【正文】 ion: 系統(tǒng)特征方程canonical state variables: 正則狀態(tài)變量physicalvariable: 物理變數(shù)energystorage elements: 儲能元件state equation: 狀態(tài)方程 Transfer function and block diagram傳遞函數(shù)和方框圖system transfer function: If the system differential equation is linear, the ratio of the output variable to the input variable, where the variables are expressed as functions of the D operator, is called the transfer function. 系統(tǒng)傳遞函數(shù) 如果描述系統(tǒng)的微分方程是線性的，那么輸出變量和輸入變量之比（這些變量可以表示成算子D的函數(shù))就稱之為傳遞函數(shù)。If the differential equation of a system is as following: 如果系統(tǒng)的微分方程如下： （）Then the system transfer function is: 那么該系統(tǒng)的傳遞函數(shù)為： （）The notation G(D) is used to denote a transfer function when it is expressed in terms of the D operator. It may also be written simply as G. 當方程式用算子D表示后，符號G(D)就表示傳遞函數(shù)。G(D)也可簡寫成G。The block diagram representation of this system (Fig. ) represents the mathematical operation G(D)u(t)=y(t)。 that is, the transfer function times the input is equal to the output of the block. The resulting equation is the differential equation of the system. 系統(tǒng)的方框圖(圖28)表達式描述了一種數(shù)學運算G(D)u(t)＝y(tǒng)(t)，即傳遞函數(shù)乘輸入等于該方框圖的輸出。所得到的方程就是該系統(tǒng)的微分方程。 Mechanical translation systems機械平移系統(tǒng)Mechanical systems obey Newton39。s law: the sum of the forces equals zero。 that is, the sum of the applied forces must be equal to the sum of the reactive forces. 機械系統(tǒng)遵守牛頓定律，即作用力之和必須等于反用力之和，總的合力等于零。The three qualities characterizing elements in a mechanical translation system are mass, elastance, and damping. 在機械平移（直線運動）系統(tǒng)中，表征元件的三個量是：質(zhì)量、彈性和阻尼。Basic elements entailing these qualities are represented as network elements. 我們把包含有這些量的基本元件表示成網(wǎng)絡元件。FIG Network elements of mechanical translation systems機械平移（直線運動）系統(tǒng)的網(wǎng)絡元件The mass M is the inertial element. A force applied to a mass produces an acceleration of the mass. The reaction force fM is equal to the product of mass and acceleration and is opposite in direction to the applied force. In terms of displacement x, velocity v, and acceleration a, the force equation is: 質(zhì)量是一個慣性元件，作用到一個質(zhì)量上的力就要使之產(chǎn)生一個加速度。反作用力等于該質(zhì)量和加速度的乘積，而且與作用力方向相反。根據(jù)位移、速度和加速度，該力的方程式為： （）The elastance, or stiffness, K provides a restoring force as represented by a spring. The reaction force fK on each end of the spring is the same and is equal to the product of the stiffness K and the amount of deformation of the spring. The displacement of each end of the spring is measured from the original or equilibrium position. End c has a position xc, and end d has a position xd, measured from the respective equilibrium positions. The force equation, in accordance with Hooke39。s law, is 剛度K提供的是恢復力，圖中用一根彈簧表示。（于是，拉長時，彈簧試圖收縮；壓縮時，彈簧試圖恢復到原來的長度。）彈簧每端的反作用力是一樣的，而且等于剛性系數(shù)K和彈簧變形量的乘積。（彈簧的網(wǎng)絡表示如圖29b所示。）測量彈簧每一端的位移量是從原始或平衡位置開始的，c端具有位置，d端具有位置，測量是從各自的平衡位置開始。根據(jù)霍克(Hooke)定律，有 （）If the end d is stationary, then xd=0 and the preceding equation reduces to: 如果固定d點，那么，上述方程就變成 （）The plot fK vs. xc for a real spring is not usually a straight line, because the spring characteristic is nonlinear. However, over a limited region of operation, the linear approximation, ., a constant value for K, gives satisfactory results. 對于一個真正的彈簧來說，力fK與變形xc之比的圖形通常并非是一直線，因為彈簧的特性是非線性的。然而，在一個有限的范圍內(nèi)，是近似線性的，即K是常數(shù)可以給出一個滿意的結(jié)果。The damping, or viscous, friction B characterizes the element that absorbs energy. The reaction damping force fB is approximated by the product of damping B and the relative velocity of the two ends of the dashpot. The direction of this force depends on the relative magnitudes and directions of the velocities Dxe and Dxf : 阻尼或粘性摩擦系數(shù)代表一個吸能元件的特性。阻尼力近似等于阻尼與阻尼器兩端相對速度之乘積。該力的方向由方程式(257)給出，取決于速度和的相對大小和方向： （）TABLE Mechanical translation symbols and units直線運動機械系統(tǒng)的符號和單位Symbol符號Quantity量. customary units美國常用單位Metric units公制單位f力ForcePoundsNewtonsx位移DistanceFeetMetersv速度VelocityFeet/secondMeters/seconda加速度AccelerationFeet/second2Meters/second2M質(zhì)量MassKilogramsK剛度Stiffness coefficientPounds/footNewtons/meterB阻尼系數(shù)Damping coefficientPounds/(foot/second)Newtons/( meter/second)Before the differential equations of a plete system can be written, the mechanical network must first be drawn. This is done by connecting the terminals of elements that have the same displacement. Then the force equation is written for each node or position by equating the sum of the forces at each position to zero. The equations are similar to the node equations in an electric circuit, with force analogous to current, velocity analogous to voltage, and the mechanical elements with their appropriate operators analogous to admittance. The reference position in all of the following examples should be taken from the static equilibrium positions. 在寫整個系統(tǒng)的微分方程式之前，第一步就是畫出機械網(wǎng)絡圖。做法是把具有相同位移的元件的端點聯(lián)結(jié)起來，然后在每個節(jié)點或位置處令合力為零，對于每個節(jié)點或位置寫出其力的方程式。該方程式與電路的節(jié)點方程是相似的，力類似于電流，速度類似于電壓，具有適當操作功能的機械元件類似于導納。在下面的幾頁中將給出若干例子。在所有的情況下，參考位置都取固定（靜態(tài)）的平衡位置。Simple Mechanical Translation System FIG (a) Simple massspringdamper mechanical system (b) corresponding mechanical network圖211 (a) 簡單的質(zhì)量彈簧阻尼機械系統(tǒng) (b)相應的機械網(wǎng)絡圖圖211 (a)所示的系統(tǒng)開始是靜止的。彈簧和質(zhì)量的末端有一個參考位置，而且從參考位置所產(chǎn)生的任一位移分別標為和，加到彈簧末端的力一定是通過彈簧的壓縮來實現(xiàn)平衡的。通過彈簧的作用，還傳遞一個相同的力，并月作用在點。為了畫出其機械網(wǎng)絡，首先要標出點和及參考點。然后在、兩點之間聯(lián)接網(wǎng)絡元件。例如，彈簧的一端位置為，另一端位置為。因此彈簧就連接在該兩點之問。整個機械網(wǎng)絡示于圖21(b)中。位移和相當于電路的節(jié)點。在每個節(jié)點處，力的代數(shù)和必等于零。因此，可以寫出如下方程： （258） （259）解這兩個方程，可以求出兩個位移和以及與其相應的速度和。把方程式(258)和(259)合并，就可以得到一個關于對、對或?qū)Φ姆匠淌健? （260） （261） （262）方程式(261)的解說明由一個給定的運動引起的運動，方程式(260)和(262)的解說明由一個給定的力引起的運動和。由上面的三個方程可以得到三個傳遞函數(shù)： （263） （264） （265）注意，最后一個方程等于前兩個方程的乘積，即