dün sözlükte noldu laaaaaaaaaayynnn

The main island has an area of approximately 91 km2. A volcanic peak rising from just west of the Mid-Atlantic Ridge, much of the island is a wasteland of lava flows and cinder cones; no fewer than forty-four distinct dormant craters have been identified.[5]

The island originally had its own native flora until Portuguese explorers released goats in the 1500s which ate much of it. The later introduction of rabbits, sheep, rats and donkeys, and over 200 imported species further marginalized the original flora.[17] By 1843 the island was barren with few plants. However, due to the introduction of species by the British, Ascension Island's Green Mountain is now one of the few large-scale planned forests, and is gradually growing with each year. Its highest point is at 2,817 feet (859 m).[5]

Off the east coast of Ascension is the islet of Boatswain Bird Island. It is a haven for sea birds providing refuge from the rats, cats and people that came to Ascension Island from Europe and Africa. Following a successful campaign headed by the Royal Society for the Protection of Birds, the main island was in 2006 declared free of feral cats, and sea birds are now once again nesting on Ascension Island.

Ascension's climate is tropical, with temperatures at the coast ranging from about 68 to 88 degrees Fahrenheit (20–31 °C), and about 10 degrees Fahrenheit (5 to 6 degrees Celsius) cooler at the highest point. Rain showers may occur at any time during the year, but tend to be heavier between January and April.
[edit] Flora and fauna
Main article: Ascension scrub and grasslands
Black volcanic rocks

The endemic flora includes plants like Pteris adscensionis, Asplenium ascensionis, Euphorbia origanoides as well as the extinct species Oldenlandia adscenionis, Sporobolus durus and Dryopteris ascensionis and the recently discovered Anogramma ascensionis (Ascension Island parsley fern).

In June 2005 the first National Park on Ascension Island, the Green Mountain National Park, was opened. Non-indigenous plants teem there, and the crown of Green Mountain is a lush halo of bamboo. Flanking one side is a large stand of tall Norfolk pine, trees planted by British mariners, which were to have been used as replacement masts for sailing ships.

A few wild flowers narrowly abound such as periwinkle; cactus is present with land crabs in several large colonies near the sea and mountains. Prosopis juliflora, or the Mexican Thorn, is an introduced species which has thrived on the barren lava of the island in recent years; however, its spread has been destructive to other species, and current encroachment on the edges of beaches threatens those that utilize this space, such as the green turtle.[18]

The protected green turtle is perhaps the most notable of the endemic fauna, coming ashore to lay their eggs on the beaches from November to May. Sooty Terns or "Wideawake Birds" nest in great seashore lava "fairs". Other seabirds include some types of boobies, petrels and tropicbirds (named boatswain (pronounced BO-sun) birds by the inhabitants of the island), White Tern, Brown Noddy, Black Noddy and Ascension Frigatebird. The Ascension Flightless Crake became extinct around the beginning of the 19th century. Following the eradication of feral cats from the island, several species of seabird previously confined to Boatswain Bird Island are making a return to the main island.[18]

On land are found such non-native birds such as canaries, francolins, mynas, sparrows, and waxbills. A variety of mammals have been introduced: donkey, sheep, cats and rats among others. Reptiles consist of two species of lizards. In summer, flies are known to be problematic.

The largest native land animal is the land crab Johngarthia lagostoma (formerly Gecarcinus lagostoma).[19]

Offshore, there is a variety of open-ocean fish, including sharks, wahoo, tuna, bonito, barracuda, marlin, blackfish and sailfish.

The only action during World War II occurred on 9 December 1941. At around mid-day, the U-boat U-124 approached Georgetown on the surface with the intention of sinking any ships at anchor or shelling the cable station. A two-gun shore battery at Cross Hill, above Georgetown, fired on the submarine. The guns scored no hits but the U-boat submerged and retreated. The battery remains largely intact to this day, together with its guns, BL 5.5 inch Mark I naval guns removed from HMS Hood during a refit in Malta in 1938.

With the Space Race and the Cold War, the Americans returned in 1956.[3] Wideawake Airfield was expanded in the mid 1960s. The runway, with its strange hump, was extended, widened, and improved to allow its use by large aircraft, and later to act as an emergency runway for the Space Shuttle, although the Shuttle never had occasion to use it.[3] The United States Air Force uses the island as part of its Eastern Range. NASA established a tracking station on the island in 1967, which it operated for more than 20 years before closing it down in 1990.[3] The island retains a role in Space exploration as the European Space Agency now operates an Ariane monitoring facility there.[3] The BBC Atlantic Relay Station was installed in 1966 for short-wave broadcasts to Africa and South America.

In 1982 a British task force used Ascension Island as a staging post during the Falklands War,[3] though according to Matthew Parris,[8] "... at the start of the Falklands conflict Washington at first refused Britain permission to use the USA-operated airfield facilities for refuelling RAF jets. Only after Mrs Thatcher intervened with Ronald Reagan did the Americans reluctantly concede." The Royal Air Force deployed a fleet of Vulcan bombers and Victor tankers at the airfield. The opening shots of the British offensive were launched from Ascension by Vulcans in Operation Black Buck. The RAF also used the base to supply the Task Force. Because of the increase in air traffic during the war, Wideawake was the busiest airfield in the world for a short period. The Royal Navy's fleet stopped at Ascension for refuelling on the way. Following the war, the British retained an increased presence on the island, establishing RAF Ascension Island, and providing a refuelling stop for the regular airlink between RAF Brize Norton in Oxfordshire, and RAF Mount Pleasant in the Falkland Islands.
Wideawake Airfield

As of 2007, NASA continues to list Ascension Island as a "downrange site" used for range safety instrumentation.[9] In particular, the Post-Detect Telemetry System used to acquire launch vehicle telemetry includes a station on Ascension.[10]

In 2008 British diplomats requested sovereignty, at the United Nations Commission on the Limits of the Continental Shelf (UN CLCS), over 77,220 square miles (200,000 km2) of submarine territory around the island. This would enable exploration into new reserves of oil, gas and minerals, though none are thought to exist.[

Ascension is part of a British overseas territory together with Saint Helena and Tristan da Cunha.[5] Executive authority is vested in Elizabeth II,[5] who is represented by the Governor of Saint Helena, Ascension and Tristan da Cunha. As the Governor resides in Jamestown, Saint Helena, an Administrator is appointed to represent the Governor on Ascension Island.
Ascension Government House

As a result of changes in the constitutional arrangements for Ascension Island, the first Island Council of seven members was elected and took office on 1 November 2002. This Council was dissolved by order of the Governor of Saint Helena on 24 October 2005, and a new election was held on 16 November 2005, a total of 697 electors choosing between ten candidates contesting the seven seats.[12]

Six of the seven members resigned in January 2007 in the belief that they were "assisting to legitimise a democracy that doesn’t really exist on Ascension Island".[13] Consequently, a general election was called, but by the close of nominations there were only two candidates. As a result of the boycott, the election was abandoned, and the governor suspended the Island Council for 12 months. It was stated that an election would take place in April 2008 but following consultations this was extended to October.[14] With 8 nominations the elections were duly held and 7 candidates were elected to form a new Island Council, which was sworn in on 28 October.[15]

Ascension Island has its own local system of law, much of which is based on the laws of Saint Helena and some parts of English law with modifications.[5] The Island Council advises on new or revised laws. Where local legislation does not exist, Saint Helenian law may be used where appropriate and suitable for local adaptation, or specific Ascension Island law is enacted. Employment legislation is a mixture of contract law and the Workmen's Protection Ordinance, which guarantees a contract, as well as obligating employers to provide free accommodation, medical cover, food (or a food allowance), travel etc.

The Saint Helena, Ascension and Tristan da Cunha Constitution Order 2009 was made by HM the Queen and the Privy Council on 8 July and came into operation in September 2009.[5] The new Constitution replaces the 1988 version and among other changes limits the Governor's powers, includes a Bill of Rights, establishes independence of the judiciary and the public service and formally designates the Governor of St Helena as, concurrently, the Governor for Ascension and Tristan da Cunha. It also ends the "dependency" status of Ascension and Tristan da Cunha on Saint Helena that had been in place, for administrative convenience, since 1922.[16]

State-space systems
Representations: From transfer function to state-space.
Consider a linear, shift invariant, system:
! P(z) !
y(k) u(k)
We can express this as a transfer function,
y(z) = P(z) u(z) =
b(z)
a(z)
u(z)
where a(z) and b(z) are polynomials, so,
P(z) =
b(z)
a(z)
=
b0zm + b1zm−1 + · · · + bm
zn + a1zn−1 + · · · + an
.
For causal systems the order of b(z) is less than or equal to the order of a(z). So m " n above.
Assume for now that m < n,
Roy Smith: ECE 147b 8: 2
State-space systems
Approach:
• Represent the plant, P(z) (or P(s)) as an nth order differential equation.
• Represent nth order differential equation as a 1st order matrix differential equation with
dimension n.
• Design methods now involve linear algebra.
• Easy to handle large systems (with Matlab).
• Easy to handle systems with multiple inputs and outputs.
• Easy to simulate systems.
x(k + 1) = Ax(k) + B u(k),
y(k) = C x(k) +Du(k).
A, B, C and D can be matrices. x(k) is a vector (state vector).
Roy Smith: ECE 147b 8: 1
State-space systems
Chain of delays:
Consider the first equation: !(z) =
1
a(z)
u(z)
We want to develop a chain of delay model to get !(k):
First step: Write the expression for n delays:
!(k) = z−1 !(k + 1)
...
...
!(k + n − 1) = z−1!(k + n)
In pictures ...
" z−1 ! ! z−1 ! z−1 "
!(k) !(k + 1) !(k + n − 2) !(k + n − 1) !(k + n)
Second step: Express !(k + n) in terms of !(k), . . . , !(k + n − 1) and u(k).
Roy Smith: ECE 147b 8: 4
State-space systems
Outline:
1. Draw the system as an interconnected “chain of delays”,
2. Relabel the signals in the system,
3. Rewrite the input/output equations in terms of the new signals,
4. Abbreviate the equations to a matrix form (state-space).
Drawing a digital system block diagram in terms of delays is exactly the same as drawing a
continuous system block diagram in terms of integrators.
Split the system,
b(z)
1
a(z)
" ! "
y(z) !(z) u(z)
!(z) =
1
a(z)
u(z) and y(z) = b(z) !(z).
Roy Smith: ECE 147b 8: 3
State-space systems
Block diagram of: !(z) =
1
a(z)
u(z)
!(k + n) = u(k) − (a1!(k + n − 1) + · · · + an!(k)) .
z−1 z−1
a1
an−1
an
! ! ! ! ! #$
%& ' +
" "
1. $
%& +
2. −
'
" "
3. $
%& +
4.
'
"
5.
!(k) !(k + 1) !(k + n − 1) !(k + n) u(k)
Roy Smith: ECE 147b 8: 6
State-space systems
Second step: Express !(k + n) in terms of !(k), . . . , !(k + n − 1) and u(k).
To do this, write this as: !(z) a(z) = u(z),
Expanding a(z) gives,
!zn + a1zn−1 + · · · + an" !(z) = u(z)
and expressing this in terms of the highest power of z gives:
zn!(z) = u(z) − !a1zn−1 + · · · + an"!(z).
Now write this is the time domain,
!(k + n) = u(k) − (a1!(k + n − 1) + · · · + an!(k)) .
This is the form we need to include in our block diagram.
Roy Smith: ECE 147b 8: 5
“Chain of delays” block diagram
bm
bm−1
b0
z−1 z−1
a1
an−1
an
( ! ! ! ! ! ( )*
+, + )*
+, + -
" "
)*
+, +
6. −
-
" "
)*
+, +
7.
-
"
8.
! !
)*
+, +
$
-
!
$
u(k)
!(k + n − 1) !(k + n)
!(k + 1)
!(k + m)
y(k) !(k)
This could actually be constructed from shift registers, summers and multipliers.
Roy Smith: ECE 147b 8: 8
State-space systems
Numerator term: y(z) = b(z) !(z)
Expanding the b(z) polynomial gives,
y(z) = b(z) !(z),
= !b0zm + b1zm−1 + · · · + bm" !(z)
and in the time domain this is,
y(k) = b0!(k + m) + b1!(k + m − 1) + · · · + bm!(k).
As m < n all of the signals !(k) to !(k + m) are available along to the top of the chain of
delays.
So y(k) is just a linear combination of signals from the previous block diagram.
Roy Smith: ECE 147b 8: 7
State-space representations
Developing the matrix equations
Relabel our intermediate variables,
x1(k) = !(k + n − 1)
x2(k) = !(k + n − 2)
...
...
xn(k) = !(k)
Now work out what happens to each of them at time k + 1:
x1(k + 1) = !(k + n) =u(k) − (a1!(k + n − 1) + · · · + an!(k))
= u(k) − (a1x1(n) + · · · + anxn(k))
x2(k + 1) = !(k + n − 2 + 1) = x1(k)
... ...
...
xn(k + 1) = !(k + 1) = xn−1(k)
Now look at this as a matrix multiplication.
Roy Smith: ECE 147b 8: 10
State-space representations
What if m = n ?
Remove the highest order terms by polynomial division,
b(z)
a(z)
= d +
ˆb
(z)
a(z)
.
Now d is a constant and ˆb(z) has order m − 1 < n.
We deal with
ˆb
(z)
a(z)
exactly as before and then add the constant, d, to the result.
In pictures . . .
ˆb
(z)
a(z)
d
! ! ! ' !
!
9. )*
+, +
y(k) u(k)
Roy Smith: ECE 147b 8: 9
State-space representations
Matrix equations
x(k + 1) = Ax(k) + B u(k),
where
A =
10. $$$%
−a1 −a2 · · · −an−1 −an
1 0 · · · 0 0
...
. . . . . . ...
0 · · · 1 0
&(
and B =
11. $$$%
1
0...
0
&(
This is the “state-update” equation (or sometimes just the “state”equation).
What about the output y(k)?
y(k) = b0!(k + m) +b1!(k + m − 1) · · · +bm!(k)
= b0xn−m(k) +b1xn−m−1(k) · · · +bmxn(k)
= C x(k)
where C = )0 . . . 0 b0 . . . bm*. If m = n − 1 then there are no leading zeros in C.
Roy Smith: ECE 147b 8: 12
State-space representations
Matrix equations
x1(k + 1) = −a1 x1(k) −a2 x2(k) · · · −an−1 xn−1(k) −an xn(k) + u(k)
x2(k + 1) = x1(k)
x3(k + 1) = x2(k)
...
xn(k + 1) = xn−1(k)
or . . .
12. $$$%
x1(k + 1)
x2(k + 1)
...
xn(k + 1)
&(
=
13. $$$%
−a1 −a2 · · · −an−1 −an
1 0 · · · 0 0
...
. . . . . . ...
0 · · · 1 0
&(
14. $$$%
x1(k)
x2(k)
...
xn(k)
&(
+
15. $$$%
1
0...
0
&(
u(k)
Define the state: x(k) =
16. $$$%
x1(k)
x2(k)
...
xn(k)
&'''(
to get the final equations.
Roy Smith: ECE 147b 8: 11
State-space systems
Other domains:
Discrete time,
time invariant:
x(k + 1) = Ax(k) + B u(k),
y(k) = C x(k) + Du(k)
Continuous time,
time invariant:
dx(t)
dt
= Ax(t) + B u(t),
y(t) = C x(t) + Du(t)
Nonlinear,
time invariant:
dx(t)
dt
= f(x(t), u(t)),
y(t) = g(x(t), u(t))
Nonlinear,
time varying:
dx(t)
dt
= f(t, x(t), u(t)),
y(t) = g(t, x(t), u(t))
Roy Smith: ECE 147b 8: 14
State-space systems
Equal numerator and denominator order case:
ˆb
(z)
a(z)
d
! ! ! ' !
!
17. )*
+, +
y(k) yˆ(k) u(k)
We can calcuate the state-space representation for
ˆb
(z)
a(z)
:
x(k + 1) = Ax(k) + B u(k),
ˆy(k) = C x(k),
and as, y(k) = ˆy(k) + du(k), we have,
x(k + 1) = Ax(k) + B u(k),
y(k) = C x(k) + du(k).
Roy Smith: ECE 147b 8: 13
State-space examples:
Thermal system:
Suppose that T1(t) is the output of interest and e(t) and T0(t) are both inputs.
Now select state variables which will allow us to put this into the generic state-space matrix
equation form.
Try x(t) = +T1(t)
T2(t),.
Then, rearranging gives,
dT1(t)
dt
=
−k12
m1c1
T1(t) +
k12
m1c1
T2(t)
dT2(t)
dt
=
k12
m2c2
T1(t) +
−k12 − k20
m2c2
T2(t) +
k20
m2c2
T0(t) +
1
m2c2
e(t)
So,
A =#
$$%
dT1(t)
dt
dT2(t)
dt
&(
= A +T1(t)
T2(t), + B +T0(t)
e(t) ,, where A =
18. $$$%
−k12
m1c1
k12
m1c1
k12
m2c2
−k12 − k20
m2c2
&'(
Roy Smith: ECE 147b 8: 16
State-space systems
Examples: A thermal control system:
Heater
terminals
e(t)
T (t)
T (t)
T (t)
2
0
1
Ti(t) temperature of volume i
e(t) energy into the volume 1
mi mass of volume i
ci specific heat for volume i
kij thermal conductance for i, j interface
We can derive the state-space representation directly from the thermal energy equations.
For volume 1: m1c1
dT1(t)
dt
= k12(T2(t) − T1(t))
For volume 2: m2c2
dT2(t)
dt
= −k12(T2(t) − T1(t)) − k20(T2(t) − T0(t)) + e(t)
Roy Smith: ECE 147b 8: 15
State-space examples:
DC Motor connected to a rotational load
L R
J
V Vemf in
+
+
−
−
"
i
19.
20. f
The “back emf” is proportional to motor speed: Vemf = K
d"
dt
.
The motor has a series resistance, R, and inductance, L, so Vin = Vemf + L
d i
dt
+ Ri.
The motor torque is proportional to the motor current: # = K" i.
There is a friction torque, #f opposing the motor and proportional to its speed: #f = b
d"
dt
.
The rotational load has inertia J so the torque balance equation is: J
d2 "
dt2 + #f = #.
Roy Smith: ECE 147b 8: 18
State-space examples
Exercises:
1. What is B?
2. What is C?
3. What is D?
4. What would C and D be if we had both T1(t) and T2(t) as outputs?
5. Calculate the transfer functions from e(t) and T0(t) to T1(t).
Roy Smith: ECE 147b 8: 17
State-space examples:
DC Motor connected to a rotational load
We are interested in the model from the input voltage, Vin, to the rotor angle, ".
Exercise:
1. How many states are required for this model?
2. Derive a state-space representation.
3. What are the poles of the system?
Roy Smith: ECE 147b 8: 19