l5 - 16.06 Lecture 5 Steady-State Errors Karen Willcox...

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Unformatted text preview: 16.06 Lecture 5 Steady-State Errors Karen Willcox September 11, 2003 Todays Topics 1. Steady-state 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 steady-state errors in feedback systems. 2 Steady-State Errors Consider the unity feedback system: How do we determine the steady-state 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 steady-state 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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l5 - 16.06 Lecture 5 Steady-State Errors Karen Willcox...

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