【正文】 nse as shown in (a). What is the zerostate response excited by the input u(t) shown in (b)? Translation: (a)所示的系統(tǒng)，(b)所示輸入u(t)激勵(lì)的零狀 態(tài)響應(yīng)是什么？Answer: Write out the function of g(t) and u(t): then y(t) equals to the convolution integral: If 0=t=1, 0=r=1, 0=tr=1: If 1=t=2: Calculate integral separately: Consider a system described by What are the transfer function and the impulse response of the system?Translation: 考慮如式所描述的系統(tǒng)，它的傳遞函數(shù)和沖激響應(yīng)是什么？Answer: Applying the Laplace transform to system inputoutput equation, supposing that the System is initial relaxed: System transfer function: Impulse response: Let y(t) be the unitstep response of a linear timeinvariant system. Show that the impulseresponse of the system equals dy(t)/dt.Translation: y(t)是線性定常系統(tǒng)的單位階躍響應(yīng)。假如角度都很小時(shí)，能否考慮系統(tǒng)為線性？Answer: For (a), the application of Newton’s law to the linear movements yields: Assuming and to be small, we can use the approximation =, =1. By retaining only the linear terms in and , we obtain and: Select state variables as , and output For (b), the application of Newton’s law to the linear movements yields: Assuming , and , to be small, we can use the approximation =, =, =1, =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)。0,1,1]。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.