A Cyber-Physical System Model of a Thermostat (Part 1)

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From the course by University of California, Santa Cruz

Cyber-Physical Systems: Modeling and Simulation

9 ratings

University of California, Santa Cruz

Cyber-Physical Systems: Modeling and Simulation

9 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 Cyber Components: Finite State Machines, Computations, Algorithms, and a First CPS Model

Finite-State Machines (Part 1)5:44

Finite-State Machines (Part 2)3:04

Finite-State Machines (Part 3)5:41

Simulation of a Finite State Machine6:37

A Finite-State Machine for Controlling the Temperature in a Room5:31

Simulation of a Finite State Machine to Control the Temperature of a Room7:19

A Finite State Machine Modeling a Chess Game7:13

A Cyber-Physical System Model of a Thermostat (Part 1)6:28

A Cyber-Physical System Model of a Thermostat (Part 2)4:53

Simulation of a Cyber-Physical System Model of a Thermostat7:50

Models of Computations6:28

A General Discrete-Time Model of a Linear Time-Invariant Algorithm4:55

Meet the Instructors

Ricardo Sanfelice
Professor
Department of Electrical and Computer Engineering

[MUSIC]

With the models of finite state machines and

of the physical part of a cyber physical system,

now we can write down a full cyber physical system with what we have learned.

Let's consider the problem of controlling the temperature of a room again.

The dynamics of the temperature were introduced in an earlier video and

given by the following expression.

Where this aT, Tr and T delta were properly defined constants and

u is a signal that can only take values in 0 and 1.

That means that when it's 0 the heater is off, and when it's 1 the heater is on.

This can be modeled as a cyber physical system, physical path only and

we would like to do right now would be to come up with a model

here that will control the temperature to this particular

T min T max range we mentioned in a previous video.

So here we'll have the cyber, and

our goal would be design an algorithm,

That keeps T within T min and T max,

where this constants T min and

T max which is the range of temperature we

would like to have is related to these

constants in the following way.

The reason of this constant will become clear when we start the simulations and

it will in particular guarantee that these thresholds T min and

T max can be thresholds where the temperature kind of stay within.

So how we keep TE

(Tmin and Tmax)?

Well, based on what we already learned when we illustrated the finite

state machine with [INAUDIBLE], we can now come out with the following logic

First we can say that when the heater is

on we will define a variable q been equal to ON,

and when q is equal to OFF We

have that the heater is OFF, okay?

So this will define my state

of a finite state machine and

from here we notice that Q now will be on and off.

This is the set of values where q and

can take values from and

a logic will be if q is equal to ON and

the temperature T is larger or

equivalent to max then we would

like to have is q+ equal to OFF.

And if q is equal to OFF and T is less or

equivalent to Tmin then we

will have q+ equal to ON.

So that's our logic.

And that somewhat suggest how the transition function should change.

It looks like these are the terministic transition function and

moreover the logic is telling us what are the conditions for transition?

So what we have learned these conditions

could go in to the definition of l while

these assignments after the events

will go in to the definition of delta.

Since now the value of the state is on and off,

but the input that I need to apply to the temperature system is 001,

this output here which we label as theta for the finite-state machine,

we'll need to convert on of 2, 0 and 1, okay?

So this is how we can now write down a finite-state machine

using the objects that we will find in a previous video.

[MUSIC]

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