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ΨΗΦΙΑΚΟΣ ΕΛΕΓΧΟΣ (22Δ802) Β΄ ΕΞΑΜΗΝΟ 2014-15 Καθηγητής Πέτρος Π. Γρουμπός 2610 996449 Ώρες Γραφείου: Τετάρτη Πέμπτη Παρασκευή 11:00-12:00 Γραφείο: 1 ος όροφος Τομέας Συστημάτων & Αυτομάτου Ελέγχου Τμήμα ΗΜ&ΤΥ ΚΕΦΑΛΑΙΟ 4
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3 Contents 1 Description of Linear Discrete Systems 2 Pulse Response Function 3 Pulse Transfer Function 4 Open/closed-loop Pulse Transfer Function 5 Response of the CCS 6 Performance Specifications of the CCS 7 State Space Description of the CCS
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4 1 Description of Linear Discrete Systems
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5 The system considered in the class is the linear time-invariant system, i.e. the relation between the output and input is unchangeable over time. r(kT)→y(kT); r(kT-iT)→y(kT-iT), k=0,1,2,…; i=…,-2,-1,0,1,2,…
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6 2 Pulse Response Function Pulse response function is the basis for studying pulse transfer function. G(s) x(t)x * (t) y(t) y * (t) Fig. 4.1 Continuous system with impulse sampling signal input
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7 2 Pulse Response Function
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9 4.2 Pulse Response Function
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10 4.2 Pulse Response Function
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11 4.3 Pulse Transfer Function
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12 4.3 Pulse Transfer Function G(z) X(z)Y(z) Fig. 4.2. Diagram of Pulse Transfer System
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13 4.3 Pulse Transfer Function
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14 4.3 Pulse Transfer Function
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15 4.4 Open/closed-loop Pulse Transfer Function 4.4.1 Laplace transform of the sampled signal G(s) x(t)x * (t) y(t) Y(s) X*(s)X(s)
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16 4.4 Open/closed-loop Pulse Transfer Function
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17 4.4 Open/closed-loop Pulse Transfer Function
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18 4.4.2 Properties of X*(s) 4.4 Open/closed-loop Pulse Transfer Function
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19 4.4 Open/closed-loop Pulse Transfer Function
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20 4.4.3 How to get pulse transfer function (1) System with sampler G(s) x(t)x * (t) y(t) y * (t) Fig. 4.3 system with sampler 4.4 Open/closed-loop Pulse Transfer Function
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21 4.4 Open/closed-loop Pulse Transfer Function Fig. 4.4 system without sampler G(s) x(t)y(t) X(s) Y(s) (2) System without sampler
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22 G(s) x(t)x * (t) y(t) y * (t) 4.4 Open/closed-loop Pulse Transfer Function (3) The methods to get pulse transfer function
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23 4.4.4 Pulse transfer function and difference equation Pulse transfer function can be converted to the difference equation, and vice versa. 4.4 Open/closed-loop Pulse Transfer Function
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24 4.4 Open/closed-loop Pulse Transfer Function
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25 4.4 Open/closed-loop Pulse Transfer Function
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26 4.4 Open/closed-loop Pulse Transfer Function
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27 4.4.5 Pulse transfer function of the system with ZOH The transfer function of the zero order holder is The transfer function of the system with zero order holder is 4.4 Open/closed-loop Pulse Transfer Function
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28 4.4 Open/closed-loop Pulse Transfer Function
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29 4.4.6 Open loop pulse transfer function of the system (1) Pulse transfer function of cascaded elements without sampler between them Fig. 4.5 cascade connection without sampler G 1 (s)G 2 (s) R(s) C 1 (s) C * (s)C(s) C(z)R(z) R*(s) G(z) T (s) 4.4 Open/closed-loop Pulse Transfer Function
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30 4.4 Open/closed-loop Pulse Transfer Function
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31 (2) Pulse transfer function of cascaded elements with sampler between them Fig. 4.6 cascade connection with sampler G 1 (s)G 2 (s) R(s)C 1 (s)C * (s)C(s) C(z)R(z) R*(s) G(z) T C 1* (s) C 1 (z) 4.4 Open/closed-loop Pulse Transfer Function
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32 4.4 Open/closed-loop Pulse Transfer Function
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33 4.4 Open/closed-loop Pulse Transfer Function
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34 (3) Pulse transfer function of parallel elements G 1 (s) U*(s) G 2 (s) Y(s) Y*(s) U(s) U*(s) Y 1 (s) Y 2 (s) 4.4 Open/closed-loop Pulse Transfer Function
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35 G 1 (s) U*(s) G 2 (s) Y(s) Y*(s) U(s) Y 1 (s) Y 2 (s) 4.4 Open/closed-loop Pulse Transfer Function
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36 4.4.7 Closed-loop pulse transfer function of the system (1) Sampler is located after the comparator Fig. 4.7 sampler is located after the comparator G (s) E(s) C(s) E(z) E*(s) Ф(z) H (s) R(s) R*(s) R(z) C*(s) C(z) B(s) - 4.4 Open/closed-loop Pulse Transfer Function
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37 4.4 Open/closed-loop Pulse Transfer Function
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38 4.4 Open/closed-loop Pulse Transfer Function
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39 (2) Sampler is located at the feedback channel Fig. 4.8 Sampler is located at the feedback channel G (s) E(s) C(s) E*(s) H (s) R(s) R*(s) R(z) C*(s) C(z) B(s) - 4.4 Open/closed-loop Pulse Transfer Function
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40 4.4 Open/closed-loop Pulse Transfer Function
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41 (3) Sampler is located at the forward channel Fig. 4.9 sampler is located at the forward channel G (s) E(s) E(z) E*(s) H (s) R(s) R*(s) R(z) C*(s) C(z) B(s) - T 4.4 Open/closed-loop Pulse Transfer Function
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42 (3) Sampler is located at the forward channel Fig. 4.9 sampler is located at the forward channel G (s) E(s) E(z) E*(s) H (s) R(s) R*(s) R(z) C*(s) C(z) B(s) - T 4.4 Open/closed-loop Pulse Transfer Function
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43 4.4 Open/closed-loop Pulse Transfer Function
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44 G 2 (s) E(s) C(s) R(s) - G 1 (s) E*(s)U(s) 4.4 Open/closed-loop Pulse Transfer Function
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45 4.4 Open/closed-loop Pulse Transfer Function
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. ΕΥΧΑΡΙΣΤΩ ΓΙΑ ΤΗΝ ΠΡΟΣΟΧΗ ΣΑΣ Καθ.Γρουμπός Π. Πέτρος groumpos@ece.upatras.gr
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