Figure 1 shows the wheel suspension system for a car. The wheel follows the road given...
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Figure 1 shows the wheel suspension system for a car. The wheel follows the road given by the position x, (t). x₂(t) x₂ (1) B M1 M2 ODD K1 K2 x₂ (1) Figure 1 Wheel suspension system a) Apply Newton's laws to each of the two masses to derive the equations for the vertical motion of the wheel and the car, using the symbols in the Figure 1. b) Use the values M, = 40 kg, M, = 250 kg, B = 500 Ns/m, K, = 20000 N/m and K₂ = 10000 N/m, and write the equations on numerical form, separating x, and x₂- c) Derive the transfer function from the road position x, (t) to the car motion x₂ (t), h(s) = 2(1) Xo(t) d) You can now tune the different parameters to obtain your perfect driving experience. Write a simulation diagram for the model. Analyse the model in Simulink. e) Introduce the states , = x₁,₂ = x₁, x₂, 2x₂, and u = xo. Write the equations derived above as four first order differential equations. With x (t) as input to the system and wheel position x, and car position x₂ as measurements, introduce the state space model. Figure 1 shows the wheel suspension system for a car. The wheel follows the road given by the position x, (t). x₂(t) x₂ (1) B M1 M2 ODD K1 K2 x₂ (1) Figure 1 Wheel suspension system a) Apply Newton's laws to each of the two masses to derive the equations for the vertical motion of the wheel and the car, using the symbols in the Figure 1. b) Use the values M, = 40 kg, M, = 250 kg, B = 500 Ns/m, K, = 20000 N/m and K₂ = 10000 N/m, and write the equations on numerical form, separating x, and x₂- c) Derive the transfer function from the road position x, (t) to the car motion x₂ (t), h(s) = 2(1) Xo(t) d) You can now tune the different parameters to obtain your perfect driving experience. Write a simulation diagram for the model. Analyse the model in Simulink. e) Introduce the states , = x₁,₂ = x₁, x₂, 2x₂, and u = xo. Write the equations derived above as four first order differential equations. With x (t) as input to the system and wheel position x, and car position x₂ as measurements, introduce the state space model.
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Related Book For
Applied Regression Analysis and Other Multivariable Methods
ISBN: 978-1285051086
5th edition
Authors: David G. Kleinbaum, Lawrence L. Kupper, Azhar Nizam, Eli S. Rosenberg
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