A simplified quarter-car suspension system is illustrated in Figure 1. The road position r and the...
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A simplified quarter-car suspension system is illustrated in Figure 1. The road position r and the car position z are indicated. Assume their initial positions (in a static equilibrium position) are ro and zo respectively. m 4 www 7" NI Figure 1 (a) Sketch a free body diagram for the mass, including the gravitational force. Hence write an equation which describes the static equilibrium condition when the car is at rest. (10 Marks) (10 Marks) (b) Now, defining the system input to be u= r-ro and output y=z-Zo respectively, write a dynamic differential equation which relates u and y and hence show that the transfer function from u to y is G(s) = cs + k ms² + cs + k (10 Marks) (c) Use a canonical form or otherwise to derive a state-space representation for Use the controllability matrix to show for which parameter combinations your state-space representation is controllable. G(s). (10 Marks) (Total 30 Marks) A simplified quarter-car suspension system is illustrated in Figure 1. The road position r and the car position z are indicated. Assume their initial positions (in a static equilibrium position) are ro and zo respectively. m 4 www 7" NI Figure 1 (a) Sketch a free body diagram for the mass, including the gravitational force. Hence write an equation which describes the static equilibrium condition when the car is at rest. (10 Marks) (10 Marks) (b) Now, defining the system input to be u= r-ro and output y=z-Zo respectively, write a dynamic differential equation which relates u and y and hence show that the transfer function from u to y is G(s) = cs + k ms² + cs + k (10 Marks) (c) Use a canonical form or otherwise to derive a state-space representation for Use the controllability matrix to show for which parameter combinations your state-space representation is controllable. G(s). (10 Marks) (Total 30 Marks)
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