lecture 16

# lecture 16 - Discrete Equivalents Continuous-control...

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1 Discrete Equivalents Continuous-control designs are well established and one can take advantage of a good continuous design by finding a discrete equivalent to the continuous compensator. This method of design is called emulation . The task is to find a discrete transfer function that will have approximately the same characteristics over the frequency range of importance as a given transfer function.

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2 Three methods: Numerical differentiation and integration. Matched pole-zero: using sT e z = Hold equivalence: zero order hold. Design of discrete equivalents via numerical differentiation and integration The PID controller in the continuous-data domain is described by s K s K K s G I D p c + + = ) ( The proportional component p K is implemented digitally by a constant gain p K .
3 The time derivative of a function f ( t ) at kT t = can be approximated by the backward difference rule , using the values of f ( t ) measured at kT t = and T k ) 1 ( - , that is, ]) ) 1 [( ) ( ( 1

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lecture 16 - Discrete Equivalents Continuous-control...

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