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Unformatted text preview: Cruise control example calculations Open-loop system dynamics m ˙ v ( t ) =- bv ( t ) + u ( t ) + F hill ( t ) . Denote by v des the desired highway speed of the car. Open-loop behavior Consider the following situation. The car has been traveling across flat terrain for a long time. That is, F hill ( t ) = 0 , for t ∈ (-∞ , 0) . The driver has been using throttle position u ( t ) = bv des , for t ∈ (-∞ , 0) . Therefore we have v (0) = v des . Now consider the sudden appearance of a hill of constant non-zero slope from time t = 0 . That is, F hill ( t ) = F h , for t ≥ . Now compute the car’s velocity’s response to the hill with the input held constant. Start with the differential equation from time t = 0 . m ˙ v ( t ) =- bv ( t ) + u ( t ) + F hill ( t ) , ˙ v ( t ) =- b m v ( t ) + 1 m u ( t ) + 1 m F hill ( t ) , ˙ v ( t ) =- b m v ( t ) + b m v des 1( t ) + 1 m F h 1( t ) ....
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This note was uploaded on 05/27/2010 for the course MAE MAE143B taught by Professor Prof.bitmead during the Spring '10 term at UCSD.
- Spring '10