l19 - 16.060 Lecture 19 State Space Design John Deyst...

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16.060 Lecture 19 State Space Design John Deyst October 20, 2003 Today’s Topics 1. Pole Assignment with full state feed back 2. Design with sensor feedback
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Possibly the most important implication for controllability, as we have discussed it in the last two lectures, is the assurance it gives us for freedom in the design of feedback control systems. In particular we have Feedback Control Theorem - Any specified set of closed loop system poles can be obtained by feeding back all of the states, if and only if the systems is controllable. To achieve this, consider the system For which A, B is a controllable pair. Hence the matrix. has n linearly independent columns
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Then, suppose we can determine or measurs all of the states and feed them back so Hence or Which has the block diagram
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We want to determine the values for the elements of the feedback gain matrix K so that the resulting system has its n poles located where we want them to be. In other words, for the system which has the characteristic equation we want to choose K so the roots are where we want them to be. The left side of the equation is an nth order polynomial. The
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l19 - 16.060 Lecture 19 State Space Design John Deyst...

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