線(xiàn)性系統(tǒng)課后答案第2章(完整版)
【正文】 systems shows in . Show that the unitstep responses of the positivefeedback system are as shown in (a) for a=1 and in (b) for a=. Show also that the unitstep responses of the negativefeedback system are as shown in Fig (c) and (d), respectively, for a=1 and a=. Fig Translation: 。相應(yīng)的輸出表示為y1,y2 和y3。對(duì)于所有的t，w和to，都是常數(shù)。理想低通濾波器是因果的嗎？現(xiàn)實(shí)世界中有可能構(gòu)造這種濾波器嗎？Answer: Consider two different time: ts and tr, ts tr, the value of g(tstr) denotes the output at time ts, excited by the impulse input at time tr. It indicates that the system output at time ts is dependent on future input at time tr. In other words, the system is not causal. We know that all physical system should be causal, so it is impossible to built the filter in the real world. Consider a system whose input u and output y are related by where a is a fixed constant. The system is called a truncation operator, which chops off the input after time a. Is the system linear? Is it timeinvariant? Is it causal?Translation: 考慮具有如式所示輸入輸出關(guān)系的系統(tǒng)，a是一個(gè)確定的常數(shù)。在x(0)不等于零的情況下，下面哪種說(shuō)法是正確的？Answer: A linear system has the superposition property: In case 1: So y3y1+y2. In case 2: So y3=(y1+y2). In case 3: So y3y1y2. Consider a system whose input and output are related by for all t. Show that the system satisfies the homogeneity property but not the additivity property.Translation: 考慮輸入輸出關(guān)系如式的系統(tǒng),證明系統(tǒng)滿(mǎn)足齊次性,但是不滿(mǎn)足可加性.Answer: Suppose the system is initially relaxed, system input: a is any real constant. Then system output q(t): So it satisfies the homogeneity property. If the system satisfies the additivity property, consider system input m(t) and n(t), m(0)=1, m(1)=2。說(shuō)明正反饋系統(tǒng)的單位階躍響應(yīng)，當(dāng)a=1時(shí)，(a)所示。g是月球表面的重力加速度常數(shù)。0]。D=[0]。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)。(c)(b)所示，相應(yīng)地，對(duì)a=1和a=。因而對(duì)具有某種連續(xù)性質(zhì)的系統(tǒng)，可加性導(dǎo)致齊次性。它截?cái)鄷r(shí)間a之后的輸入。其中u表示輸入，y表示輸出。在此系統(tǒng)上進(jìn)行三次實(shí)驗(yàn)，輸入分別為u1(t), u2(t) 和u3(t)，t=0。Answer: Define: So: Then: So: It proves that g(t,T) depends only on tT. Consider a system with impulse respo
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