A simple representation of a vehicle suspension system is shown in Figure above. Assume that the forces produced by the springs and dampers act at the end points P and Q and that x₁ and x2 are the displacements of these points from equilibrium. The force exerted by a damper is proportional to the velocity of one end of the damper relative to the other end, and the springs obey Hooke's law. Assume that the mass of the platform can be neglected so that the spring motions can be regarded as independent. The control force 4u is applied one-quarter of the way from one end of the platform. b₁ =b₂=1, k₁=1, k₂ =2 a) Derive the two-dimensional state-space model of this simple representation of a vehicle suspension system. b) If the ends of the platform are each given an initial displacement of 10 units, find a control law that returns the platform to equilibrium at t = 1 sec. c) Plot x1, x2, and u versus time (Provide the MATLAB code)

A simple representation of a vehicle suspension system is shown in Figure above. Assume that the forces produced by the springs and dampers act at the end points P and Q and that x₁ and x2 are the displacements of these points from equilibrium. The force exerted by a damper is proportional to the velocity of one end of the damper relative to the other end, and the springs obey Hooke's law. Assume that the mass of the platform can be neglected so that the spring motions can be regarded as independent. The control force 4u is applied one-quarter of the way from one end of the platform. b₁ =b₂=1, k₁=1, k₂ =2 a) Derive the two-dimensional state-space model of this simple representation of a vehicle suspension system. b) If the ends of the platform are each given an initial displacement of 10 units, find a control law that returns the platform to equilibrium at t = 1 sec. c) Plot x1, x2, and u versus time (Provide the MATLAB code)

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

4u
1
Q
A simple representation of a vehicle suspension system is shown in Figure above. Assume that the forces
produced by the springs and dampers act at the end points P and Q and that x₁ and x2 are the displacements of
these points from equilibrium. The force exerted by a damper is proportional to the velocity of one end of the
damper relative to the other end, and the springs obey Hooke's law. Assume that the mass of the platform can be
neglected so that the spring motions can be regarded as independent. The control force 4u is applied one-quarter
of the way from one end of the platform. b₁ b₂ =1, k₁=1, k₂ =2
a)
Derive the two-dimensional state-space model of this simple representation of a vehicle
suspension system.
b)
If the ends of the platform are each given an initial displacement of 10 units, find a control
law that returns the platform to equilibrium at t = 1 sec.
c)
Plot x1, x2, and u versus time (Provide the MATLAB code)

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