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EE392m - Spring 2005. Gorinevsky. Control Engineering. 5-3. Sampling: continuous time view. • Sampled and continuous time together. • Continuous time physical system + digital controller. – ZOH = Zero Order Hold. Sensors. Control computing. Actuators. Physical system. D/A, ZOH. A/D, Sample
The zero-order hold (ZOH) is a mathematical model of the practical signal reconstruction done by a conventional digital-to-analog converter (DAC). That is, it describes the effect of converting a discrete-time signal to a continuous-time signal by holding each sample value for one sample interval. It has several applications in
Currently: Design with differential equations, Laplace domain, state-space. In other words: Use continuous-time techniques. ADC takes time: ZOH Phenomena. DAC output looks good. Cannot say what the signal value is in-between sampling times. This may be troublesome when hold-times are long. Consequence: Design
Lecture 6 Outline: Zero-Order Hold Sampling, Upsampling. 0 Announcements: 0 HW 2 posted. 0 Please respond to HW poll, including time on analysis questions vs. Matlab; may affect HW 2 (4 units~12 hours/wk), also keep track of time spent on HW2. 0 Review of Last Lecture. 0 Sampling and Reconstruction with Zero-.
13 Jan 2011 Reconstruction with zero-order hold. 15. Examples of sampling and reconstruction. 19. Comments on Lab 1. 24. Sampling part of Lab 1. 24. Reconstruction part of Lab 1. 25. Lowpass reconstruction filters. 26. DT lowpass reconstruction filters. 29. Reading: EE 224 handouts 2, 16, 18, 19, and lctftsummary
is known as zero-order extrapolator or zero order hold. It holds the value of f(kT) for kT ? t < (k + 1)T until the next sample f((k + 1)T) arrives. Figure 1 illustrates the operation of a. ZOH where the green line represents the original continuous signal and brown line represents the reconstructed signal from ZOH. 0. 1. 2. 3. 4. 5. 6.
n. + an?1? n?1. + ··· + a1? + x(kT). If the data hold circuit is an n th. -order polynomial extrapolator, it is called an n th. -order hold. It uses the past n + 1 discrete data x((k ? n)T), x((k ? n + 1)T), ···, x(kT) to generate h(kT + ?). ZERO-ORDER HOLD. If n = 0 in the above equation, we have a zero order hold so that h(kT + ?) = x(kT).
BACKGROUND: ZERO ORDER HOLD. 7. The ZOH is a simple type of hold circuit. Hold circuits are required in digital systems to interface. 8 digital time signals to continuous time plants. In a digital control system, a digital to analogue. 9 converter (DAC) usually performs the operation of the ZOH. 10. 1.3. SETUP MATLAB
Sampling with a Zero-Order Hold. • In impulse-train sampling, narrow and large-amplitude pulses which approximate impulses are in practice difficult to generate and t ransmit. • Thus, it is often more convenient to generate the sampled signal in a form referred to as a zero-order hold. • Such a system samples x(t) at a given
25 Jan 2008 the Laplace transform of e. ?. (t) is. E. ?. (s) = ?. ? n="0" e(nT)e. ?nT s. = ?. ? n="0" e(nT)z. ?n?. ?. ?. ?. ?z=eTs . E. ?. (s) takes a similar form to the z-transform. The hold circuit (a latch in D/A converter) holds output for a sampling interval T. The output of a ZOH (zero order hold)?E(s) is expressed by.
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