机械控制理论基础习题答案.doc

机械控制理论基础习题答案 习题：2.2，2.6 2.2. Write the (a) loop, (b) node equations for the circuit shown after the switch S is closed. 2.2. 当开关S闭合后，写出电路的(a)回路，(b)节点方程式。 321 3 2 1 (a) loop (b) node Node 1 between R1 and R2, Node 2 between R2 and L, and Node 3 between L and C2 1. 2. 3. 2.6. (a) Derive the differential equation relating the position y(t) and the force f(t). (b) Draw the mechanical network. (c) Determine the transfer function G (D)=y/f. 2.6. (a)求位置y(t)与力f(t)有关的微分方程；(b)画出机械网络图；(c)确定传递函数G(D)＝y/f。 K2(b) Draw the mech K BfK1K B f K1 K3 (a) node xa node xb (c) where , , 习题：3.8 3.8 Solve the following differential equations. Assume zero initial conditions. Sketch the solutions. (a) (1) r=1, k=0, w=0 q=k-w=0 The steady state output is therefore: xss=b0 D2 xss =0. Inserting these values into previous equation(1): 16 xss =16 b0=1 xss =b0= (2) The homogeneous equation is formed by letting the right side of the differential equation equal zero: (3) the transient response is the solution of the homogeneous equation, is obtained by assuming a solution of the form xt=Amemt (4) where m is a constant yet to be determined the characteristic equation of system: (5) m1=4j, m2=-4j values of m are complex, by using the Euler identity and then combining terms, transient solutions are (6) x= xt + xss= (7) Assume zero initial conditions, i.e., t=0, x(0)=0, Dx(0)=0, inserting these values into previous equation(7): , , x= xt + xss= (b) (1) r=9, k=0, w=0 q=k-w=0 The steady state output is therefore: xss=b0 D xss =0, D2 xss =0. Inserting these values into previous equation(1): 3 xss =9, b0=3 xss =b0=3 (2) The homogeneous equation is formed by letting the right side of the differential equation equal zero: (3) the transient response is the solution of the homogeneous equation, is ob