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Unformatted text preview: 6.003: Signals and Systems Lecture 5 September 24, 2009 1 6.003: Signals and Systems Feedback and Control September 24, 2009 Last Time Understanding the structure of a control problem automatic control → feedback Analyzing feedback systems feedback → cyclic paths → persistent outputs Designing control systems constructing well-behaved response properties Example: Steering a Car Algorithm: steer left when car is right of center and vice versa. steer left steer left straight ahead? steer right steer right steer right straight ahead? Bad algorithm → poor performance. Here we get persistent oscillations! Last Time We investigated a VERY simple model for the car. The car could move laterally in a lane without rotating! see previous ( − 1 ) → command 1 see previous ( ) → command see previous ( +1 ) → command − 1 see previous ( +1 ) → command − 1 see previous ( ) → command Even that simple system could go unstable. Last time, we learned how to stablize it. Today We will investigate more realistic models of steering. We will analyze more realistic (and more complex) feedback systems. Steering Controller Design a system to automatically steer a car. p moving car, velocity V Assume a sensor reports position p within the lane: p = 0 : in center p > : right of center p < : left of center 6.003: Signals and Systems Lecture 5 September 24, 2009 2 Steering Controller Model the system. Let X represent the desired position in the lane (normally ). Turn the steering wheel ( φ ) in proportion to the difference between the desired and current positions. + α steering system − 1 X Φ P The relation between the angle of the steering wheel and the position of the car in the lane is complicated: • turning the steering wheel causes the car to rotate. • forward motion of the car then alters its position in the lane. Check Yourself What is the (CT) relation between φ (angle of steering wheel) and θ (angle of car)? θ 1. θ ∝ φ 2. θ ∝ sin φ 3. ˙ θ ∝ φ 4. θ ∝ ˙ φ 5. none of the above Check Yourself What is the (CT) relation between θ (angle of car) and p (position of car in lane)?...
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- Spring '11
- Automobile, α, Steering