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Unformatted text preview: Carleton University Department of Systems and Computer Engineering
94.260C Systems and Simulation Fall 199 5! One Hoff jEEE limit" _--_—-__u-----__..._-________..____..._________..-_—..-_....____-____.......___-......-_____-__-____-.____—..___ 1 For the systems shown below: [5 Marks] (i) Find the state equations and write them in a matrix form.
[5 Liar-ks] (ii) Draw the simulation diagram using integrators, adders and sealers. Make
sure to indicate the sign of variables at the inputs of each adder. 290-) M 't",”’/”,l,f,17’ I ’ Fn‘eh‘m , b 2. The impulse response of a ﬁrst order linear system is:
h(t:) = 36“”2 ; (:20
= 0 ,' t < 0 [3 Marks] (i) Write down the differential equation of this system.
[2 Marks] (ii) What is the system transfer function? [5 Marks] (iii) Use the convolution method to calculate the forced response of the system
when the input, x(t), is: X(t:) 2 ;1st52
D ; otherwise 94.260C Systems and Simulation Carleton university
Department of Systems and Computer Engineering Fall 1993/94 1. Mid-Term Exam
( 50 minutes, closed book) The state equations of a linear system are: MO = 2m) -x1(r) exam 4x30)
(1:2?) =x1(t) -xz(t)
d3?) =x2(t) ~2x3(1) Draw the system simulation diagram. (f(t) is the system input)
A second order linear system has thefoilowing 1/0 differential equation: 4'2 (l) d (I) _
“:2 +3 it +2y(t) —x(t) where y(t) is the system output and x(t) is the system input. Find the forced response
when the input x(t) = u(t) - u(t - 2). u(t) is the unit step function. Consider the following system: ( f(t) is the input; and x(t) is the output) dx(t)
dt =ﬂt) -5 x(t) -2 2(t) (12(1) =0.5 t
dt x( ) (i) Find the transfer function H(s)
(ii) Find the poles and zeros of H(s) ...
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- Spring '08
- John Bryant