自动控制理论11

1、Lecture 16Bode Analysis, stability, Gain and Phase MarginsNorth China Electric Power UniversitySun HairongTopics of this lectureGain and phase margins .System type and steady-state error from bode diagram. (Reading Module 16)Sample problems1. Gain and phase margins(GM & PM) in the Nyquist diagram To

2、 know some parametersThe frequency at which the phase is -180.The frequency at which the Mdb is 0db.ApplicationIf GM1,the system is stable, otherwise its not.If PM0,the system is stable, otherwise its not.2. Gain and phase margins (GM & PM) in Bode diagram The frequency at which the phase is -180.Th

3、e frequency at which the Mdb is 0db.If GM0db,the system is stable, otherwise its not.If PM0,the system is stable, otherwise its not.Example:The open-loop transfer function is given byPMPlot the Bode diagram and point out the gain and phase margins System typeWhen The general transfer function may be

4、 wrote as The above equation is called systems low-frequency asymptotes.And the system is called “Type v” system.3. System type and steady-state error from Bode diagramsType 0 systemThe general transfer function may be wrote as The systems low-frequency asymptotes isPlot the bode diagram of type 0 s

5、ystem.The K in the plot is also the position error constant.Type 1 systemThe general transfer function may be wrote as The systems low-frequency asymptotes isPlot the bode diagram of type 1 system.The K in the plot is also the velocity error constant.20lgKType 2 system The general transfer function

6、may be wrote as The systems low-frequency asymptotes isPlot the bode diagram of type 2 system.The K in the plot is also the acceleration error constant.20lgKsample problem 1 Plot the Bode diagram for K=45, and determine the gain and phase margins. Calculate the maximum value of K consistent with sta

7、bility, and check the answer using Rouths array. SP16.1 page 331sample problem 2 For the following system, sketch the Bode diagram, and from the straight-line approximations to the gain and phase plots, estimate the maximum value of K for which the system is stable.P16.1 page 338sample problem 3 FigP16.4 (Page 339) shows a unity-gain feedback control system, calculate the value