t) cnatural (t) then the lti system is results incnatural (t) 0 then the lti system is stable. results in natural remaining constant or unstable. c (t) t: if t, if oscillating, then the lti system is marginally stable. Introduction: iftheinputisunbounded,forcedresponsecouldbe unbounded as well, bounded-inputbounded-output(bibo)stability: - a system is stable if (hard to determine the stability) every bounded input yields a bounded output. (stable systems) A system is unstable if every bounded input yields a unbounded output. (marginally stable and unstable systems) Stable systems have closed-loop transfer functions with poles only in the left half-plane. Unstable systems have closed-loop transfer functions with at least one pole in the right half-plane and/or poles of multiplicity greater than 1 on the imaginary axis.
