Lecture 2: Systems Engineering

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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

EEN 112: Introduction to Electrical and Computer Engineering

Professor Eric Rozier, 1/23/2013

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
• Farmer must drive…
• If left alone…
• The wolf will eat the goat.
• The goat will eat the cabbage.

W

C

Farmer, Wolf, Goat, Cabbage

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

F

G

W

C

What do we learn from this exercise?
• 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.

Algorithms
• al-Khwarizmi
• Persian mathematician, astronomer, and geographer born780 A.D.
• Invented a few things…
• Decimal system
• Algebra
• Trigonometry
Algorithms
• 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, Inputs, and Outputs
• 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
• 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.
Example System: Thermostat
• Thermostat
• What is the goal?
• What problem does it solve?
• How would we characterize the state?
• What would the inputs and outputs be?
Example System: Thermostat
• 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
Example System: Thermostat
• 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
Example System: Thermostat
• 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
Example System: Thermostat

Thermostat

Signal: Heat

Signal: Cool

Heater

Air Conditioner

Sensor

Thermostat
• Some important points…
• Four systems here, each with their implementations…
• Need to communicate with each other…

Signal: Heat

Signal: Cool

Heater

Air Conditioner

Sensor

Networking and Communication
• 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!
Networking and Communication
• But how do we get information from the sensor?
• It needs to send a number… how do we do that?
Networking and Communication
• 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.
Some simple things we can represent with 1’s and 0’s
• True or false…
• 1 – true
• 0 – false
• We already were doing this with pure signals.
Some simple things we can represent with 1’s and 0’s
• Integers
• Examples
• 00000000 – 0 - 00000010 - 2
• 00000001 – 1 - 00001010 – 10
• 00000011 – 3 - 10010011 – 147

### Negative numbers and real numbers are more complex…

We will cover those later…

Boolean Algebra
• 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”
Boolean Algebra
• 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
AND
• X AND Y
OR
• X OR Y
NOT
• NOT X
Abbreviations
• ^ - And
• v – Or
• ! – Not
• !X ^ Y
Commutative laws
• X ^ Y = Y ^ X
• X v Y = Y v X
Associative laws
• X ^ (Y ^ Z) = (X ^ Y) ^ Z
• X v (Y v Z) = (X v Y) v Z
Distributive laws
• X ^ (Y v Z) = (X ^ Y) v (X ^ Z)
• X v (Y ^ Z) = (X v Y) ^ (X v Z)
Some exercises
• !x ^ !y
• !(x ^ y)
• !x ^ x
• (x v y) ^ !(x ^ y)
Derived operators
• 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)
Homework
• Prove the equivalence of the expressions in De Morgan’s Laws with truth tables (show they are the same!)