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Unformatted text preview: 16.06 Lecture 5 SteadyState Errors Karen Willcox September 11, 2003 Todays Topics 1. Steadystate errors 2. The importance of integrators 3. PI control Reading : 4.3, l.n. 1 1 Introduction Recall from the last lecture that high loop gains reduce the sensitivity to parameter variations and disturbance inputs. Today, we will see that they also reduce steadystate errors in feedback systems. 2 SteadyState Errors Consider the unity feedback system: How do we determine the steadystate error, e ss ? 2 Use the final value theorem: e ss = = (1) For G ( s ) the following general form is assumed: G ( s ) = (2) 3 Definitions (a) Gain (b) Type number 3 (c) Position error constant , K p (d) Velocity error constant , K v (e) Acceleration error constant , K a Equation (2) shows that So, equation (1) can be written: e ss = (3) 4 4 Table of steadystate errors Using equation (3), we can construct a handy table: e.g. type 2 system, unit ramp input 5 5 A physical explanation of the table 5.1 Consider a type system Type 0, step input: If c is constant, then e ss must be This means: 6 Type 0, ramp input: 7 5.25....
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 Fall '03
 willcox
 Aeronautics

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