{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# HW4 - ME 131 Vehicle Dynamics Homework 4 Due Tuesday March...

This preview shows pages 1–2. Sign up to view the full content.

ME 131 Vehicle Dynamics Homework 4 Due Tuesday, March 16th, 2010 1 Cruise Control Design and Simulation 1.1 Upper Level Controller Design We would like to simulate the engine dynamics of our vehicle for testing and analysis. For designing purposes it has been suggested that we use a first-order filter model for our vehicle: τ d dt ¨ x + ¨ x = ¨ x des (1) Let’s choose a PI control law of the form: ¨ x des = - k p ( v - v des ) - k i R ( v - v des ) dt (a) Find the ordinary differential equation relating v des to v . Show that if v des = constant then v ss = v des . By assuming the solution to be v ( t ) = e λt and setting v des = ˙ v des = 0, find the characteristic equation. It is often easier in control system design to work in the Laplace domain. In this domain the plant model and the PI controller may be represented as: P ( s ) = v ¨ x des = 1 s ( τs + 1) (2) C ( s ) = k p + k i s (3) The closed-loop system representing the transfer function from v to v des can be found by the formula: T ( s ) = P ( s ) C ( s ) 1 + P ( s ) C ( s ) (4) (b) Show that by setting s = λ the denominator of the closed-loop transfer function is the characteristic equation found above.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

HW4 - ME 131 Vehicle Dynamics Homework 4 Due Tuesday March...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online