CSE 416 DIGITAL CONTROL Lecture 03 Sampling and

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CSE 416: DIGITAL CONTROL Lecture 03: Sampling and Reconstruction Dr. Ahmed Mahmoud, 14/10/2019

CSE 416: DIGITAL CONTROL Lecture 03: Sampling and Reconstruction Dr. Ahmed Mahmoud, 14/10/2019

Sampled-Data Control Systems (1) 14/10/2019 CSE 416: DIGITAL CONTROL 2

Sampled-Data Control Systems (1) 14/10/2019 CSE 416: DIGITAL CONTROL 2

Sampled-Data Control Systems (2) 14/10/2019 CSE 416: DIGITAL CONTROL 3

Sampled-Data Control Systems (2) 14/10/2019 CSE 416: DIGITAL CONTROL 3

Sampled-Data Control Systems (3) • Use a reconstruction device; Data hold. • The purpose

Sampled-Data Control Systems (3) • Use a reconstruction device; Data hold. • The purpose of the data hold is to reconstruct the sampled signal into a form that closely resembles the signal before sampling. • The simplest is the zero-order hold. 14/10/2019 CSE 416: DIGITAL CONTROL 4

Sampler and Zero-Order Hold • The Laplace transform of the error function after the

Sampler and Zero-Order Hold • The Laplace transform of the error function after the sample and hold: • The starred the function: 14/10/2019 CSE 416: DIGITAL CONTROL 5

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The Ideal Sampler 14/10/2019 CSE 416: DIGITAL CONTROL 7

The Ideal Sampler 14/10/2019 CSE 416: DIGITAL CONTROL 7

Definition of The Ideal Sampler • The output signal of the ideal sampler: •

Definition of The Ideal Sampler • The output signal of the ideal sampler: • The zero-order hold transfer function: • The correct sampler/hold function is modelled by: 14/10/2019 CSE 416: DIGITAL CONTROL 8

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Results from Fourier Transform 14/10/2019 CSE 416: DIGITAL CONTROL 13

Results from Fourier Transform 14/10/2019 CSE 416: DIGITAL CONTROL 13

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14/10/2019 CSE 416: DIGITAL CONTROL 16

Shannon’s Sampling Theorem 14/10/2019 CSE 416: DIGITAL CONTROL 17

Shannon’s Sampling Theorem 14/10/2019 CSE 416: DIGITAL CONTROL 17

Data Reconstruction (1) 14/10/2019 CSE 416: DIGITAL CONTROL 18

Data Reconstruction (1) 14/10/2019 CSE 416: DIGITAL CONTROL 18

Data Reconstruction (2) 14/10/2019 CSE 416: DIGITAL CONTROL 19

Data Reconstruction (2) 14/10/2019 CSE 416: DIGITAL CONTROL 19

Zero-Order Hold 14/10/2019 CSE 416: DIGITAL CONTROL 20

Zero-Order Hold 14/10/2019 CSE 416: DIGITAL CONTROL 20

• Example: 14/10/2019 CSE 416: DIGITAL CONTROL 21

• Example: 14/10/2019 CSE 416: DIGITAL CONTROL 21

Pulse Transfer Function • The transfer function of the plant in sampled control systems

Pulse Transfer Function • The transfer function of the plant in sampled control systems is always augmented with the hold transfer function: 14/10/2019 CSE 416: DIGITAL CONTROL 22

Starred Function Derivations (1) • Given any function as: • Hence, 14/10/2019 CSE 416:

Starred Function Derivations (1) • Given any function as: • Hence, 14/10/2019 CSE 416: DIGITAL CONTROL 23

Starred Function Derivations (2) • Example: Find the Z transform of: 14/10/2019 CSE 416:

Starred Function Derivations (2) • Example: Find the Z transform of: 14/10/2019 CSE 416: DIGITAL CONTROL 24

Starred Block Diagrams (1) 14/10/2019 CSE 416: DIGITAL CONTROL 25

Starred Block Diagrams (1) 14/10/2019 CSE 416: DIGITAL CONTROL 25

Starred Block Diagrams (2) 14/10/2019 CSE 416: DIGITAL CONTROL 26

Starred Block Diagrams (2) 14/10/2019 CSE 416: DIGITAL CONTROL 26

Starred Block Diagrams (3) 14/10/2019 CSE 416: DIGITAL CONTROL 27

Starred Block Diagrams (3) 14/10/2019 CSE 416: DIGITAL CONTROL 27