線性系統(tǒng)課后答案第2章-資料下載頁(yè)
2025-07-27 10:51本頁(yè)面
【正文】 , =1. By retaining only the linear terms in , and , , we obtain , and: Select state variables as , and output : + The soft landing phase of a lunar module descending on the moon can be modeled as shown in . The thrust generated is assumed to be proportional to the derivation of m, where m is the mass of the module. Then the system can be described by Where g is the gravity constant on the lunar surface. Define state variables of the system as: , , , Find a statespace equation to describe the system. Translation: 登月艙降落在月球時(shí)。產(chǎn)生的沖激力與m的微分成正比。系統(tǒng)可以描述如式所示形式。g是月球表面的重力加速度常數(shù)。定義狀態(tài)變量如式所示，試圖找出系統(tǒng)的狀態(tài)空間方程描述。Answer: The system is not linear, so we can linearize it. Suppose: So: = Define state variables as: , , , Then: =+ = Find a state equation to describe the network shown in also its transfer function.Translation: ，以及它的傳遞函數(shù)。Answer: Select state variables as: : Voltage of left capacitor: Voltage of right capacitor: Current of inductorApplying Kirchhoff’s current law: = From the upper equations, we get: They can be bined in matrix form as: =+ Use MATLAB to pute transfer function. We type:A=[1,0,0。0,0,1。0,1,1]。B=[1。1。0]。C=[0,1,0]。D=[0]。[N1,D1]=ss2tf(A,B,C,D,1)Which yields: N1 = 0 D1 = So the transfer function is: Find a state equation to describe the network shown in . Compute also its transfer matrix.Translation: ，計(jì)算它的傳遞函數(shù)矩陣。Answer: Select state variables as Fig shown. Applying Kirchhoff’s current law: = From the upper equations, we get: They can be bined in matrix form as: =+ +Applying Laplace Transform to upper equations: Find the transfer functions from to and from to of the hydraulic tank system shown in . Does the transfer function from to equal the product of the two transfer functions? Is this also true for the system shown in ?Translation: 。從到的傳遞函數(shù)等于兩個(gè)傳遞函數(shù)的乘積嗎？？Answer: Write out the equation about , and : Applying Laplace transform: So: But it is not true for , because of the loading problem in the two tanks. 1
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