1、精選優質文檔-傾情為你奉上基于MATLAB語言環境的二階慣性系統PID控制仿真目錄一、課程設計要求3二、PID控制簡述3三、系統性能分析5四、參數整定6五、PID三參數變化對系統的影響7六、人機交互界面設計9七、心得體會15一、課程設計要求1在MATLAB語言環境下，給定參數下的二階慣性系統，要求分析在單位階躍函數作用下，系統的動態響應性能；2在系統的前向通道加入比例、積分、微分控制器，調整系統控制器的比例、積分、微分參數，需求系統的最佳輸出性能；3利用所學知識分析三參數增大或減小時，對系統動靜態性能的影響，并用仿真實驗驗證其正確性。4.設計人機交互界面，可通過對界面輸入參數，實現參數修改于曲

2、線顯示。注：二階系統前向通道傳遞函數為。二、PID控制簡述PID控制器由比例單元（P）、積分單元（I）和微分單元（D）組成。其輸入e (t)與輸出u (t)的關系為： u(t)=kpe(t)+1/TIe(t)dt+TD*de(t)/dt 式中積分的上下限分別是0和t 。因此它的傳遞函數為：G(s)=U(s)/E(s)=kp1+1/(TI*s)+TD*s 。其中kp為比例系數； TI為積分時間常數； TD為微分時間常數。比例(P)控制比例控制是一種最簡單的控制方式。其控制器的輸出與輸入誤差信號成比例關系。當僅有比例控制時系統輸出存在穩態誤差(ady-state error)。積分(I)控制在積分

3、控制中，控制器的輸出與輸入誤差信號的積分成正比關系。對一個自動控制系統，如果在進入穩態后存在穩態誤差，則這個控制系統是有穩態誤差的或簡稱有差系統(System with Steady-state Error)。為了消除穩態誤差，在控制器中必須引入項”。積分項對誤差取決于時間的積分，隨著時間的增加，積分項會增大。這樣，即便誤差很小，積分項也會隨著時間的增加而加大，推動控制器的輸出增大使穩態誤差進一步減小，直到等于零。因此，比例+積分(PI)控制器，可以使系統在進入穩態后無穩態誤差。微分(D)控制在微分控制中，控制器的輸出與輸入誤差信號的微分(即誤差的變化率)成正比關系。自動控制系統在克服誤差的調

4、節過程中能會出現振蕩甚至失穩。其原因是由于存在有較大慣性組件(環節)或有滯后(delay)組件，具有抑制誤差的作用，其變化總是落后于誤的變化。解決的辦法是使抑制誤差的作用的變化“超前”，即在誤差接近零時，抑制誤差的作用就應該是零。這就是說，在控制器中僅入“比例”項往往是不夠的，比例項的作用僅是放大誤差的幅值，而目前需要增加的是“微分項”，它能預測誤差變化的趨勢，這樣，有比例+微分的控制器，就能夠提前使抑制誤差的控制作用等于零，甚至為負值，從而避免了被控量的嚴重超調。所以對有較大慣性或滯的被控對象，比例+微分(PD)控制器能改善系統在調節過程中的動態特性。PID控制器的參數整定PID控制器的參數

5、整定是控制系統設計的核心內容。它是根據被控過程的特性確定PID控制器的比例系數、積分時間和微分時間大小。PID控制器參數整定的方法很多，概括起來有兩大類：一是理論計算整定法。它主要是依據系統的數學模型，經過理論計算確定控器參數。這種方法所得到的計算數據未必可以直接用，還必須通過工程實際進行調整和修改。二是工程整定方法，它主要依賴工程經驗，直接在控制系統的試驗中進行，且方法簡單、易于掌握，在工程實際中被廣泛采用。PID控制器參數的工程整定方法，主要有臨界比例法反應曲線法和衰減法。三種方法各有其特點，其共同點都是通過試驗，然后按照工程經驗公式對控制器參數進行整定。但無論采用哪一方法所得到的控制器參

6、數，都需要在實際運行中進行最后調整與完善。現在一般采用的是臨界比例法。利用該方法進行PID 整定步驟如下：(1)首先預選擇一個足夠短的采樣周期讓系統工作(2)僅加入比例控制環節，直到系統對輸入的階躍響應出現臨界振蕩，記下這時的比例放大系數和臨界振蕩周期(3)在一定的控制度下通過公式計算得到PID控制器的參數。三、系統性能分析穩定性判斷程序如下：num=1;den=100 4 81; z,p,k=tf2zp(num,den) jj=find(real(p)>0);n=length(jj); if(n>0) disp('The System is Unstable');

7、 else disp('The System is Stable'); end axis equal; pzmap(p,z); title('The pole Map of system');運行結果：z =Empty matrix: 0-by-1p =-0.0200 + 0.8998i -0.0200 - 0.8998ik = 0.0100The System is Stable所以系統是穩定的。系統的極點分布圖如下：系統的性能指標判斷程序如下：num=1;den=100 4 80;step(num,den);figure(1);hold on得出性能指標如下

8、：上升時間tr：1.79s峰值時間tp：3.58s最大超調量：92%調節時間ts：150s穩態誤差：0.988衰減率：0.0625由各指標可知，該系統的最大超調量過大，調節時間太長，且穩態誤差接近于1，需要進行整定。四、參數的整定調節器參數整定的實質就是選擇合適的調節器參數，使其閉環控制系統的特征方程的每一個根都能滿足穩定性的要求，即選擇調節器的參數比例度。積分時間以及微分時間的大小，是特征方程所有實根的實數部分均為負數，從而保證系統式穩定的；與此同時還要使衰減指數在0.2210.366之間，以滿足衰減率在0.750.9的要求加入PID調節器，調節PID調節器各項參數，可得當Kp=200,Ti

9、=0.32;Td=3;系統的各參數為：上升時間tr：0.537s峰值時間tp：0.997s最大超調量：5%調節時間ts：12s穩態誤差：0衰減率：0.6由上述各指標可知系統的穩態誤差已消除，調節時間也在工業可接受標準范圍內。五、PID三參數變化對系統的影響設PID控制器的傳遞函數為：G（s）=Kp(1+1/Tis+Tds)1、 比例控制的影響：下面的程序研究在不同的Kp值下，閉環系統的單位階躍響應曲線及根軌跡圖，程序如下：G0=tf(1,100 4 80);P=1 10 20 50 79;hold onfor i=1:length(P)G=feedback(P(i)*G0,1);step(G)

10、;grid on,axis(0,160,0,1)endhold off由圖可知：隨著Kp的增大，閉環系統的靈敏度增大，穩態誤差減小，響應的震蕩增強。輸入程序：figure,rlocus(G0)k=rlocfind(G0)可得根軌跡圖如下：由根軌跡圖知道，無論K值怎么變化，根軌跡都不會跨入右半平面，即系統一直是穩定的。2、 積分控制的影響 將Kp的值固定在Kp=70，采用PI控制策略，則我們可以通過下面的程序繪制不同的Ti值下閉環系統的單位階躍響應曲線。程序如下：G0=tf(1,100 4 80);Kp=1;Ti=0.3:0.05:0.7;hold onfor i=1:length(Ti);Gc

11、=tf(Kp*1,1/Ti(i),1,0);G=feedback(Gc*G0,1);step(G);grid on,axis(0,350,0,1.1);end得出圖如下：由圖可知，隨著Ti的減小，系統的調節時間變短，但是當Ti太小時，系統將變的不穩定。PI控制能使系統由有差系統變為無差系統，但是積分作用不能太強。在題所示系統中，Ti的選值不能小于0.3,。3、微分控制的影響令Kp=100,Ti=0.32，通過以下程序得出在不同的Td值下閉環系統的階躍響應曲線，程序如下：G0=tf(1,100 4 80);Kp=100;Ti=0.32;Td=2:0.5:5;hold onfor i=1:leng

12、th(Td);Gc=tf(Kp*Ti*Td(i),Ti,1,Ti,0);G=feedback(Gc*G0,1);step(G);grid on,axis(0,100,0,1.5);end由上圖曲線可以看出，Td的取值越大，系統響應速度越快，同時系統的超調量將小。六、人機交互界面設計人機交互界面采用matlab的GUI模塊設計。程序如下：function varargout = PID(varargin)% PID M-file for PID.fig% PID, by itself, creates a new PID or raises the existing% singleton*.%

13、H = PID returns the handle to a new PID or the handle to% the existing singleton*.% PID('CALLBACK',hObject,eventData,handles,.) calls the local% function named CALLBACK in PID.M with the given input arguments.% PID('Property','Value',.) creates a new PID or raises the% existi

14、ng singleton*. Starting from the left, property value pairs are% applied to the GUI before PID_OpeningFunction gets called. An% unrecognized property name or invalid value makes property application% stop. All inputs are passed to PID_OpeningFcn via varargin.% *See GUI Options on GUIDE's Tools m

15、enu. Choose "GUI allows only one% instance to run (singleton)".% See also: GUIDE, GUIDATA, GUIHANDLES% Copyright 2002-2003 The MathWorks, Inc.% Edit the above text to modify the response to help PID% Last Modified by GUIDE v2.5 07-Dec-2011 11:37:11% Begin initialization code - DO NOT EDITg

16、ui_Singleton = 1;gui_State = struct('gui_Name', mfilename, . 'gui_Singleton', gui_Singleton, . 'gui_OpeningFcn', PID_OpeningFcn, . 'gui_OutputFcn', PID_OutputFcn, . 'gui_LayoutFcn', , . 'gui_Callback', );if nargin && ischar(varargin1) gui_State

17、.gui_Callback = str2func(varargin1);endif nargout varargout1:nargout = gui_mainfcn(gui_State, varargin:);else gui_mainfcn(gui_State, varargin:);end% End initialization code - DO NOT EDIT% - Executes just before PID is made visible.function PID_OpeningFcn(hObject, eventdata, handles, varargin)% This

18、function has no output args, see OutputFcn.% hObject handle to figure% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)% varargin command line arguments to PID (see VARARGIN)% Choose default command line output for PIDhandle

19、s.output = hObject;% Update handles structureguidata(hObject, handles);% UIWAIT makes PID wait for user response (see UIRESUME)% uiwait(handles.figure1);% - Outputs from this function are returned to the command line.function varargout = PID_OutputFcn(hObject, eventdata, handles) % varargout cell ar

20、ray for returning output args (see VARARGOUT);% hObject handle to figure% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)% Get default command line output from handles structurevarargout1 = handles.output;function edit1_Cal

21、lback(hObject, eventdata, handles)% hObject handle to edit1 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)% Hints: get(hObject,'String') returns contents of edit1 as text% str2double(get(hObject,'St

22、ring') returns contents of edit1 as a doubleinput=str2num(get(hObject,'String');if(isempty(input) set(hObject,'String',' ')endguidata(hObject,handles);% - Executes during object creation, after setting all properties.function edit1_CreateFcn(hObject, eventdata, handles)%

23、hObject handle to edit1 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called% Hint: edit controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc set(hObject,'BackgroundColor

24、','white');else set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor');endfunction edit2_Callback(hObject, eventdata, handles)% hObject handle to edit2 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with han

25、dles and user data (see GUIDATA)% Hints: get(hObject,'String') returns contents of edit2 as text% str2double(get(hObject,'String') returns contents of edit2 as a doubleinput=str2num(get(hObject,'String');if(isempty(input) set(hObject,'String',' ')endguidata(hO

26、bject,handles);% - Executes during object creation, after setting all properties.function edit2_CreateFcn(hObject, eventdata, handles)% hObject handle to edit2 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns

27、 called% Hint: edit controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc set(hObject,'BackgroundColor','white');else set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor');endfunction edit3_Callback(hObject, eventdata, ha

28、ndles)% hObject handle to edit3 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)% Hints: get(hObject,'String') returns contents of edit3 as text% str2double(get(hObject,'String') returns contents

29、of edit3 as a doubleinput=str2num(get(hObject,'String');if(isempty(input) set(hObject,'String',' ')endguidata(hObject,handles);% - Executes during object creation, after setting all properties.function edit3_CreateFcn(hObject, eventdata, handles)% hObject handle to edit3 (see

30、 GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called% Hint: edit controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc set(hObject,'BackgroundColor','white');else

31、set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor');end% - Executes on button press in clear.function clear_Callback(hObject, eventdata, handles)% hObject handle to clear (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structur

32、e with handles and user data (see GUIDATA)% - Executes on button press in pushbutton2.function pushbutton2_Callback(hObject, eventdata, handles)% hObject handle to pushbutton2 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (

33、see GUIDATA)% - Executes on button press in pushbutton3.function pushbutton3_Callback(hObject, eventdata, handles)% hObject handle to pushbutton3 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)% - Executes on button press in pushbutton4.function pushbutton4_Callback(hObject, eventdata, handles)% hObject handle to pushbutton4 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user dat