Simulation of a Cyber-Physical System Model for Estimation Over a Network

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Из курса от партнера University of California, Santa Cruz

Cyber-Physical Systems: Modeling and Simulation

6 оценки

University of California, Santa Cruz

Cyber-Physical Systems: Modeling and Simulation

6 оценки

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.

Из урока

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

Познакомьтесь с преподавателями

Ricardo Sanfelice
Associate Professor
Department of Computer Engineering

[MUSIC]

In this video we're going to simulate an estimator that receives information from

a network that takes values of the output of a physical component, a physical plant.

And we've already seen in previous video a piece of these,

in particular physical component, and also the physical component with a network.

I already prepared a simulating file for this.

And it is here.

What we see here is a plant with a state that is being a push on field.

The output is being measured by a network.

The network transmit information over a window using

a non-deterministic choice of time instances.

And those will be such that the next event doesn't occur sooner than

T in min but it doesn't occur also later than T in max.

Once the information arrives into the system, the estimator going to use that

impossibly to reconstruct the state of the system exponentially fast.

So the immunization file will do for us

the selection of not only the simulation horizon but also the constants

that corresponds to the maximum time until the next event and the minimum time

until the next event correspondent to transmission of information.

And the times in which those occur are chosen randomly at

the initialization time.

And then we have the inital conditions for the plant, the physical component which is

a four dimensional system, and then the initial condition for the network.

Now the estimator might have also some initial values which

are similarly not supposed to be similar in any means by

those of the plan of the physical system to estimate.

And the system are having constants are linear.

It then flows and it's given by this constants given here,

a then the system matrix b, the input matrix which is equal to 0, and

then the entity is the output matrix.

Now the estimator is designed using methods that we're not

explaining in this video but adx tab will assign again that will

inject the information that arise at the event in an impulsive manner in order to

create improvement in the estimator we have of the actual state.

I noticed that all we'll receive for this system

is one state rather than four components which is the dimension of the state.

And the variables elimination are set to be similar as before in

previous simulations.

So let's run this initialization file and

let's make sure that this has created the right values.

So 10.2 for the window, and

50 seconds for the simulation, this sounds what we want, perfect.

Now we can run the simulation.

For which we'll have to compile and then it's going to start running, As expected

The output of estimator we call it z hat which is an estimate

of z which is a state of a physical component.

And what we expect is that the z hat components,

the four components of z hertz converge to the four components of z.

Okay, we finished the simulation.

And now we burn prep.

Okay, so what we see here are, in each plot, the state of the system and

also the estimate that is being provided at the output of the estimator.

As you see in the first plot the initial conditions are off, and

similarly trajectories that we obtain from the system and

from the estimator is different.

But after some events what you see is that estimates get close to the actual

true system state.

And after some jumps, one, two,

three, and four, that are pretty close and remain pretty close.

In theory they converge in the limit exponentially.

And the same happens for variables as well.

The estimator implements hybrid algorithm that is triggered

whenever has a jump, whenever information arrives.

And for that the implementation of a simulation needs to take care of

the mechanism carefully.

One can look into this just by going under the hood of the estimator block.

Now the estimator block is no more than a general hybrid system.

So we actually picked that from the, not necessarily from this higher

physical system block but from the higher equation block which is this one,

right here which is an optimize block.

All right, so that's the simulation of a estimation problem where

we have a series interconnection of three blocks.

It is three blocks used, how it models.

And the plant is not necessarily have this purely continuous time.

And as you saw the [INAUDIBLE] is nondeterministic and

the estimator is actually higher.

[MUSIC]

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