Simulation of an Analog to Digital Converter

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From the course by University of California, Santa Cruz

Cyber-Physical Systems: Modeling and Simulation

6 ratings

University of California, Santa Cruz

Cyber-Physical Systems: Modeling and Simulation

6 ratings

Cyber-physical systems (CPS for short) combine digital and analog devices, interfaces, networks, computer systems, and the like, with the natural and man-made physical world. The inherent interconnected and heterogeneous combination of behaviors in these systems makes their analysis and design an exciting and challenging task. CPS: Modeling and Simulation provides you with an introduction to modeling and simulation of cyber-physical systems. The main focus is on models of physical process, finite state machines, computation, converters between physical and cyber variables, and digital networks. The instructor of this course is Ricardo Sanfelice (https://hybrid.soe.ucsc.edu), Associate Professor in the Department of Computer Engineering at the University of California Santa Cruz.

From the lesson

Modeling Interfaces for Cyber-Physical Systems: Conversion, Networks, and Complete CPS Models

Analog to Digital Conversion6:08

A Model of an Analog to Digital Converter9:38

Digital to Analog Conversion10:28

A Model of a Digital to Analog Converter4:01

Simulation of an Analog to Digital Converter5:34

A Model of an Implemented Finite-State Machine8:56

Simulation of an Implemented Finite State Machine4:54

A Digital Communication Network13:16

Simulation of a Digital Communication Network7:52

A Cyber-Physical System Model for Estimation Over a Network12:10

Simulation of a Cyber-Physical System Model for Estimation Over a Network6:32

A Cyber-Physical System Model for Sample and Hold Control9:03

Simulation of a Cyber-Physical System Model for Sample and Hold Control10:17

Meet the Instructors

Ricardo Sanfelice
Associate Professor
Department of Computer Engineering

[MUSIC]

In this video, I will illustrate how to simulate an analog to

digital converter using the Harrell equation toolbox.

In this video, we're going to model the analog to each converter using the model

that we saw in a previous video which is given in the following picture.

We have an input VS that at every DS star seconds

is being sampled and restoring a memory state column s.

The timer of tau s grows with ordinary time and

whenever it hits the value TS star we have a reset of the timer and

then the memory state is being updated with the value of the input.

So I already coded that using the Harvard

equation toolbox block corresponding to ADC.

You can find that one by going to the Library browser.

And then click on the CPS modules that you'll

find in Harvard equation tools, so here they are.

And the converter is this one right here.

So, we're providing a sine wave to it and

that wane wave will be sample at a particular rate.

And that rate, the measurement or

memorize version of the input will restore in a component of the state

which will be a ms, while another component of the state x would be and

tau s component that triggers the event of the system.

So, in the linear decision file, what we have is the initial value of

the state for the simulation is 0 for the memory and 0 for the timer.

The rate for sampling is chosen to be pi

over 8 and the horizon for simulation here and

by these numbers, the usual choices for the rule and the tolerances.

So we can launch this, By running the script

then going to the block, and then running the simulation.

I will show you how these ADCs coder inside this block

by the proper choices of F, C, G and D.

And we will see that the events are treated according to the timer and

whenever those happening.

Memory state is being recorded.

So before we go there, let's see what result we get from this simulation.

And what we see right here is what we expect.

With a rate of pi over 8 which is the first monthly this number here,

we set a timer which starts at 0, counts to the particular threshold and

then gets reset to 0 and this occurs periodically.

While at each one of those events the memory state that collects

the input to the system is updated with the value of input and

held constant until the next event.

So now let's dig into the details of the block code in the ADC.

Perhaps the more interesting one is the jump set which receives the parameter,

the constant here is to define the rate for sampling.

And whenever tau s is larger that TS you will report a jump.

And whenever it's within the right range you will not report the jump.

The choice here of the quality, for

not reporting the jump at the highest value of tau s is arbitrary.

It could be done only on the condition for reporting the jump actually.

For the set you'll read just the complement of that,

so these values are flipped and that implements the floor set.

The jump map will actually read resetting

the timer to zero as you see over here it's a component of the state text.

Here it's set to zero, and the memory

state which is the first component of the state of the system is reset to

the input which is given to the gen map as an input.

And then the floor map will actually keep the memory state to zero,

and the timer will grow according to linear time.

And there is a simulation of ADC using Harrell equation toolbox for

in this case sampling a periodic sinusoidal signal

[MUSIC]

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