Transcription of Fix Point Implementation of ClAlihControl Algorithms
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Fix Point Implementation of ClAlihControl Algorithms
Fix Point Implementation of ClAlihControl AlgorithmsAntonCer inAnton CervinLund UniversityOutline A-D and D-A Quantization Computer arithmetic Floating- Point arithmetic Fixed- Point arithmetic Controller realizationsGraduate Course on embedded Control Systems Pisa 8-12 June2009 Finite-Wordlength ImplementationControl analysis and design usually assumes infinite-precisionarithmetic, parameters/variables are assumed to be real numbersError sources in a digital Implementation with finite wordlength: Quantization in A-D converters Quantization of parameters (controller coefficients) Round-off and overflow in addition, subtraction, multiplication,division, function evaluation and other operations Quantization in D-A convertersGraduate Course on embedded Control Systems Pisa 8-12 June2009 The magnitude of the problems depends on The wordlength The type of arithmetic used (fixed or floating Point ) The controller realizationGraduate Course on embedded Control Systems Pisa 8-12 June2009A-D and D-A QuantizationA-D and D-A converters often have quite poor resolution, A-D: 10 16 bits D-A.
Outline • A-D and D-A Quantization • Computer arithmetic –Floating-point arithmetic –Fixed-point arithmetic • Controller realizations Graduate Course on Embedded Control Systems – Pisa 8 …
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