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The dynamics for the car Audi A2 (see Figure 2) is modelled by the standard state-space representation *(t) = Ax(t)+ Bu(t) y(t) Cx(t) + Du(t) with the following matrix values [o A = D = The above representation is obtained by allocating x1 (t) and x2(t) as the car's position and velocity, respectively. Recall the input u(t) represents the propelling force produced by the car's engine (in N). The output of the system is represented by y(t), which in this case are the same as the states.

The dynamics for the car Audi A2 (see Figure 2) is modelled by the standard state-space representation *(t) = Ax(t)+ Bu(t) y(t) Cx(t) + Du(t) with the following matrix values [o A = D = The above representation is obtained by allocating x1 (t) and x2(t) as the car's position and velocity, respectively. Recall the input u(t) represents the propelling force produced by the car's engine (in N). The output of the system is represented by y(t), which in this case are the same as the states.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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2. The dynamics for the car Audi A2 (see Figure 2) is modelled by the standard state-space representation *(t) = Ax(t) +Bu(t) y(t) Cx(t) + Du(t) with the following matrix values [o A = D= The above representation is obtained by allocating x1 (t) and x2(t) as the car's position and velocity, respectively. Recall the input u(t) represents the propelling force produced by the car's engine (in N). The output of the system is represented by y(t), which in this case are the same as the states. (a) Obtain the free response of the system y free(t) if the initial position is 0 m (x1(0) = 0) and the initial velocity is 1 m/s (x2(0) = 1) (b) Obtain the forced response of the system y forced (t) when the input is a step input with amplitude 1000 N { t <0 1000 t20 u(t) %3D (c) Determine whether the free response of the car's dynamics is asymptotically stable or not Figure 2: Audi A2
Transcribed Image Text:2. The dynamics for the car Audi A2 (see Figure 2) is modelled by the standard state-space representation *(t) = Ax(t) +Bu(t) y(t) Cx(t) + Du(t) with the following matrix values [o A = D= The above representation is obtained by allocating x1 (t) and x2(t) as the car's position and velocity, respectively. Recall the input u(t) represents the propelling force produced by the car's engine (in N). The output of the system is represented by y(t), which in this case are the same as the states. (a) Obtain the free response of the system y free(t) if the initial position is 0 m (x1(0) = 0) and the initial velocity is 1 m/s (x2(0) = 1) (b) Obtain the forced response of the system y forced (t) when the input is a step input with amplitude 1000 N { t <0 1000 t20 u(t) %3D (c) Determine whether the free response of the car's dynamics is asymptotically stable or not Figure 2: Audi A2
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