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# Lecture 2: Systems Engineering - PowerPoint PPT Presentation

Lecture 2: Systems Engineering. EEN 112: Introduction to Electrical and Computer Engineering. Professor Eric Rozier, 1 / 23 / 2013. CROSSING THE RIVER…. Farmer, Wolf, Goat, Cabbage. A farmer needs to transport a wolf, a goat, and a cabbage across the river. F. G. Boat has two seats

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Lecture 2: Systems Engineering

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Lecture 2: Systems Engineering

EEN 112: Introduction to Electrical and Computer Engineering

Professor Eric Rozier, 1/23/2013

A farmer needs to transport a wolf, a goat, and a cabbage across the river.

F

G

• Boat has two seats

• Farmer must drive…

• If left alone…

• The wolf will eat the goat.

• The goat will eat the cabbage.

W

C

As a group, formulate a solution to transport everything across the river, without anything being eaten.

F

G

W

C

• Sometimes we have to move backwards to move forwards.

• Even simple systems need thought to formulate a plan for accomplishing their goals.

We call this plan, an algorithm.

• al-Khwarizmi

• Persian mathematician, astronomer, and geographer born780 A.D.

• Invented a few things…

• Decimal system

• Algebra

• Trigonometry

• al-Khwarizmi also introduced the idea of solving problems using step-by-step procedures for calculations.

• Algorithms – A method of solving a problem or accomplishing a task expressed as a finite list of well defined instructions.

• Starting from an initial state and an initial input, the instructions describe a computation that, when executed will proceed through a finite number of well defined successive states, eventually producing output, and terminating at a final ending state.

• States are a way of measuring the condition of a system, and it’s environment.

• Inputs are a way of getting information to a system.

• Outputs are a way of getting information from a system.

• Algorithms let us define, formally, what we want machines and automated systems to do.

• Algorithms are written to have precise meanings, and to be generally applicable.

Systems Engineering and Cyberphysical Systems

• We build systems to do jobs, solve problems, and accomplish tasks.

• Often these systems are cyberphysical systems, i.e. they combine computational components with the real world.

• An algorithm is a way of telling the components how to do their job, and how to work together.

• Thermostat

• What is the goal?

• What problem does it solve?

• How would we characterize the state?

• What would the inputs and outputs be?

• Thermostat

• What is the goal?

• What problem does it solve?

• How would we characterize the state?

• What would the inputs and outputs be?

• Break into groups

• Define the problem

• Define what the thermostat needs to do

• Thermostat

• Regulate temperature

• Specification

• Must be able to sense temperature

• Based on the temperature must be able to signal cooling or warming the room, or to do nothing.

• State: temperature, heating state, cooling state

• Thermostat

• Pseudocode algorithm

• tempLow = L

• tempHigh = H

• loop()

• Test temperature, store the value in T

• If (T < L) send a heating signal

• If (T > H) send a cooling signal

Thermostat

Signal: Heat

Signal: Cool

Heater

Air Conditioner

Sensor

• Some important points…

• Four systems here, each with their implementations…

• Need to communicate with each other…

Signal: Heat

Signal: Cool

Heater

Air Conditioner

Sensor

• Systems communicate via signals, over wires, or wirelessly via electromagnetic radiation.

• In our thermostat system, the heater and cooler can be switched on or off by a pure signal on the wire. I.e., if electrons are flowing, turn on, if not, turn off!

• But how do we get information from the sensor?

• It needs to send a number… how do we do that?

• What if we encode the signal into pulses?

• Detect if the value is above or below some threshold, and decide it represents a 1, or a 0.

• Strings of 1’s and 0’s can be interpreted as a number.

• True or false…

• 1 – true

• 0 – false

• We already were doing this with pure signals.

• Integers

• Examples

• 00000000 – 0- 00000010 - 2

• 00000001 – 1- 00001010 – 10

• 00000011 – 3- 10010011 – 147

We will cover those later…

• Using true/false values in complicated ways

• Thermostat system

• Let’s make a change to the basic system

• Add a switch with values “Heat” and “Cool”

• Cool the room if T > H and Switch is set to “Heat”

• Heat the room if T < L and Switch is set to “Cool”

• Gets back to gators and grades…

• Represent truth as 1, and false as 0

• We can operate on values using the following basic operators:

• AND

• OR

• NOT

• X AND Y

• X OR Y

• NOT X

• ^ - And

• v – Or

• ! – Not

• !X ^ Y

• X ^ Y = Y ^ X

• X v Y = Y v X

• X ^ (Y ^ Z) = (X ^ Y) ^ Z

• X v (Y v Z) = (X v Y) v Z

• X ^ (Y v Z) = (X ^ Y) v (X ^ Z)

• X v (Y ^ Z) = (X v Y) ^ (X v Z)

• !x ^ !y

• !(x ^ y)

• !x ^ x

• (x v y) ^ !(x ^ y)

• X XOR Y

• (x v y) ^ !(x ^ y)

• Exclusive Or

• X  Y

• (!X v Y)

• Implication

• X = Y

• (!X XOR Y)

De Morgan’s Laws

• The negation of a conjunction, is the disjunction of the negations

• !(X ^ Y) <-> (!X) v (!Y)

• !(X v Y) <-> (!X) ^ (!Y)

• Prove the equivalence of the expressions in De Morgan’s Laws with truth tables (show they are the same!)