%%?Learning?PID?Tuning?II:?Stability?Margin
%?The?PID?controller?is?the?most?widely?used?controller?in?various
%?engineering?systems.?However?appropriately?tuning?a?PID?controller?is
%?not?an?easy?task?althrough?it?has?only?three?parameters?at?most.?The
%?difficulty?particially?comes?from?some?comfilict?requirements?of?control
%?system?performance?and?partially?is?due?to?complicated?impacts?of?PID
%?parameters?on?control?performance.?This?submission?provides?the?second
%?tutorial?on?PID?tuning?using?the?stability?margin.
%
%%?Ziegler-Nichols?Tuning?Rule
%?Ziegler-Nichols?tuning?rule?was?the?first?such?effort?to?provide?a
%?practical?approach?to?tune?a?PID?controller.?According?to?the?rule?a?PID
%?controller?is?tuned?by?firstly?setting?it?to?the?P-only?mode?but?adjusting
%?the?gain?to?make?the?control?system?in?continuous?oscillation.?The
%?corresponding?gain?is?referred?to?as?the?ultimate?gain?（Ku）?and?the
%?oscillation?period?is?termed?as?the?ultimated?period?（Pu）.?Then?the?PID
%?controller?parameters?are?determined?from?Ku?and?Pu?using?the
%?Ziegler-Nichols?tuning?table.
%?
%?
%?
%?ControllerKcTiTd
%?P?Ku?/?2???
%?PI?Ku?/?2.2??Pu?/?1.2??
%?PID?Ku?/?1.7??Pu?/?2??Pu?/?8?
%?
%?
%?
%%?Determine?the?Ultimate?Gain?and?Period
%?The?key?step?of?the?Ziegler-Nichols?tuning?approach?is?to?determine?the
%?untimate?gain?and?period.?However?to?determine?the?ultimate?gain?and
%?period?experimentally?is?time?comsuming.?Since?the?continuous?oscillation
%?mode?correcponds?to?the?critical?stable?condition?for?linear?systems
%?such?a?condition?can?be?easily?determined?through?stability?margins.
%?Other?tools?such?as?the?Routh?criterion?and?the?Evans?root?locus?cannot
%?deal?with?a?time-delay?directly.
%?
%?Let?the?plant?have?gain?margin?Gm?at?crossover?frequency?Wcg.?This
%?equivalent?to?connect?with?a?unit?gain?controller.?Therefore?if?the
%?controller?gain?increases?by?Gm?then?the?system?will?oscillate?at
%?frequency?Wcg.?Therefore?Ku?and?Pu?can?be?determined?from?Gm?and?Wcg?as
%?follows:
%
%?$$K_u=G_m$$
%
%?or
%
%?$$20\log_{10}（K_u）?=?G_m?（dB）\\?\Rightarrow\\?K_u=10^{Gm/20}$$?
%
%?$$P_u=\frac{2\pi}{\omega_{cg}}$$
%
%%?Example:?PI?controller?for?a?first-order?plus?time-delay?system
%?The?plant?has?a?unit?gain?time?constant?10?and?time?delay?2
T=10;
dt=2;
G=tf（1[T?1]）;
G.InputDelay=dt;
%?use?the?Ziegler-Nichols?PID?design?tool
[kkupu]=znpidtuning（G2）;?
%?verify?Ku?and?Pu?using?step?response?of?G*ku?in?5?periods
step（feedback（ss（G*ku）1）5*pu）

%%?Closed-loop?step?response
%?the?PI?controller?transfer?function
C=k.kc*（1+tf（1[k.ti?0]））;
%?get?the?closed-loop?model?in?state?space?form?since?MATLAB/Control?Toolbox
%?support?time-delay?only?in?state-space?form.?
H=minr

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

?????文件???????1788??2008-02-01?08:40??znpidtuning.m

?????文件???????3434??2008-05-15?08:26??使用幫助：新手必看.htm

?????文件??????10634??2008-02-05?14:49??html\learningpid.html

?????文件???????4430??2008-02-05?14:48??html\learningpid_01.png

?????文件???????3675??2008-02-05?14:48??html\learningpid_02.png

?????文件???????7744??2008-02-05?14:49??html\learningpid_03.png

?????文件???????5354??2008-02-01?14:10??html\learningpid_eq105252.png

?????文件???????1125??2008-02-01?14:10??html\learningpid_eq1339.png

?????文件???????1625??2008-02-01?14:10??html\learningpid_eq14982.png

????..A.SH.?????13824??2008-10-11?13:42??html\Thumbs.db

?????目錄??????????0??2008-10-11?13:42??html

?????文件???????3702??2008-02-05?14:48??learningpid.m

?????文件????????183??2008-09-03?11:09??Matlab中文論壇--助努力的人完成畢業設計.url

-----------?---------??----------?-----??----

????????????????57518????????????????????13