13控制原理課件-wanghuidiagran

1、2022/7/29Chapter 2-1CHAPTER 2Mathematical Models of Systems By Hui Wang2022/7/29Chapter 2-1Outline of this chapterIntroduction Differential Equation of Physical SystemsTransfer FunctionState Equation of SystemsBlock Diagram, Signal Flow Graphs LinearizationThe relation of various models2022/7/29Chap

2、ter 2-1Why modeling? Analysis and Design Loop1Laws. PhysicalAssumptions RealSystemPhysical ModelMathematical Model MathAnalysisComputerSimulation ModelResponsesPrediction ExpectedResponsesAugment structureModify parametersRealAbstract Differential Equations2Structure DiagramsTransfer functionsBlock

3、diagramsState model.2022/7/29Chapter 2-1Block Diagram2022/7/29Chapter 2-1Block diagram The block diagram as transfer function, also is a basic concept, which plays a very important role in control theory.G(D)u(t)y(t)Figure 2.8 Block diagram The block diagram (see Figure 2.8) represents the mathemati

4、cal operation G(D)u(t)=y(t); that is, the transfer function times the input is equal to the output of the block.G(s)U(s)Y(s)2022/7/29Chapter 2-1Block diagram G(s)U(s)Y(s)G(s)U(s)Figure 2.8 Block diagram For control systems with several components, the transfer function of each component is usually p

5、laced in a boxInput-output relationships are indicated by gain . Sometims simplified just by All of this, forms what is called a block diagram2022/7/29Chapter 2-1Block Diagram 方塊圖是控制系統(tǒng)或?qū)ο笾忻總€環(huán)節(jié)（元件）的功能和信號流向的圖解表示。每一個方塊填寫環(huán)節(jié)（元件）的傳遞函數(shù)，指向方塊的箭頭表示該環(huán)節(jié)的輸入信號，離開方塊的箭頭表示該環(huán)節(jié)的輸出信號，它是輸入信號與方塊內(nèi)的傳遞函數(shù)運算后的結(jié)果。注意箭頭方還標明了相應的信

6、號符號（有時“”會省略）。 根據(jù)方塊圖與傳遞函數(shù)的定義，可以直接由系統(tǒng)各個環(huán)節(jié)之間的關(guān)系用圖解的方式描述系統(tǒng)的信息傳遞一種建模方法。2022/7/29Chapter 2-1Modeling by block diagram We can model a process by block diagram. hARq0qinTaking Laplace transform respectively 1/RH(s)Q0(s) 1/AsH(s)Qin(s)- Q0(s)+Qin(s)KIfThen2022/7/29Chapter 2-1Modeling by block diagram-direct

7、steam heaterenvironment temperature TesteamW,Pqa, Thot-liquidcold-liquidqc, TcTTTCGCGTRef. TObjective: T; by control WDue to Pressure of steam changed often, adding steam flow control loop, thus make up of a T plus G cascaded control system.Main disturbance is TcConsidering each component of the sys

8、tem as followsControl pathTG01(s)WT2022/7/29Chapter 2-1Modeling by block diagram-direct steam heaterenvironment temperature TesteamW,Pqa, Thot-liquidcold-liquidqc, TcTTTCGCGTRef. TDisturbance pathTdG02(s)TcTdWhere T+Td=T2 paths that causing WG03(s)WG04(s)Steam PGv(s)control U2022/7/29Chapter 2-1Mode

9、ling by block diagram-direct steam heaterenvironment temperature TesteamW,Pqa, Thot-liquidcold-liquidqc, TcTTTCGCGTRef. TsController1-GC (second loop) Controller2-TC (main loop) GGC(s)uGGT(s)Wu1GTC(s)u1GTT(s)TTs2022/7/29Chapter 2-1Modeling by block diagram-direct steam heaterOverall system block dia

10、gram model is as follows GTT(s)TTGTC(s)TsGGC(s)uGGT(s)u1G03(s)WG04(s)Steam PGv(s)G01(s)G02(s)TcTd2022/7/29Chapter 2-1Block diagram: Example 1 (Cascade or Series)N block diagrams are in series2022/7/29Chapter 2-1Block diagram:Example 2 (Parallel)N block diagrams are paralled2022/7/29Chapter 2-1-Block

11、 diagram:Example 3 (Feedback)Note! Note! 2022/7/29Chapter 2-1Block diagram:Example 3 (Feedback)U(s)Y(s)Where “+” means positive feedback and “” implied negative feedback.2022/7/29Chapter 2-1Block Diagram Simplification2022/7/29Chapter 2-1Block Diagram Simplification2022/7/29Chapter 2-1 a. 綜合點前移 圖(1)

12、表示了綜合點前移的等效變換。 (a) 原始結(jié)構(gòu)圖 (b) 等效結(jié)構(gòu)圖 圖(1)綜合點前移的變換挪動后，信號關(guān)系為: 綜合點與引出點的移動挪動前的結(jié)構(gòu)圖中，信號關(guān)系為:2022/7/29Chapter 2-1 b. 綜合點之間的移動圖(2)為相鄰兩個綜合點前后移動的等效變換。 (a)原始結(jié)構(gòu)圖 (b) 等效結(jié)構(gòu)圖圖(2) 相鄰綜合點的移動挪動前，總輸出信號 : 挪動后，總輸出信號 : 2022/7/29Chapter 2-1 c. 引出點后移在圖(3)中給出了引出點后移的等效變換。 (a)原始結(jié)構(gòu)圖 (b) 等效結(jié)構(gòu)圖 圖(3) 引出點后移的變換挪動后的支路上的信號為:2022/7/29Chap

13、ter 2-1 若干個引出點相鄰，引出點之間相互交換位置，完全不會改變引出信號的性質(zhì)。如圖(4)所示。圖(4) 相鄰引出點的移動d.相鄰引出點之間的移動2022/7/29Chapter 2-1Block Diagram SimplificationExample-1: Find the transfer function ofStep1: Apply Feedbackpick-off point2022/7/29Chapter 2-1Block Diagram SimplificationStep2: Move pick-off point forwardStep3: Using feedba

14、ck, parallel and series2022/7/29Chapter 2-1Block Diagram SimplificationFinally, get overall system transfer function using series2022/7/29Chapter 2-1Block Diagram SimplificationExample-2: Find the transfer function of the Fig. follow Step1: (1) moving point from a to c forwardsThere 2 cross-sum-poin

15、ts in forward path: a and b . ababG2(s)c (2) changing position with point , get Fig. (a)c2022/7/29Chapter 2-1Loop 1Step2: apply feedback for internal loop 1, get Fig.(b)2022/7/29Chapter 2-1Loop 2Step3: apply feedback again for sub-loop2, get Fig.(c)2022/7/29Chapter 2-1Step4: Find the transfer functi

16、on of overall system, see Fig.(d) 2022/7/29Chapter 2-1Block Diagram SimplificationOthers simplification steps? And results?The closed-loop transfer function of this system is 2022/7/29Chapter 2-1Block Diagram SimplificationExample-3 Another method of example-2Rather than moving point , here let poin

17、t backward 2022/7/29Chapter 2-1Block Diagram Simplification: Example 3same result as before!2022/7/29Chapter 2-1Block Diagram SimplificationExample-3: Find the transfer function of the system as followsapply feedback to 2 sub-loops respectively, transfer functions areLoop1Loop2Loop1Loop22022/7/29Chapter 2-1Block Diagram SimplificationExample-3: Find the transfer function o