l16 - 16.06 Lecture 16 Controllability John Deyst October...

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Unformatted text preview: 16.06 Lecture 16 Controllability John Deyst October 9, 2003 Todays Topics 1. Simple examples of controllable and uncontrollable systems 2. Definition of controllability 3. Controllability conditions for scalar inputs 1 The basic concept of controllability is that we can use inputs u ( t ) to drive the state x ( t ) to any point in the state space. The primary issue is whether the structure of the system makes this possible or impossible. Lets look at some simple examples to motivate the dis- cussion Example of an Aircraft Flying a Straight Path We model distance along the path as the state x , and its derivative (speed along the path) as x 2 . Out input is acceleration along the path If the input is zero the trajectory in state space is a straight line (speed along the path is constant) 2 Inputs have the effect of directly changing speed x 2 , and indirectly changing its integral x 1 . For example, if inputs are constant....
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l16 - 16.06 Lecture 16 Controllability John Deyst October...

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