13控制原理课件-wanghui第五章频域分析

1、1CHAPTER 5 Frequency ResponseBy Hui Wang FTP:9/1682Outline of Chapter 5IntroductionBode Plots (Logarithmic plots)Direct Polar PlotsNyquists Stability CriterionPhase Margin and Gain Margin and Their Relation to Stability 3Frequency Response1. IntroductionThe two basic methods for predicting and adjus

2、ting a systems performance: The root-locus methods Advantage: it displays the location of the closed-loop poles as a parameter (gain) is varied it explicitly gives information about transient performance The actual time response is easily obtained by means of the inverse Laplace transform because th

3、e precise root locations are known. Disadvantages: does not provide steady state performance information cannot handle constraints on frequency ranges for measurement noise and disturbance rejectionNeed a new tool to address these issues4Frequency Response1. Introduction The frequency-response metho

4、ds - a good complement to Root Locus We can infer stability and performance, namely steady state performance, from the same plot It is easy to include constraints on frequency ranges Permit evaluation of the effect of noise, exclude the noise by designing a passband and therefore improve the system

5、performance Can use measured data when no model is available (also good for system identification) Time delays are handled correctly, contrary to root locus Analysis and design techniques are graphical (asymptotic lines) and easy to use5In this chapter: Two graphical representation of transfer funct

6、ions are presented: the logarithmic（对数的） plots the polar（极坐标的） plots. Developing the Nyquists stability criterion using these plots. The performance of frequency domain.Frequency Response1. Introduction6Frequency Response1. Introduction: Frequency characteristicConsidering a system G(s)X(s)Y(s)Syste

7、m block diagramIf the input isLT7Frequency Response1. Introduction: Frequency characteristic8Frequency Response1. Introduction: Frequency characteristicLT-1For a stable system, all transient components will approach to zero when time t goes infinity, only steady-state response keep down.tWhere b can

8、 be found by residues theorem. 9Frequency Response1. Introduction: Frequency characteristicWhere G(j) is a complex number, can be expressed bySimilarly, G(-j) 10Frequency Response1. Introduction: Frequency characteristicorWhich is the magnitude of steady state response.Where is usually calledfrequen

9、cy characteristic. There are two methods to obtain G(jw): analyzing and experiment.11Frequency Response1. Introduction: Frequency characteristicDefinition: The frequency response of a system is described as the steady-state response with a sine-wave forcing function for all values of frequency.Such

10、as:Input:Output:The magnitude ratio of the frequency responseThe angle of the frequency response When a linear system with transfer function G(s) is excited by a sinusoid of frequency , the steady state output is a sinusoid of the same frequency, with magnitude scaled by |G(j)| and phase shifted by

11、G(j).12Frequency Response1. Introduction: Frequency response from the pole-zeros plotThe transfer function of linear and stable system:The frequency response:jj1p1p2p3z1j1-p1j1-p2j1-p3j1-z1See P.113-11413Frequency Response1. Introduction: From frequency response to time response Once the frequency r

12、esponse of a system has been determined, the time response can be determined by inverting the corresponding Fourier transform.Differential equation system Transfer function Frequency characteristic s=D s=jj=D 14Frequency Response1. Introduction: Frequency response curvesThe frequency domain plots be

13、long to two categories:1) The plot of the magnitude of the output-input ratio vs. frequency in rectangular coordinates and the corresponding phase angle vs. frequency. For exampleIn logarithmic coordinates these are known as bode plots or log magnitude diagram and phase diagram.10.707aa0-45-90See P.

14、114-11515 For a given sinusoidal input signal, the input and steady-state output are of the following forms:the closed-loop frequency response is given by0()(1)(3)(2)mThe Frequency-response characteristics of C(j)/R(j) in rectangular coordinates10.707b3M()(1)(3)(2)b2mFrequency Response1. Introductio

15、n: Frequency response curvesSee P247 & Fig.8.1162) The output-input ratio is plotted in polar coordinates with frequency as a parameter.-generally used only for the open-loop response and commonly referred to as Nyquist plots.ImG(j)=0=The Nyquist plots is a arc of which the center of the circle is (

16、0.5,j0) and the radius is 0.5ReG(j)Example 1: the transfer function is G(s)0.51ReImFrequency Response1. Introduction: Frequency response curves17The log magnitude and the angle are combined into a single curve of log magnitude vs. angle, with frequency as a parameter. This curve is called the Nichols chart