Excel PID Drone Simulation (.xlsx)
NetLogo Simulations
Google Docs version (lame)
auto08 Big Picture: appreciate the ambition of automation and generic notion of building something whose adaptive behavior can be specified by a finite number of settings coupled to a feedback mechanism
auto01 Fundamentals: define "automatic" and explain what components of an automatic machine (sensor, actuator, mechanism, control) do
auto04 Mechanics of Examples: explain how cams and followers, steam engine governor, thermostat work
auto05 Feedback: explain the concept; give everyday examples; distinguish positive and negative; describe possible system behaviors verbally and with charts
auto07 PID Controllers: describe to person-on-the-street what PID controller does; explain association of past, present, future with I, P, D; describe what's going on in an output over time chart; carry out simple math of difference equations in a PID table
auto06 Causal Loop Diagrams: interpret CLD, construct from text, distinguish positive and negative causal relations, recognize balancing/reinforcing loop
auto03 Taxonomy: recognize/explain difference between automation as following rules/seeking goal; open/closed loop
auto02 History: describe linguistic origins of "automatic" and "cyber"; convey sense that automation is not new but a long-term human project; describe automata and famous historical exemplars of automation (centrifugal governor, Jacquard loom)
auto08 Big Picture
auto01 Fundamentals
auto04 Mechanics of Examples
auto05 Feedback
auto07 PID Controllers
auto06 Causal Loop Diagrams
auto03 Taxonomy
auto02 History
auto08 Big Picture
auto01 Fundamentals
auto04 Mechanics of Examples
auto05 Feedback
auto07 PID Controllers
auto06 Causal Loop Diagrams
auto03 Taxonomy
auto02 History
mostly "flipped" classroom
readings/lectures BEFORE class
review/stop+think Qs accompany readings→answers to be written down
class built around problems, activities, and Q&A, drawing on written answers
default expectation is cameras on, ready to be "called on," minimize time "waiting on turning mic on"
SHORT exposition → heads-down Q (→ heads-together) → report back → feedback
problem set sections per topic
class session 2-4 "items"
Quercus module: each item is a (non-graded) quiz
typical protocol
Name | Table |
---|---|
Athaliah | 1 |
Benner | 1 |
Bo | 2 |
Christina | 2 |
Chyna | 3 |
Cindy | 4 |
Eden Racca | 4 |
Elizabeth | 4 |
Hajir | 5 |
Hyemin | 5 |
Julia | 6 |
Luckyna | 6 |
Marco | 7 |
Nicholas | 7 |
Oliver | 8 |
Purnima | 9 |
Reese | 9 |
Samita | 9 |
Shae-Linn | 10 |
Tiago | 10 |
Waanmathi | 11 |
Yahui | 11 |
Yandrickx | 12 |
Yuxuan | 12 |
Zhiqi | 12 |
ROUND 1
[auto01] Write a definition for the term "automatic."
Name | Table |
---|---|
Athaliah | 1 |
Benner | 13 |
Bo | 2 |
Christina | 12 |
Chyna | 3 |
Cindy | 10 |
Eden Racca | 4 |
Elizabeth | 9 |
Hajir | 5 |
Hyemin | 8 |
Julia | 6 |
Luckyna | 7 |
Marco | 7 |
Nicholas | 6 |
Oliver | 8 |
Purnima | 5 |
Reese | 9 |
Samita | 4 |
Shae-Linn | 10 |
Tiago | 3 |
Waanmathi | 11 |
Yahui | 2 |
Yandrickx | 12 |
Yuxuan | 1 |
Zhiqi | 7 |
Zoie | 4 |
ROUND 2
[auto02] What ancient Greek word is the origin of our prefix "cyber-"?
What are some examples of feedback that you've come across today?
(Q20005)
Automatic machines can be controlled to do what humans want by minimizing error through feedback.
machine
automatic
control
feedback
cybernetics
A machine is "(1): an instrument (such as a lever) designed to transmit or modify the application of power, force, or motion
(2): an assemblage of parts that transmit forces, motion, and energy one to another in a predetermined manner"
An automatic machine is one that, once turned on, operates without human intervention.
Regulation of a system to achieve desired performance.
control that does not have access to feedback.
control that does have access to feedback.
Evaluative information about a process that is available to a controller of that process
the science of automatic control systems in both machines and living things
closed loop
open loop
from Kubernetes (κυβερνήτης, Greek for "governor", "helmsman" or "captain" or "steerer"; becomes gubernet- in Latin)
Earliest usages were more social than technical: governance of society
These things were "AUTOMATIC" in that humans supplied the energy or the power but the device could carry out the sequence of activities "on its own."
αὐτόματον, automaton, "acting of one's own will." First used by Homer to describe an automatic door.
Automaton clock in Gloucester, United Kingdom
Henri Maillardet automaton, London, c1810 - Franklin Institute
See also: Lucas, Jim. 2018. "6 Simple Machines: Making Work Easier"
SMORE. "Work, energy, and simple machines"
transferring a force from one place to another,
changing the direction of a force,
increasing the magnitude of a force, or
increasing the distance or speed of a force.
Actuator: generates force
Mechanism: transmit and focus force
Sensor: detects states
Controller: Compares sensor output to
goal and adjusts actuator
Actuator: ?
Mechanism: ?
Sensor: ?
Controller: ?
button
switch
heater
temperature
sensor
at 100c
throw switch
V. Ryan (no relation) aka
This produces an up and down motion of the grey part which is called the "follower."
See also: "Eccentric Cam Mechanism"
V. Ryan (no relation) aka
Differently shaped cams yield different patterns of motion
Wikipedia says the camshaft was first described in 1206 by Arab engineer Al-Jazari. He employed it as part of his automata, water-raising machines, and water clocks such as the castle clock.
Exercise
3. [auto04] What would a charting of the follower's motion be for this cam?
follower
time
time
command
rotation
2
3
7
4
follower
time
command
rotation
2
3
7
4
follower
time
2
3
6
4
What might a flow chart for this automatic machine look like?
command
sequence
2
3
7
5
follower
command
sequence
2
3
7
5
Exercise
3. [auto04] What would a charting of the follower's motion be for this cam?
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
7
1
2
4
9
8
6
5
3
7
1
2
4
9
8
6
5
3
7
1
2
4
8
6
5
3
Q: simple causal loop: description via broadcast work together drawing (pairs)
ROUNDs of 2
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
12
10
7
1
2
4
11
9
8
6
5
3
12
10
7
1
2
4
11
9
8
6
5
3
13
13
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
12
10
7
1
2
4
11
9
8
6
5
3
12
10
7
1
2
4
11
9
8
6
5
3
13
13
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
12
10
7
1
2
4
11
9
8
6
5
3
12
10
7
1
2
4
11
9
8
6
5
3
13
13
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
12
10
7
1
2
4
11
9
8
6
5
3
12
10
7
1
2
4
11
9
8
6
5
3
13
13
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
12
10
7
1
2
4
11
9
8
6
5
3
12
10
7
1
2
4
11
9
8
6
5
3
13
13
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
12
10
7
1
2
4
11
9
8
6
5
3
12
10
7
1
2
4
11
9
8
6
5
3
13
13
ROUNDs of 3
7
1
2
4
9
8
6
5
3
7
1
2
4
9
8
6
5
3
7
1
2
4
8
6
5
3
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
7
1
2
4
9
8
6
5
3
7
1
2
4
9
8
6
5
3
7
1
2
4
8
6
5
3
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
Zoie
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
7
1
2
4
9
8
6
5
3
7
1
2
4
9
8
6
5
3
7
1
2
4
8
6
5
3
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
7
1
2
4
9
8
6
5
3
7
1
2
4
9
8
6
5
3
7
1
2
4
8
6
5
3
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
7
1
2
4
9
8
6
5
3
7
1
2
4
9
8
6
5
3
7
1
2
4
8
6
5
3
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
7
1
2
4
9
8
6
5
3
7
1
2
4
9
8
6
5
3
7
1
2
4
8
6
5
3
ROUNDs of 4
7
1
2
4
6
5
3
7
1
2
4
6
5
3
7
1
2
4
6
5
3
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
1
2
4
5
3
7
1
2
4
6
5
3
7
1
2
4
6
5
3
7
1
2
4
6
5
3
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
1
2
4
5
3
7
1
2
4
6
5
3
7
1
2
4
6
5
3
7
1
2
4
6
5
3
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
1
2
4
5
3
7
1
2
4
6
5
3
7
1
2
4
6
5
3
7
1
2
4
6
5
3
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
1
2
4
5
3
7
1
2
4
6
5
3
7
1
2
4
6
5
3
7
1
2
4
6
5
3
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
1
2
4
5
3
ROUND of 2
[auto02] Draw a flowchart for a simple cam/follower automation
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
12
10
7
1
2
4
11
9
8
6
5
3
12
10
7
1
2
4
11
9
8
6
5
3
13
13
ROUND of 3
[auto02] Draw a flowchart for a simple cam/follower automation
7
1
2
4
9
8
6
5
3
7
1
2
4
9
8
6
5
3
7
1
2
4
8
6
5
3
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
ROUND of 4
[auto02] Draw a flowchart for a simple cam/follower automation
7
1
2
4
6
5
3
7
1
2
4
6
5
3
7
1
2
4
6
5
3
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
1
2
4
5
3
Heads-Down, Think and Write on your own white board
Find your table
Breakout rooms open, go to your room
Decide on order
Timer starts
Hear from everyone, craft collective response, write on table's white board
15 second warning - finish up
Return to main room. Instructor resets deck. Individual called to report for group
Feedback/takeaway
instruction
rotation
1
4
3
2
follower
1
2
3
4
Exercise
[auto04] Quick draw flowchart for cam- or card-based automation if it's basically "instruction 1, instruction 2, instruction 3, instruction 4, repeat." Use the graphical pieces below.
Exercise
[auto04] Quick draw flowchart for cam- or card-based automation if it's basically "instruction 1, instruction 2, instruction 3, instruction 4, repeat."
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
12
10
7
1
2
4
11
9
8
6
5
3
12
10
7
1
2
4
11
9
8
6
5
3
13
13
17th century
Credited to Christiaan Huygens,
adapted by James Watt 1788.
Concept: balls spin under steam pressure; faster pressure, faster spin; faster spin, pull arms down; arm motion opens pressure release; pressure decrease leads to speed decrease and valve closes
17th century
Credited to Christiaan Huygens,
adapted by James Watt 1788.
Concept: balls spin under steam pressure; faster pressure, faster spin; faster spin, pull arms down; arm motion opens pressure release; pressure decrease leads to speed decrease and valve closes
steam
steam
Exercise
[auto02] The Jacquard loom and the centrifugal steam engine governor are fundamentally different approaches to automation. Can you say why/how?
Exercise
[auto02] The Jacquard loom and the centrifugal steam engine governor are fundamentally different approaches to automation. Can you say why/how?
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
12
10
7
1
2
4
11
9
8
6
5
3
12
10
7
1
2
4
11
9
8
6
5
3
13
13
CLOSE ENOUGH TO GOAL?
Action
Adjust
Exercise
4. [auto04] The centrifugal governor slows a machine down if it is going too fast and speeds it up if it is going too slow (compared to a chosen speed). What does this look like in a flow chart? Arrange these items to capture this logic.
Exercise
4. [auto04] The centrifugal governor slows a machine down if it is going too fast and speeds it up if it is going too slow (compared to a chosen speed). What does this look like in a flow chart? Arrange these items to capture this logic.
7
1
2
4
9
8
6
5
3
7
1
2
4
9
8
6
5
3
7
1
2
4
8
6
5
3
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
TOO FAST?
TOO SLOW?
SLOW DOWN
SPEED UP
GO
But where do these diamonds get the information they need to decide?
SENSORS!
One horse runs. Others say "chill out, Max."
Two horses run. Others say, "Dudes, relax."
Three horses run. Nearby others say, "Hey, something happening?" And speed up a bit.
Others see change. Start hurrying
More horses perceive the change and pick up the pace...
Reinforcing
Loop
INPUT
OUTPUT
How many different kinds of feedback have you seen today?
In open-loop automation the control of the process is independent of the output.
In closed loop automation, the control of the process depends on feedback based on the output of the process.
Exercise
5. [auto04] Consider these four "systems" - are they "open" or "closed" loops? If they are closed loop, what's the feedback and how does the system use it?
Exercise
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
12
10
7
1
2
4
11
9
8
6
5
3
12
10
7
1
2
4
11
9
8
6
5
3
13
13
something about A has an effect on B
something about B has an effect on A
something about A has an effect on B
something about B has an effect on A
the more B panics, the more A panics
the more A panics, the more B panics
Each measurable cause/effect is represented by a word or phrase
Arrows point from causes to effects
Arrows are labeled + or - to indicate positive or negative (inverse) causal relationships.
population
births
deaths
TIME
Horses Running
What's going on here?
Describe the process of turning on a faucet and get it to the right temperature to wash your hands?
Positive Causal Relationship: the more A, the more B OR
the less A the less B
Negative Causal Relationship: the more A, the less B OR
the less A the more B
more hot → higher actual
higher actual → bigger gap
bigger gap → less hotter
We might start out too cold,
add warm, still be a bit cold,
TIME
GAP
TIME
GAP
We might start out too cold,
add more warm, getting close,
just a bit more warm, ahhh, just right.
Add warm, still be a bit cold,
add more warm, now we are a bit too warm,
turn back the warm a bit, ahhh, just right.
Horses Running
TIME
TIME
GAP
SYSTEM OUTPUT
TIME
How does the get the water to hand washing temperature system look?
If you have a friend who is alternately warm and cold relationally, what does the system look?
How do accidents happen?
Which curve do we associate with COVID?
Reinforcing
Loop
This is a positive feedback loop. AKA a "reinforcing" (R) loop. R loops always have an even number of minus signs.
Balancing
Loop
Reinforcing
Loop
This is a positive feedback loop. AKA a "reinforcing" (R) loop. R loops always have an even number of minus signs.
Balancing
Loop
This is a negative feedback loop. AKA a "balancing" (B) loop. B loops always have an odd number of minus signs.
The more open the throttle,
the faster the machine.
The faster the machine,
the higher the rotational frequency.
The higher the rotational frequency,
the higher the angle.
The higher the angle,
the less open the throttle.
The less open the throttle,
the slower the machine.
"When A grows, B grows"
A
B
Linked Causes and Effects
"A influences B"
A
B
A
B
"When A grows, B shrinks"
Exercise
Benner
Waanmathi
Fiza
Nicholas
Luckyna
Hajir
Athalia
Bo
Cindy
Zoie
Tiago
Shae-Linn
Samita
Reese
Oliver
Marco
Julia
Min
Elizabeth
Eden
Chyna
Christina
Zhiqi
Vivian
Yandrickx
Yahui
12
10
7
1
2
4
11
9
8
6
5
3
12
10
7
1
2
4
11
9
8
6
5
3
13
13
"When things go well, I get over confident and start to cut corners. Things start slipping and I get careful and then things go better."
"The hungrier I am, the more I eat.
The more I eat, the less hungry I am."
"The hotter I am, the more I sweat. The more I sweat, the cooler I get. The colder I am the more I shiver. The more I shiver, the warmer I get."
The warmer the earth is, the more thawing and melting. The more things thaw and melt, the more CO2 gets released. The more CO2 in the atmosphere, the more sunlight gets reflected back. The more reflected sunlight, the warmer the earth.
Hungry
Eating
"The hungrier I am, the more I eat.
The more I eat, the less hungry I am."
Things Go Well
Confidence
"When things go well, I get over confident and start to cut corners. Things start slipping and I get careful and then things go better."
Cut Corners
causal loop for insulin/glucagon
https://storage.googleapis.com/ltkcms.appspot.com/fs/yd/images/cover/negative-feedback-loop.base?v=1587496185
Amplifier
amplifies
sound from
microphone.
Sound comes
out of speaker
and goes into
microphone.
If amplifier affects higher
pitched sounds more then higher pitch amplification outpaces
lower pitches and we hear screeeeeeeeeeech.
Temperature
Thawing and Melting
CO2 Release
Sunlight Reflected Back
The warmer the earth is, the more thawing and melting. The more things thaw and melt, the more CO2 gets released. The more CO2 in the atmosphere, the more sunlight gets reflected back. The more reflected sunlight, the warmer the earth.
R loops produce unconstrained growth in a system.
SET TEMPERATURE
THERMOMETER
SWITCH
But HOW are these causally related?
HOW does the "system" behave?
balancing loop
This is a negative feedback loop. AKA a "balancing" (B) loop. B loops always have an odd number of minus signs.
TIME
TEMP
SET TEMP
ACTUAL TEMP
GAP
Furnace switches off but some heat continues to flow
Furnace ON
B loops produce systems that oscillate or settle down.
Next
Expert helmspersons pay attention to what's going on, how things are changing, and where things have been so far.
How far off the target am I at the moment?
Is my error increasing or decreasing?
How well or how badly have I been doing overall?
PRESENT
PAST
FUTURE
Proportion = what is the current error?
Derivative = how is error changing?
Integral = how much error has accumulated?
PAST
FUTURE
PRESENT
https://youtu.be/wkfEZmsQqiA