A Finite-State Machine for Controlling the Temperature in a Room

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From the course by University of California, Santa Cruz

Cyber-Physical Systems: Modeling and Simulation

5 оценки

University of California, Santa Cruz

Cyber-Physical Systems: Modeling and Simulation

5 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.

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
Associate Professor
Department of Computer Engineering

The class of finite state machines that we defined in the previous video,

is what is called a pure finite state machine,

and it allows transitions when the inputs change.

In many cases, we would like to have transitions when

certain conditions that might involve the input,

the state, and maybe also the output happen.

For instance, consider the problem of controlling the temperature of a room.

We already saw the model of

the physics for that problem.

This will require transitions of the heater

from on to off

and from off to on,

when the temperature

is in certain range.

Let's take a simple situation.

Suppose that we have a mode of operation that corresponds to on.

This is when the heater is on and then a mode of operation that corresponds to off,

which is when the heater is off.

It is expected that if you would like your temperature to remain within the range,

let's say minimum temperature or maximum temperature,

they're not in T max respectively,

that you will transition from on to off when the

temperature has reach the value T max and that you'll have

a transition from off

to on when the temperature has reach the threshold T min.

Now we can think about this logic as a finite state machine with two modes.

In such a model we could have two modes.

Q will be in the set of a state on, off.

This will define my capital Q for the finite state machine.

But now, transitions occur

when the following conditions hold.

We can think about V being the input to the machine equal to the temperature.

So, when the input to the machine is large or equal than T max,

and the current mode is on, then a transition

should occur, while when the input is less or equal than T min,

and the mode of operation corresponds to off,

another transition will occur.

The function L is the guard

function and now transitions can occur.

When that function has a particular sign,

we can actually say when

this function is less

or equal than zero,

and this is arbitrary, it could be larger or equal than zero or some other condition.

With that guard function now we can have a model of a finite state machine

that has a transition function that governs the evolution of the state.

It's output also depends on a function of the state.

And now the transitions occur when the function L,

which is the guard function,

satisfies this condition.

So now this model right here

which expands the previous model

which is known as pure finite state machines,

leads to another model of a finite state machine with guards.

As you see with this example,

this function can craft according to the conditions of transitions

that one would like the changes

to happen and then the evolution of the state will change when those conditions are true.

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