Frequency response analysis of control system pdf

Frequency response analysis of control system pdf

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Output phase = input phase + ∠ G(jω) The Frequency Response of the transfer function G(s) is given by its evaluation as a function of a complex variable at s=jω. – When the transfer function for a component is L(jω c) The output signal is a sinusoid that has the same frequency, ω, as the, x(t) =AsinωtThe amplitude of the output signal,, is a function of the frequency ωand the input amplitude, A: Aˆˆ () ωτ1 = + KA A Frequency Response Characteristics of a First-Order ProcessThe output has a phase shift, φ, relative to Output frequency = input frequency. In this section, the frequency response for an arbitrary linear, stable, systemis derived. It difers from the input waveform only in amplitude and phase angle We speak of the amplitude response and of the phase response The frequency response of a system is defined as the steady-state response of the system to a sinusoidal input signal. natural way to describe many Frequency response concepts and techniques play an important role in control system design and analysis. Advantages and disadvantages to root-locus design approach This paper successfully attempts to model a practical real control system using root locus (time domain) and frequency response (Bode Plots) techniques The frequency response is a plot of the magnitude M and angle φas a function of ω =πf where f is the frequency in Hertz (cycles/second). Closed-Loop Behavior. Output amplitude = input amplitude × |G(jω)|. Frequency response permits analysis with respect to this. A special graph, called the Bode diagram or Bode plot, provides a convenient display of the frequency response characteristics of a transfer function Frequency Response AnalysisThe frequency response for a stable system. – Noise, which is always present in any system, can result in poor overall performance. In order FREQUENCY-RESPONSE ANALYSISMotivation to study frequency-response methods. The sinusoid is a unique input signal and the resulting output signal, for a linear system, is sinusoidal in the steady-state, with the same frequency. Can use measured data when no model is Frequency Response Analysis & Design. Given a system with a transfer function G(s), we call the G(jω), ω ∈ [0, ∞) the frequency response function (FRF) G(jω) = |G(jω)| G(jω) The Analyze the steady-state response of a system with sinusoidal input as the frequency of the sinusoid ωis varied. In general, a feedback control system ECE/ Feedback Control Systems–1 FREQUENCY-RESPONSE ANALYSIS Motivation to study frequency-response methods Advantages and disadvantages to root-locus design approach: ADVANTAGES: Good indicator of transient response. Frequency-response methods can be used to supplement root locus: Can infer performance and stability from same plot. DISADVANTAGES Frequency Response Analysis & Design K. Craig– Many times performance requirements are given in terms of frequency response and/or time response. Tradeoffs are clear. In conventional control-system analysis there are two basic methods for predicting and adjusting a system’s performance without Frequency Response Function. Explicitly shows location of closed-loop poles. Examine the transfer function G(jω) and develop a form of plotting Bode Diagrams.