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Unformatted text preview: ME 131 Vehicle Dynamics Homework 5 Solutions 1 Automated Highway System Our goal in this homework is to simulate an automated highway system (AHS). More about this topic may be read in Chapter 7 of Rajamani and I strongly encourage reading this section to gain understanding before attempting the assignment. The final result will be a simulation of a platoon of 5 vehicles exhibiting local and string stability. 1.1 Dynamic Vehicle Model We will use a simple first-order filter to model the dynamics of our vehicles. We have seen this in homework 4 in designing the cruise control system. Although a simple model will suffice in these simulation I want to mention that in actual implementation we would use a more complicated engine model, as in the lower level controller in homework 4. A first-order filter in the Laplace domain can be shown to be: x i x ides = 1 ( s + 1) (1) Where i is the i th vehicle. (a) What is the transfer function relating the vehicles velocity to the desired acceleration, T ( s ) = x i x ides ? Integrating x i by multiplying by the Laplace operator, 1 s , yields; T ( s ) = x i x ides = 1 s ( s + 1) (2) (b) How is this relationship represented in the time domain?...
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- Spring '09