自动控制理论甲1第七周作业英文

1、k71A unit-step response of a second order system is known as followingh(t) 10 12.5e1 2t sin(1.6t 53.1 )Find the percent overshoot %, peak time t psystem。and settling timets ofthey(t)2. For a unity-feedback second order system, when its unit-step response1.3is given as the Fig, determinethe the1.0ope

2、n-loop transfer function system.of e / 1 2 ;（h:）tt p 1 21.02.0Fig. Unit-step response of a second order system03The unit-impulse responses k(t) of the systems are known as following, determine the closed-loop transfer function(s) of these systems.（1） k(t) 0.0125e1 25t（2） k(t) 5t 10sin(4t 45 )4. (P66

3、0. 3.13)5. (P661. 3.16)For the mechanical system of Fig.2.11a the se equation forExle 2, Sec.2.6, is given in phase-variable form. With the input as u xa , thevariabkes are x1 xb, and x2 xb . Use M=5, K=10, and B=15. Theseinitial conditions are xb (0) 1and xb (0) 2 . (a) Find the homogeneoussolution

4、 for x(t). (b) Find the complete solution with u(t)=1(t).6. (P661. 3.17; P6634.15)autonomous system(注意(b)改为：by Laplace transformmethod.) For the010 701x 0 x ,y 100 x 5 3matrix (t) by(a) Find the system eigenvalues. (b) Evaluate the s Laplace transform method.e transmis7(P662. 4.12) System 1A linear

5、system is described byx 2x 0u,1y 1 0 x(1) 312 Where u=1(t) and theinitial conditions are x1(0)=0 and x2(0)=1. (a) Using Laplacetransforms, find X(s). Put the elements of this vector over a common denominator. (b) Find the transfer function G(s). (c) Find y(t).8(P663. 4.14)(1) A system is described b

6、yx 61x 1u ,y x(1)0 015 (a) Find x(t) with x(0)=0 and u(t)=1(t). (b) Determine the transfer function G(s)=Y(s)/U(s).9.P.667.5.11 (3). Given(3) D3 y 11D2 y 38Dy 40 y 2D2u 6Du uObtain se and output equations using (a)phase variables, (b) canonical variables.10.(P.669 5.18(2) A system is described by(2) x x u ,21010y x103(a) Derive the system transfer function G(s)=Y(s)/U(s); (b) Draw an appropriatese-variable diagram; (c) For zero initial se and a unit-st x2(t).nput evaluate x1(t) and u ，