# UK Constitution and Government/Parliament

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## Parliament

Parliament is the supreme law-making body in the United Kingdom. It is
made up of two *Houses of Parliament*, namely the *House of Commons* and
the *House of Lords*, as well as the Sovereign. The Sovereign\'s
involvement in the life and working of Parliament is purely formal.

In constitutional theory, Parliament in its strictest sense is sometimes
referred to as the *Queen-in-Parliament*; this contrasts with the more
ordinary use of the term \"Parliament\", meaning just the two Houses of
Parliament. Within the British constitutional framework, the
Queen-in-Parliament is supreme (\"sovereign\"), able to make, alter, or
repeal any law at will.

Both Houses of Parliament meet at the *Palace of Westminster*.

## Parliaments and Sessions

As with most legislatures, Parliament does not continue in perpetual
existence. Typically, the \"life\" of a Parliament is around four years.

Parliament is initially *summoned* by the Sovereign. This now always
occurs after there has been a general election. Once assembled, and a
Speaker has been chosen by the House of Commons, Parliament is formally
*opened* by the Sovereign. The business of the two Houses is arranged
into *sessions*, which usually last a year (running from around October
or November each calendar year). However, there is usually a long
*recess* during the summer months, when business is temporarily
suspended.

The opening of each parliamentary session is conducted in accordance
with a great deal of traditional ceremony. The Sovereign takes his or
her seat on the throne situated in the chamber of the House of Lords,
and the Gentleman Usher of the Black Rod (one of that House\'s officers)
is commanded to summon the House of Commons. When Black Rod reaches the
door of the Commons, it is slammed shut in his face, to symbolise the
right of the Commons to debate without royal interference. Black Rod
then solemnly knocks on the door with his staff of office; on the third
knock, the door is opened, and he is permitted to enter and deliver his
message. MPs then proceed from the Commons to the House of Lords, to
hear the *Speech from the Throne*, more commonly known as the *Queen\'s
Speech*. The Speech outlines the Government\'s legislative proposals for
the session; while worded as if it\'s the Sovereign\'s own policy, the
Speech is in fact entirely drafted by Government ministers.

Each session is ended by a *prorogation*. The Commons are formally
summoned to the House of Lords, where another formal Speech is read out,
summing up the work of the two Houses of Parliament over the course of
the session. In practice the Sovereign no longer attends for the
prorogation; *Lords Commissioners* are appointed to perform the task,
and one of their number also reads out the Speech.

By law, each Parliament must come to an end no later than five years
from its commencement; this is known as *dissolution*. Because a
dissolution is necessary in order to trigger a general election, the
Prime Minister was effectively able to choose to hold elections at a
time that seems the most advantageous to his or her political party.

After the 2010 General Election the Liberal Democrat party made the
introduction of a law on fixed term parliaments a requirement for
forming a coalition government with the Conservative party. A coalition
was necessary as the result of the election meant no party had an
overall majority of seats. The main opposition party from the previous
parliament, the Conservative party, gained the most seats and under
parliamentary protocol had the first opportunity to try and form a
government. They concluded a formal deal with the Liberal Democrats to
govern together. The Liberal Democrats had insisted on fixing the term
of parliaments to reduce the inherent advantage the governing party had
in being able to choose the moment to hold an election. There are
provisions in the Fixed Term Parliaments Act to allow an early election
with the consent of Parliament. These provisions were used in 2017.

Although the duration of Parliament has been restricted to five years
since 1911, legislation was passed during both World Wars to extend the
life of the existing Parliament; this meant that the Parliament summoned
in 1935 eventually continued in existence for around ten years, until
1945.

## House of Commons

### Composition

While sometimes described as the \"lower house\", the House of Commons
is by far the most important of the two Houses of Parliament. Members of
the House of Commons are known as *Members of Parliament*, or *MPs*.

The entire United Kingdom is subdivided into *constituencies*, each of
which returns one MP to sit in the House of Commons. There are presently
650 constituencies, however the exact number fluctuates over time as the
boundaries of constituencies are periodically reviewed by Boundaries
Commissions set up for each part of the UK. Constituencies are intended
to have roughly equal numbers of voters, but in practice the smallest
and largest constituencies can have a significant difference in size.

At each *general election* all seats in the House of Commons become
vacant. If a seat becomes vacant during the life of a Parliament (i.e.
between general elections), then a *by-election* is held for that
constituency. The election for each constituency is by secret ballot
conducted according to the *First-Past-the-Post* system: the candidate
with the most votes is *returned* as MP.

#### Qualifications of voters

A person must be aged at least eighteen in order to vote.

The following nationalities are entitled to vote at parliamentary
elections:

-   British citizens
-   citizens of the Republic of Ireland
-   citizens of Commonwealth countries

Irish and Commonwealth citizens must have been resident in the United
Kingdom. British citizens who are resident abroad are only able to vote
if they had been resident in the United Kingdom within the previous 15
years.

Certain categories of people are unable to vote:

-   the Sovereign
-   members of the House of Lords
-   people serving prison sentences
-   persons convicted of \"corrupt practices\" (electoral malpractice)
    within the previous five years
-   the insane

By convention, close relatives of the Sovereign also do not vote.

#### Qualifications of MPs

Anyone who is not disqualified to vote is also qualified to be an MP,
except the following:

-   undischarged bankrupts
-   persons convicted of treason
-   members of legislatures outside of the United Kingdom that are not
    in Commonwealth countries
-   civil servants
-   members of certain specific public bodies, and holders of certain
    specific statutory offices
-   members of the armed forces
-   judges

#### Resignation as an MP

Since the 17th century, the House of Commons has asserted that MPs may
not resign. However, in practice members are able to resign by the legal
fiction of appointment as *Crown Steward and Bailiff of the three
Chiltern Hundreds of Stoke, Desborough, and Burnham*, or as *Crown
Steward and Bailiff of the Manor of Northstead*. Neither of these
offices carries any duties, but have been preserved in force so that
those appointed to them automatically lose their seats in the House of
Commons as having accepted an *office of profit under the Crown*.

### Speakership and procedure

The House of Commons is presided over by the *Speaker*. There are also
three Deputy Speakers, with the titles of *Chairman of Ways and Means*,
*First Deputy Chairman of Ways and Means*, and *Second Chairman of Ways
and Means*.

The Speaker and his or her deputies are elected at the commencement of a
Parliament, and serve until its dissolution. Following a general
election, the *Father of the House* (the member with the longest
unbroken service in the House, who is not also a Minister of the Crown)
takes the chair. If the Speaker from the previous Parliament has been
returned as a member of the new Parliament, and intends to continue in
office, then the House votes on a motion that the member take the chair
as Speaker. Otherwise, or if the motion for his or her re-election
fails, then members vote by secret ballot in several rounds; after each
round, the candidate with the fewest votes is eliminated. The election
ends when one member secures a majority of votes in a particular round.
Thereafter, the Speaker-elect leads the House of Commons to the House of
Lords, where the Lords Commissioners (five Lords representing the
Sovereign) officially declare the Royal Approbation (approval) of the
Speaker, who immediately takes office. The Speaker traditionally lays
claim to all of the House\'s privileges, including freedom of speech in
debate, which the Lords Commissioners then confirm on behalf of the
Sovereign.

If a Speaker should choose to resign from his post during the course of
Parliament, then he must preside over the election of his successor. The
new election is otherwise conducted in the same manner as at the
beginning of a Parliament. The new Speaker-elect receives the Royal
Approbation from Lords Commissioners; however, the ceremonial assertion
of the rights of the Commons is not repeated.

The Speaker is expected to act impartially. He or she is an important
figure within the House of Commons, controlling the flow of debate by
selecting which members get to speak in debates, and by ensuring that
the customs and procedures of the House are complied with. The Speaker
and his deputies do not generally speak during debates, nor vote at
divisions.

The Speaker also exercises disciplinary powers. He or she may order any
member to resume his or her seat if they consistently contribute
irrelevant or repetitive remarks during a debate. An individual who has
disregarded the Speaker\'s call to sit down may be requested to leave
the House; if the request is declined, then the Speaker may \"name\" the
member. The House then votes on whether to suspend the member in
question for a certain number of days, or even, in the case of repeated
breaches, for the remainder of the session. In the most serious cases,
the House may vote to expel a member. In the case of grave disorder, the
Speaker may adjourn the House without a vote.

The House votes on all questions by voice first. The Speaker asks all
those in favour of the proposition to say \"Aye,\" and those opposed to
say \"No\". The Speaker then assesses the result, saying \"I think the
Ayes have it\" or \"I think the Noes have it\", as appropriate. Only if
a member challenges the Speaker\'s opinion is a *division*, or formal
count, called. During a division, members file into two separate lobbies
on either side of the Commons chamber. As they exit each lobby, clerks
and tellers count the votes and record the names. The result is then
announced by the Speaker. In the event of a tied vote, the Speaker (or
other occupant of the Chair) has a *casting vote*; however, conventions
exist that the Speaker would cast a vote to maintain the *status quo.*
In effect moving bills on to further scrutiny, but not pass a bill into
law.

## House of Lords

### Composition

Generally speaking, membership of the House of Lords is by appointment
for life. However, up until 1999, hereditary peers were also members of
the Lords; when this right was abolished, a compromise measure allowed
them to elect ninety of their number to continue as members.

Certain office-holders are also ex officio members of the House of
Lords:

-   the Earl Marshal
-   the Lord Great Chamberlain
-   the Archbishop of Canterbury
-   the Archbishop of York
-   the Bishops of London, Durham, and Winchester

The Earl Marshal and Lord Great Chamberlain are mostly ceremonial
offices. In addition to the three ex officio bishops, the 21
longest-serving diocesan bishops also sit in the Lords.

The general qualifications for sitting and voting in the Lords are:

-   to have reached the age of 21
-   to be a British citizen, or a citizen of the Republic of Ireland, or
    a citizen of a Commonwealth country
-   to not have been convicted of treason
-   to not have been declared insane

### Speakership and procedure

The *Lord Speaker* is elected by the House. Until recently his or her
duties were carried out by the Lord Chancellor, a Minister of the Crown.

In contrast with the Speaker of the House of Commons, the Lord Speaker
has a relatively minor role, since the House of Lords is generally
self-governing: the House itself decides upon points of order and other
such matters. The seat used by the Lord Speaker is known as *the
Woolsack*.

Similar to the House of Commons, the Lords also vote by voice first. The
Lord Speaker (or whoever else is presiding) puts the question, with
those in favour saying \"Content,\" and those opposed saying
\"Not-Content.\" If the Lord Speaker\'s assessment of the result is
challenged, a division follows, with members voting in the appropriate
lobby just as is done in the Commons. The officer presiding may vote
from his or her place in the chamber rather than from a lobby. In the
case of a tie, the result depends on what type of motion is before the
House. A motion that a bill be advanced to the next stage or passed is
always decided in the positive, while amendments to bills or other
motions are decided in the negative, if there is an equality of votes.

## Acts of Parliament

Legislation passed by Parliament is in the form of an *Act of
Parliament*.

A draft law is known as a *Bill*. A bill passes into law provided that
it has either been passed by both Houses of Parliament, or the
provisions of the Parliament Acts have been complied with; and provided
it has received the Royal Assent.

A bill must pass through several stages in both of the two Houses. A
bill is \"read\" three times in each House. The First Reading for Public
Bills is almost always a formality. The Second Reading is a debate on
the merits of the general principles behind the bill. Next follow the
Committee and Report stages. The Third Reading is a vote upon the bill
as a whole, as amended during the Committee and Report stages. Once the
House into which the bill was first introduced has finished with it, the
bill is then introduced into the other House. Any amendments by the
second House then have to be agreed to by the first before the bill can
proceed.

Bills are classified as either *Government Bills* or as *Private
Members\' Bills*. Ministers of the Crown introduce Government Bills;
private members introduce Private Members\' Bills.

Bills are also classified as *Public*, *Private*, *Personal* or
*Hybrid*. Public bills create laws applied generally (for instance,
reforming the nation\'s electoral system). Private bills affect a
specific named company, person or other entity (for instance,
authorising major constructions on specific named public lands).
Personal bills are private bills that confer specific rights to specific
named individuals (for example by granting the right to marry a person
one would not normally be allowed to wed). Hybrid bills are public bills
that directly and specially affect private interests.

### Public Bills

A Public Bill\'s First Reading is usually a mere formality, allowing its
title to be entered in the Journals and for its text to be printed by
the House\'s authority.

After two weeks, one of the bill\'s supporters moves \"that the bill be
now read a second time\". At the second reading debate, the bill\'s
general characteristics and underlying principles, rather than the
particulars, are discussed. If the vote on the Second Reading fails, the
bill dies. It is, however, very rare for a Government bill to be
defeated at the Second Reading; such a defeat signifies a major loss.

In the House of Commons, following the Second Reading, various
procedural resolutions may need to be passed. If the bill seeks to levy
or increase a tax or charge, then a *Ways and Means Resolution* has to
be passed. If it involves significant expenditure of public funds, then
a *Money Resolution* is necessary. Finally, the government may proceed
with a *Programme Motion* or an *Allocation of Time Motion*. A Programme
Motion outlines a timetable for further debate on the bill and is
normally passed without debate. An Allocation of Time Motion, commonly
called the *Guillotine*, limits time available for debate. Normally, a
Programme motion is agreed to by both parties while an Allocation of
Time Motion becomes necessary if the Opposition does not wish to
cooperate with the Government. In the House of Lords, there are no
Guillotines or other motions that limit the time available for debate.

Next, the bill can be committed to a committee. In the House of Commons,
the bill may be sent to the *Committee of the Whole House*, a *Standing
Committee*, a *Special Standing Committee* or a *Select Committee.* The
Committee of the Whole House is a committee that includes all members of
the House and meets in the regular chamber. The Speaker is normally not
present during the meetings; a Deputy Speaker normally takes the chair.
The procedure is used for parts of the annual Finance Bill and for bills
of major constitutional importance. More often, the bill is committed to
a Standing Committee. Though the name may suggest otherwise, the
membership of Standing Committees is temporary. There can be from
sixteen to fifty members; the strength of parties in the committee is
proportional to their strengths in the whole House. It is possible for a
bill to go to a Special Standing Committee, which is like a Standing
Committee except that it may take evidence and conduct hearings; the
procedure has not been used in several years. Finally, the bill may be
sent to a Select Committee. Select Committees are permanent bodies
charged with the oversight of a particular Government department. This
last procedure is rarely used; the quinquennial Armed Forces Bill,
however, is always referred to the Defence Select Committee.

In the House of Lords, the Bill is committed to the *Committee of the
Whole House*, a *Public Bill Committee*, a *Special Public Bill
Committee*, a *Select Committee* or a *Grand Committee*. The most common
committee used is the Committee of the Whole House. Sometimes, the bill
is sent to a Public Bill Committee of twelve to sixteen members (plus
the Chairman of Committees) or to a Special Public Bill Committee of
nine or ten members. These committees correspond in function to the
Commons Standing and Special Standing Committees, but are less often
utilised. Select Committees may also be used, like in the Commons,
though it is rare for this to be done. The Grand Committee procedure is
the only one unique to the House of Lords. The procedure is reserved for
non-controversial bills that must be passed quickly; a proposal to amend
the bill is defeated if a single member votes against it.

In both Houses, the committee used considers the bill clause-by-clause
and may make amendments. Thereafter, the bill proceeds to the
*Consideration* or *Report Stage*. This stage occurs on the Floor of the
House and offers it an opportunity to further amend the bill. While the
committee is bound to consider every single clause of the bill, the
House need only debate those clauses which members seek to amend.

Following the Report Stage, the motion *that the bill be now read a
third time* is considered. In the House of Commons, there is a short
debate followed by a vote; no further amendments are permitted. If the
motion passes, then the Bill is considered passed. In the Lords,
however, amendments may be moved. Following the vote on the third
reading, there must be a separate vote on passage.

After one House has passed a bill, it is sent to the other for its
consideration. Assuming both Houses have passed a bill, differences
between their separate versions must be reconciled. Each House may
accept or reject amendments made by the other House, or offer other
amendments in lieu. If one House has rejected an amendment, the other
House may nevertheless insist upon it. If a House insists upon an
amendment that the other rejects, then the bill is lost unless the
procedure set out in the Parliament Acts is complied with.

Once a bill has passed by both Houses, or has been certified by the
Speaker of the Commons as having passed the House of Commons in
conformity with the Parliament Acts, the bill is finally submitted to
the Sovereign for *Royal Assent*. Since 1708, no Sovereign has failed to
grant Royal Assent to a bill. Assent may be given by the Sovereign in
person, but is usually given in the form of letters patent read out in
each of the Houses; in the House of Lords the Clerk announces the Norman
French formula \"La Reyne le Veult\", and the Bill thereupon becomes an
Act of Parliament. In 1708 the formula used for the Scottish Militia
Bill was \"La Reyne s\'avisera\" (however, this was on ministerial
advice).

In theory the Sovereign has the right to either *withhold* or *reserve*
the assent, however this right is not exercised. If assent were
withheld, then the bill would fail. If assent were reserved, then
formally a final decision on the bill has been put off until a later
time; if Assent were not given before prorogation of the session, then
the bill would fail.

### Private, Personal and Hybrid Bills

In the nineteenth century several hundred private Acts were passed each
year, dealing with such matters as the alteration of local authority
powers, the setting up or alteration of turnpike trusts, etc. A series
of reforms has eliminated the necessity for much of this legislation,
meaning that only a handful of private Acts are now passed each year.

A private bill is initiated when an individual petitions Parliament for
its passage. After the petition is received, it is officially gazetted
so that other interested parties may support or contest it.
Counter-petitions objecting to the passage of the bill may also be
received. To be able to file such a petition, the bill must \"directly
and specially\" affect the individual. If those supporting the bill
disagree that such an effect exist, then the matter is resolved by the
*Court of Referees*, a group of senior Members of Parliament.

The bill then proceeds through the same stages as public bills.
Generally, no debate is held on the Floor during the Second Reading
unless a Member of Parliament files a \"blocking motion\". It is
possible for a party whose petition was denied by the Court of Referees
to instead lobby a Member to object to the bill on the Floor. After the
bill is read a second time, it is sent to one of two committees: the
*Opposed Bill Committee* if there are petitions against the bill, or the
*Unopposed Bill Committee* if there aren\'t. After taking evidence, the
committee may return a finding of *Case Proved* or *Case Not Proved*. In
the latter case, the bill is considered rejected, but in the former
case, amendments to the bill may be considered. After consideration,
third reading and passage, the bill is sent to the other House, which
follows the same procedure. If necessary, the bill may have to face two
different Opposed Bill Committees. After differences between the Houses
are resolved, the bill is submitted for Royal Assent.

Personal bills relate to the \"estate, property, status, or style\" or
other personal affairs of an individual. By convention, these bills are
brought first in the House of Lords, where it is referred to a Personal
Bill Committee before being read a \"first\" time. The Committee may
make amendments or even reject the bill outright. If the bill is
reported to the House, then it follows the same procedure as any other
private bill, including going through an Unopposed or Opposed Bill
Committee in both Houses. A special case involves bills that seek to
enable marriages between those who are within a \"prohibited degree of
affinity or cosanguinity\". In those cases, the bill is not discussed on
the Floor and is sent at the committee stage to a Select Committee that
includes the Chairman of Committees, a bishop and two lay members.

Hybrid bills are public bills that have a special effect on a private
interest. Prior to the second reading of any public bill, it must be
submitted to the Clerk, who determines if any of the House\'s rules have
been violated. If the Clerk finds that the bill does have such an effect
on a private interest, then it is sent to the *Examiners*, a body which
then may report to the House that the bill does or does not affect
private interests. If the latter, then it proceeds just like a public
bill, but if the former, then it is treated as hybrid. The first and
second readings are just as for public bills, but at the committee
stage, if petitions have been filed against the bill, it is sent to a
Select Committee, but the Committee does not have the same powers of
rejection as Private Bill Committees. After the Committee reports, the
bill is recommitted to another committee as if it were a public bill.
Thereafter, the stages are the same as for a public bill, though, in the
other chamber, the bill may have to be considered once more by a Select
Committee.

### Supremacy of the House of Commons

Under the Parliament Acts of 1911 and 1949, the House of Commons is
essentially the pre-eminent chamber in Parliament. If the Lords fail to
pass a bill (by rejecting it outright, insisting on amendments disagreed
to by the Commons, or by failing to vote on it), and the bill has been
passed by the Commons in two consecutive sessions, then the bill may be
presented for Royal Assent unless the House of Commons otherwise
directs, and provided that the bill was introduced in the Lords at least
one month before the end of each session. However, twelve months must
have passed between the Second Reading in the first session, and the
final vote on passage in the second one. Also, the bill passed by the
Commons in each session must be identical, except to take into account
the passage of time since the bill was first proposed.

The effect of the procedure set out in the Parliament Acts is that the
House of Lords may delay a bill for at least thirteen months, but would
ultimately be unable to overturn the concerted will of the House of
Commons. However, this procedure does not apply in the case of private
or personal bills, nor to bills seeking to extend the life of Parliament
beyond five years.

Under the Parliament Acts, a special procedure applies to \"money
bills\". A bill is considered a money bill if the Speaker certifies that
it relates solely to national taxation or to the expenditure of public
funds. The Speaker\'s decision is final and cannot be overturned.
Following passage by the House of Commons, the bill can be considered by
the House of Lords for not longer than one month. If the Lords have not
passed the bill within that time, it is submitted for Royal Assent
regardless. Any amendments made by the House of Lords are ignored unless
accepted by the House of Commons.

In addition to the Parliament Acts, tradition and conventions limit the
House of Lords. It is the privilege of the House of Commons to levy
taxes and authorise expenditure of public funds. The House of Lords
cannot introduce bills to do either; furthermore, they are barred from
amending supply bills (bills appropriating money to expenditure). In
some cases, however, the House of Lords can circumvent the rule by
inserting a *Privilege Amendment* into a bill they have originated. The
Amendment reads:

:   *Nothing in this Act shall impose any charge on the people or on
    public funds, or vary the amount or incidence of or otherwise alter
    any such charge in any manner, or affect the assessment, levying,
    administration or application of any money raised by any such
    charge.*

The House of Commons then amend the bill by removing the above clause.
Therefore, the privilege of the Commons is not violated as they, not the
Lords, have approved the tax or public expenditure.

## Delegated legislation

Many Acts of Parliament authorise the use of Statutory Instruments (SIs)
as a more flexible method of setting out and amending the precise
details for new arrangements, such as rules and regulations. This
delegated power is given either to the Queen in Council, a Minister of
the Crown, or to other named office holders. An Act may empower the
Government to make a Statutory Instrument and lay it before both Houses,
the SI to take legal effect if approved by a simple vote in each House;
or in other cases, if neither House objects within a set time. In
theory, Parliament does not lose control over such statutory instruments
when delegating the power to make them, while being saved the necessity
to debate and vote upon even quite trivial changes, unless members wish
to raise objections.

## English Votes For English Laws

During the creation of the Devolved Administrations of Scotland and
Wales, the idea of an English Parliament or Regional Assemblies were
discussed but ultimately not implemented. This created an issue where
the UK Parliament is acting as a *de facto* English Parliament on
matters devolved to the national assemblies. MPs from all regions were
free to debate and vote on issues which did not effect their
constituencies or constituents.

The Conservative Government of 2015 decided to address the issue in a
controversial manner. Instead of bringing a bill to the Parliament, they
proposed changes to the Statutory Instruments (SIs). Any bill brought
before the Commons which is adjudged by the Speaker to only effect
English Constituencies (or in some limited cases England and Wales) can
have a "double majority" rule imposed. In short, all MPs are allowed to
debate and vote, but for a vote to be won both a count of votes of all
MPs and a vote for English only MPs must be won.

## Privilege

Each House has a body of rights that it asserts, or which are conferred
by statute, with the aim of being allowed to carry out its duties
without interference. For example, members of both Houses have freedom
of speech during parliamentary debates; what they have said cannot be
questioned in any place outside Parliament, and so a speech made in
Parliament cannot constitute slander. These rights are collectively
referred to as *Parliamentary Privilege*.

Both Houses claim to determine their own privileges, and are
acknowledged by the courts as having the authority to control their own
proceedings, as well as to discipline members abusing the rules.
Furthermore, each House is the sole judge of the qualifications of its
members. Collectively, each House has the right of access to the
Sovereign. Individually, members must be left free to attend Parliament.
Therefore, the police are regularly ordered to maintain free access in
the neighbouring streets, and members cannot be called on to serve on a
jury or be subpoenaed as a witness while Parliament is in session.
(Arrest for crime is still possible, but the relevant House must be
notified of the same.) Parliament has the power to punish *contempt of
Parliament*, that is, violation of the privileges and rules of a House.
Any decisions made in this regard are final and are cannot be appealed
to any court. The usual modern penalty for contempt is a reprimand, or
brief imprisonment in the precincts of the House, but historically large
fines have been imposed.


# UK Constitution and Government/Government

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## Structure

*His Majesty\'s Government* is the executive political authority for the
United Kingdom as a whole. At its heart is the *Cabinet*, a grouping of
senior *Ministers of the Crown*, headed by the *Prime Minister*. Members
of the Government are political appointees, and are usually drawn from
one of the two Houses of Parliament. In addition to the heads of the
*Departments of State* (most of whom carry the title of *Secretary of
State*), the Government also includes *junior ministers* (who bear the
title of *Under Secretary of State*, *Minister of State*, or
*Parliamentary Secretary*), *whips* (responsible for enforcing party
discipline within the two Houses), and *Parliamentary Private
Secretaries* (political assistants to ministers).

When the Sovereign is the Queen, the Government is referred to as *Her*
Majesty\'s Government; likewise, when there are joint Sovereigns, the
Government is known as *Their Majesties*\' Government.

## Prime Minister

The Prime Minister (or \"PM\") is the head of the Government. Since the
early twentieth century the Prime Minister has held the office of *First
Lord of the Treasury*, and in recent decades has also held the office of
*Minister for the Civil Service*.

The Prime Minister is *asked to form a Government* by the Sovereign.
Usually this occurs after a general election has altered the balance of
party political power within the House of Commons. The Prime Minister is
expected to *have the confidence* of the House of Commons; this usually
means that he or she is the leader of the political party holding the
majority of the seats in the Commons. Since at least the 1920s the Prime
Minister himself is also expected to be a Member of Parliament (i.e.
member of the House of Commons). The Prime Minister retains office until
he or she dies or resigns, or until someone else is appointed; this
means that even when expecting to be defeated at a general election, the
Prime Minister remains formally in power until his or her rival is
returned as an MP and asked in turn to form a Government.

By law, if defeated by an actual Commons vote of \"no confidence\",
there is a period of 14 days during which an alternative Government may
be formed, if a \"vote of confidence\" can be won by a prospective Prime
Minister. If no Government can be formed within the 14 days an election
is automatically triggered, in effect allowing the electorate itself to
approve or disapprove of the Prime Minister\'s policy. The polling day
for the election is to be the day appointed by Her Majesty by
proclamation on the recommendation of the Prime Minister. The Parliament
then in existence dissolves at the beginning of the 17th working day
before the polling day.

The existence and basis of appointment of the office is a matter of
constitutional convention rather than of law. Because of this, there are
no formal qualifications for the office. However, a small number of Acts
of Parliament do make reference to the Prime Minister, and since the
1930s office has carried a salary in its own right.

The Prime Minister is often an extremely powerful figure within the
political system; the office has been said by some to be an \"elected
dictatorship\", and some Prime Ministers have been accused of being
\"presidential\". A weak Prime Minister may be forced out of office
(i.e. forced to resign) by his or her own party, particularly if there
is an alternative figure within the party seen as a better choice.

## Cabinet and other ministers

Membership of the Cabinet is not defined by law, and is only loosely
bound by convention. The Prime Minister and (if there is one) the Deputy
Prime Minister are always members, as are the three most senior
ministerial heads of Departments of State: the *Secretary of State for
Foreign and Commonwealth Affairs* (commonly known as the *Foreign
Secretary*), the *Chancellor of the Exchequer* (i.e. the minister
responsible for finance), and the *Secretary of State for the Home
Department* (commonly known as the *Home Secretary*). Most of the other
heads of departments are usually members of the Cabinet, as well as a
small number of junior ministers.

Ministers of the Crown are formally appointed by the Sovereign upon the
\"advice\" of the Prime Minister. Ministers are bound by the convention
of *collective responsibility*, by which they are expected to publicly
support or defend the policy of the Government, or else resign. They are
also bound by the less clearly defined convention of *individual
responsibility*, by which they are responsible to Parliament for the
acts of their department. Ministers are often called upon to resign who
either by their own actions, or by those of their department, are
perceived in some manner to have failed in their duty; however, it
usually takes sustained criticism over a period of time for both a
minister to feel compelled to resign, and for the Prime Minister to
accept that resignation. Occasionally a minister offers his or her
resignation, but the Prime Minister retains them in office.

Parliamentary Private Secretaries are also bound by the principle of
*collective responsibility*, even though they hold no ministerial
responsibility and take no part in the formation of policy; the position
is seen as an initial stepping-stone towards being offered ministerial
office.

## Privy Council

*His Majesty\'s Most Honourable Privy Council* is a ceremonial body of
advisors to the Sovereign. The Privy Council is used as a mechanism for
maintaining ministerial responsibility for the actions of the Crown; for
example, royal proclamations are approved by the Privy Council before
they are issued. All senior members of the Government are appointed to
be Privy Counsellors, as well as certain senior members of the Royal
Family, leaders of the main political parties, the archbishops and
senior bishops of the Church of England, and certain senior judges.

The Privy Council is headed by the *Lord President of the Council*, a
ministerial office usually held by a member of the Cabinet. By
convention the Lord President is also either the *Leader of the House of
Commons*, or the *Leader of the House of Lords*, with responsibility for
directing and negotiating the course of business in the respective
House.

Meetings of the Privy Council are usually extremely short, and are
rarely attended by more than a bare minimum of Privy Counsellors.


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## Structure

The United Kingdom is made up of three separate legal jurisdictions,
each with a separate laws and hierarchy of courts: *England and Wales*,
*Scotland*, and *Northern Ireland*.

## England and Wales

England and Wales is a *common law* jurisdiction.

### Lower courts

The lowest court in England and Wales is the *Magistrates\' Court*.
Magistrates, also known as Justices of the Peace, are laypersons
appointed by the Sovereign. The court hears \"summary\" offences
(punishable by six months or less in prison). When hearing such cases,
three magistrates sit together as a panel without a jury. In some
metropolitan areas, such as London, there are no magistrates; instead,
summary cases are tried by a single District Judge who is trained in
law.

Serious criminal cases are tried before a *Crown Court* with a judge and
a jury of twelve. The accused may also choose to have certain summary
offences referred from the magistrates\' court to the Crown Court, in
order for their case to be tried before a jury; the Crown Court also
hears appeals from magistrates\' courts. Though the Crown Court is
constituted as a single body for the whole of England and Wales, it sits
permanently at multiple places throughout its area of jurisdiction.

The counterpart to the Crown and Magistrates\' Courts in the civil
justice system is the *County Court*. There are over 200 County Courts
throughout England and Wales.

### High Court

The *High Court of England and Wales* takes appeals from the County
Court, and also has an original jurisdiction in certain matters.

The High Court is constituted into three *divisions*: the *Family
Division*, the *Chancery Division*, and the *Queen\'s Bench Division*.

The Family Division is presided over by the *President of the Family
Division*, and hears cases involving family matters such as matrimonial
breakdown, child custody and welfare, and adoption.

The Chancery Division is presided over by the *Chancellor of the High
Court* (formerly known as the *Vice-Chancellor*), and hears cases
involving land, companies, bankruptcy, and probate.

The Queen\'s Bench Division is presided over by the *President of the
Queen\'s Bench Division*, and hears cases involving torts (civil
wrongs). The Queen\'s Bench Division also includes four subordinate
courts: the *Admiralty Court* (dealing with shipping), the *Commercial
Court* (dealing with insurance, banking, and commerce), the *Technology
and Construction Court* (dealing with complex technological matters),
and the *Administrative Court* (exercising judicial review over the
actions of local government). The Queen\'s Bench Division also has
oversight of the lower courts.

## Court of Appeal

Above the High Court in civil cases, and the Crown Court in criminal
cases, is the Court of Appeal, headed by the *Master of the Rolls*, and
including 35 *Lords Justices of Appeal* as well as other judges.

The Court of Appeal is divided into a *Civil Division* (presided over by
the Master of the Rolls) and a *Criminal Division* (presided over by the
Lord Chief Justice). Generally speaking, appeals may only be heard \"by
leave\"; that is, with the permission of the either the Court of Appeal
or the judge whose decision is being contested. In some cases, it is
possible to \"leapfrog\" the High Court and bring a case directly from a
County Court.

Together, the Crown Court, the High Court, and Court of Appeal
constitute the *Senior Courts* (formerly known as the *Supreme Court of
Judicature*). Thus, since they are theoretically one body, it is
possible for judges of one court to sit in other courts. Appeals from
the Senior Courts go to the Supreme Court; it is also possible to
leapfrog from the High Court, but not from the Crown Court. Normally,
leave to appeal to the Supreme Court is not granted unless the case is
of great legal or constitutional importance.

## Northern Ireland

Northern Ireland\'s system is based on that used in England and Wales,
with a similar hierarchy of magistrates\' court, the Crown Court (for
criminal trials), county courts (for civil trials), the High Court, and
the Court of Appeal.

Appeals from Northern Ireland lie to the Supreme Court.

## Scotland

In contrast with the rest of the United Kingdom, Scotland uses a mixture
of common law and civil law. Its court system was developed
independently of that in England. The *Act of Union* (1707) guarantees
the continuance of Scotland\'s different legal system.

### Lower courts

Summary jurisdiction is exercised by *Justice of the Peace Courts*, held
either by three *Justices of the Peace* (lay magistrates) sitting
together, or by a Justice of the Peace sitting with a legally qualified
clerk. As in England and Wales, professional judges may sit in certain
metropolitan areas.

Above the Justice of the Peace Courts are the *Sheriff Courts*, of which
there are around 50. Sheriff Courts hear both criminal and civil cases,
and are held before a judge known as a Sheriff, and have a jury of
fifteen people. Sheriff Courts are grouped into six different
Sheriffdoms, headed by a Sheriff Principal who hears appeals from cases
not decided by a jury.

### High Court of Justiciary

The highest criminal court in Scotland is the *High Court of
Justiciary*. The judges of the court are also the judges of the Court of
Session (see below); as High Court judges they are known as *Lords
Commissioners of Justiciary*. The head of the court is the *Lord
Justice-General* (also the Lord President of the Court of Session), with
a deputy known as the *Lord Justice Clerk* (who holds the same office in
the Court of Session). Altogether the High Court has up to 32 individual
judges.

The High Court has exclusive jurisdiction in serious crimes, such as
murder or drug trafficking, in which case a single judge sits with a
jury of fifteen. The High Court also hears appeals from Justice of the
Peace Courts, and hears appeals in criminal cases from Sheriff Courts.

Appeals against decisions by a High Court judge in criminal cases are
heard by either two (in appeals against sentences) or three (in appeals
against conviction) High Court judges. No appeal lies beyond the High
Court.

### Court of Session

The highest civil court in Scotland is the *Court of Session*. Its
judges also sit as judges of the High Court of Justiciary (see above);
as Court of Session judges they are known as *Lords and Ladies of
Council and Session*, or *Senators of the College of Justice*. The Court
is headed by the *Lord President*, with a *Lord Justice Clerk* as
deputy. Altogether the Court of Session has up to 32 individual judges.

The Court of Session is divided into the *Outer House* (made up of
nineteen judges), and the *Inner House* (made up of the remaining
judges). The Outer House has original jurisdiction, while the Inner
House has appellate jurisdiction. The Inner House is further divided
into the First and Second Divisions, headed by the Lord President and
Lord Justice Clerk respectively. Sometimes, when many cases are before
the court, an Extra Division may be appointed. Each Division may sit as
a panel hearing an appeal from the Sheriff Court or from the Outer
House.

Appeals from the Court of Session lie to the Supreme Court.

## Supreme Court

The *Supreme Court of the United Kingdom* is the ultimate court of
appeal in all civil matters, as well as in criminal cases (other than
from Scotland), and also has original jurisdiction in devolution cases.

The Supreme Court has replaced the jurisdiction previously exercised by
the House of Lords in the latter\'s now-abolished judicial capacity. The
Supreme Court of the United Kingdom is not to be confused with the
Supreme Court of Judicature, the name formerly held by (a) the Senior
Courts, in England and Wales, and (b) the Court of Judicature, in
Northern Ireland.

The Supreme Court is headed by a President, who has a Deputy President.
There are a further ten *puisne* judges.

## Judicial Committee of the Privy Council

The *Judicial Committee of the Privy Council* formerly held original
jurisdiction in the United Kingdom in devolution cases, and continues to
hold appellate jurisdiction over the ecclesiastical courts of the Church
of England. Appeals to the Privy Council as a court of last resort also
lie from the Crown dependencies, the British overseas territories, and
from certain Commonwealth countries.

Membership of the Judicial Committee is made up of Justices of the
Supreme Court, Privy Counsellors who are or were Lord Justices of Appeal
in either England and Wales or Northern Ireland, members of the Inner
House of Scotland\'s Court of Session, and selected senior judges from
certain other Commonwealth countries. Members retire at the age of 75.

Appeals to *Her Majesty in Council* are referred to the Judicial
Committee, which formally reports to the Queen in Council, who in turn
formally confirms the report. By agreement, appeals from certain
Commonwealth countries lie directly to the Judicial Committee itself.

The Queen-in-Council also considers appeals from the disciplinary
committees of certain medical bodies such as the Royal College of
Surgeons. Also, cases against the Church Commissioners (who administer
the Church of England\'s property estates) may be considered. Appeals
may be heard from certain ecclesiastic courts (the Court of Arches in
Canterbury, and the Chancery Court in York) in cases that do not involve
Church doctrine. Appeals may also be heard from certain dormant courts,
including Prize Courts (which hear cases relating to the capture of
enemy ships at sea, and the ownership of property seized from captured
ships) and the Court of Admiralty of the Cinque Ports. Finally, the
Queen-in-Council determines if an individual is qualified to be elected
to the House of Commons under the House of Commons Disqualification Act.

## ECHR and ECJ

In addition to the above domestic courts, there are two further courts
which can be said to exercise a jurisdiction over the United Kingdom.

The *European Court of Human Rights* deals with cases concerning alleged
infringements of the *European Convention on Human Rights*.

The *European Court of Justice* deals with cases concerning alleged
infringements of European Union law.


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## Devolution

*Devolution* refers to the transfer of administrative, executive, or
legislative authority to new institutions operating only within a
defined part of the United Kingdom. Devolved institutions have been
created for Scotland, Northern Ireland, and Wales.

Devolution differs from federalism in formally being a unilateral
process that can be reversed at will; formal sovereignty is still
retained at the centre. Thus, while the US Congress cannot reduce the
powers of a state legislature, Parliament has the legal capacity to even
go so far as to abolish the devolved legislatures.

Devolution in Wales was originally restricted to the
executive/administrative sphere, whereas in Scotland and Northern
Ireland devolution extended to wide powers to pass laws.

## Scotland

The Scottish legislative authority is the Scottish Parliament. The
Scottish Parliament is a unicameral body composed of 129 members (called
Members of Scottish Parliament, or MSPs) elected for fixed four-year
terms. Each of 73 members is elected by a constituency. The remaining
are elected by eight regions, with each region electing seven members.
Each voter has one constituency vote---cast for a single
individual---and one regional vote---cast either for a party or for an
independent candidate. Regional members are allocated in such a way as
to permit a party\'s share of the regional vote to be proportional to
its share of seats in the Scottish Parliament.

The Scottish Government is the executive authority of Scotland; it is
led by the First Minister. Other members of the Scottish Cabinet are
generally given the title of Minister. The First Minister must retain
the confidence of the Scottish Parliament to remain in power.

Scotland has responsibility over several major areas, including
taxation, criminal justice, health, education, transport, the
environment, sport, culture and local government. The Parliament at
Westminster, however, retains authority over a certain number of
*reserved matters*. Reserved matters include foreign affairs, defence,
immigration, social security and welfare, employment, and general
economic and fiscal policy.

## Wales

The National Assembly for Wales is the Welsh legislative authority. It
is, like the Scottish Parliament, a unicameral body; it also uses a
similar electoral system. Forty of its sixty members are chosen from
single-member constituencies, while the remaining twenty are regional
members. (There are five regions.) The Welsh Government is led by the
First Minister and includes other Ministers, who must retain the
confidence of the Assembly.

The third Welsh Assembly can legislate using a system called \"Assembly
Measures\". This system is a lower form of Primary Legislation similar
to Acts of Parliament. They can be used to repeal laws, create provision
and amend laws. The difference with \"Assembly Measures\" and \"Acts of
the Assembly\" is that Measures do not have a bulk of powers with them,
each Measure will come with a LCO, or Legislative Competency Order,
which transfers powers from the UK Parliament to the Welsh Assembly
Government. Devolution in Wales has changed a lot since 1999.

In order for the National Assembly to have full legislative powers, they
will need to trigger a referendum through both the Assembly and both
houses of the United Kingdom parliament. Once done, Wales will for the
first time ever, will be able to legislate and make their own Acts. (To
be known as Acts of the Assembly, or Acts of the National Assembly for
Wales). In early 2011, a referendum held in Wales approved the transfer
of full legislative competence to the National Assembly in all devolved
matters.

## Northern Ireland

Northern Ireland was the first part of the United Kingdom to gain
devolution, in 1921. However, it has had a troubled history since then,
caused by conflict between the main *Unionist* and *Nationalist*
communities. Because of this historical background, the present system
of devolution requires power to be shared between political parties
representing the different communities, and there are complex procedural
checks in place to ensure cross-community support for legislation and
executive action.

The Northern Ireland Assembly comprises 108 members elected to represent
18 six-member constituencies.

The Executive (government) is made up of members from the largest
parties in the Assembly, with ministerial portfolios allocated in
proportion to party strengths. The Executive is headed jointly by a
First Minister and Deputy First Minister, who are jointly elected by the
Assembly.

The Assembly\'s legislative powers are broad, and are similar to those
of the Scottish Parliament (with the notable exception of taxation). The
transfer from the United Kingdom\'s central government of responsibility
for the criminal justice system has been highly contentious, and has
only recently been carried out.


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## General Elections

Members of the House of Commons are elected in General Elections.
General Elections are called by the Prime Minister. General Elections
are held at least once every five years. The maximum term that a
parliament can exist before a new election interrupts it is defined by
parliament. Currently, the Parliament Act
states that five years is the maximum length.

## Local Elections

From 2007 Scotland will use Single Transferable Vote to elect all of its
local councillors. England and Wales use first past the post or
multiple-member first past the post for local elections. Northern
Ireland uses STV for its local elections.

## European Elections

Members of the European Parliament for Northern Ireland are elected
using Single Transferable Vote (STV). MEPs for England, Scotland and
Wales are elected using the D\'Hondt method.

es:Sistema político del Reino
Unido/Elecciones
ms:Perlembagaan dan Kerajaan United Kingdom: Pilihan
raya


# Control Systems/Introduction

## This Wikibook

This book was written at **Wikibooks**, a free online community where
people write open-content textbooks. Any person with internet access is
welcome to participate in the creation and improvement of this book.
Because this book is continuously evolving, there are no finite
\"versions\" or \"editions\" of this book. Permanent links to known good
versions of the pages may be provided.

## What are Control Systems?

The study and design of automatic **Control Systems**, a field known as
**control engineering,** has become important in modern technical
society. From devices as simple as a toaster or a toilet, to complex
machines like space shuttles and power steering, control engineering is
a part of our everyday life. This book introduces the field of control
engineering and explores some of the more advanced topics in the field.
Note, however, that control engineering is a very large field and this
book serves only as a foundation of control engineering and an
introduction to selected advanced topics in the field. Topics in this
book are added at the discretion of the authors and represent the
available expertise of our contributors.

Control systems are components that are added to other components to
increase functionality or meet a set of design criteria. For example:

This simple example can be complex to both users and designers of the
motor system. It may seem obvious that the motor should start at a
higher voltage so that it accelerates faster. Then we can reduce the
supply back down to 10 volts once it reaches ideal speed.

This is clearly a simplistic example but it illustrates an important
point: we can add special \"Controller units\" to preexisting systems to
improve performance and meet new system specifications.

Here are some formal definitions of terms used throughout this book:

There are essentially two methods to approach the problem of designing a
new control system: the **Classical Approach** and the **Modern
Approach**.

## Classical and Modern

**Classical** and **Modern** control methodologies are named in a
misleading way, because the group of techniques called \"Classical\"
were actually developed later than the techniques labeled \"Modern\".
However, in terms of developing control systems, Modern methods have
been used to great effect more recently, while the Classical methods
have been gradually falling out of favor. Most recently, it has been
shown that Classical and Modern methods can be combined to highlight
their respective strengths and weaknesses.

Classical Methods, which this book will consider first, are methods
involving the **Laplace Transform domain**. Physical systems are modeled
in the so-called \"time domain\", where the response of a given system
is a function of the various inputs, the previous system values, and
time. As time progresses, the state of the system and its response
change. However, time-domain models for systems are frequently modeled
using high-order differential equations which can become impossibly
difficult for humans to solve and some of which can even become
impossible for modern computer systems to solve efficiently. To
counteract this problem, integral transforms, such as the **Laplace
Transform** and the **Fourier Transform**, can be employed to change an
Ordinary Differential Equation (ODE) in the time domain into a regular
algebraic polynomial in the transform domain. Once a given system has
been converted into the transform domain it can be manipulated with
greater ease and analyzed quickly by humans and computers alike.

Modern Control Methods, instead of changing domains to avoid the
complexities of time-domain ODE mathematics, converts the differential
equations into a system of lower-order time domain equations called
**State Equations**, which can then be manipulated using techniques from
linear algebra. This book will consider Modern Methods second.

A third distinction that is frequently made in the realm of control
systems is to divide analog methods (classical and modern, described
above) from digital methods. Digital Control Methods were designed to
try and incorporate the emerging power of computer systems into previous
control methodologies. A special transform, known as the
**Z-Transform**, was developed that can adequately describe digital
systems, but at the same time can be converted (with some effort) into
the Laplace domain. Once in the Laplace domain, the digital system can
be manipulated and analyzed in a very similar manner to Classical analog
systems. For this reason, this book will not make a hard and fast
distinction between Analog and Digital systems, and instead will attempt
to study both paradigms in parallel.

## Who is This Book For?

This book is intended to accompany a course of study in under-graduate
and graduate engineering. As has been mentioned previously, this book is
not focused on any particular discipline within engineering, however any
person who wants to make use of this material should have some basic
background in the Laplace transform (if not other transforms), calculus,
etc. The material in this book may be used to accompany several
semesters of study, depending on the program of your particular college
or university. The study of control systems is generally a topic that is
reserved for students in their 3rd or 4th year of a 4 year undergraduate
program, because it requires so much previous information. Some of the
more advanced topics may not be covered until later in a graduate
program.

Many colleges and universities only offer one or two classes
specifically about control systems at the undergraduate level. Some
universities, however, do offer more than that, depending on how the
material is broken up, and how much depth that is to be covered. Also,
many institutions will offer a handful of graduate-level courses on the
subject. This book will attempt to cover the topic of control systems
from both a graduate and undergraduate level, with the advanced topics
built on the basic topics in a way that is intuitive. As such, students
should be able to begin reading this book in any place that seems an
appropriate starting point, and should be able to finish reading where
further information is no longer needed.

## What are the Prerequisites?

Understanding of the material in this book will require a solid
mathematical foundation. This book does not currently explain, nor will
it ever try to fully explain most of the necessary mathematical tools
used in this text. For that reason, the reader is expected to have read
the following wikibooks, or have background knowledge comparable to
them:

Algebra\
Calculus
:   The reader should have a good understanding of differentiation and
    integration. Partial differentiation, multiple integration, and
    functions of multiple variables will be used occasionally, but the
    students are not necessarily required to know those subjects well.
    These advanced calculus topics could better be treated as a
    co-requisite instead of a pre-requisite.

Linear Algebra
:   State-space system representation draws heavily on linear algebra
    techniques. Students should know how to operate on matrices.
    Students should understand basic matrix operations (addition,
    multiplication, determinant, inverse, transpose). Students would
    also benefit from a prior understanding of Eigenvalues and
    Eigenvectors, but those subjects are covered in this text.

Ordinary Differential Equations
:   All linear systems can be described by a linear ordinary
    differential equation. It is beneficial, therefore, for students to
    understand these equations. Much of this book describes methods to
    analyze these equations. Students should know what a differential
    equation is, and they should also know how to find the general
    solutions of first and second order ODEs.

Engineering Analysis
:   This book reinforces many of the advanced mathematical concepts used
    in the Engineering Analysis book,
    and we will refer to the relevant sections in the aforementioned
    text for further information on some subjects. This is essentially a
    math book, but with a focus on various engineering applications. It
    relies on a previous knowledge of the other math books in this list.

Signals and Systems
:   The Signals and Systems book will
    provide a basis in the field of **systems theory**, of which control
    systems is a subset. Readers who have not read the Signals and
    Systems book will be at a severe
    disadvantage when reading this book.

## How is this Book Organized?

This book will be organized following a particular progression. First
this book will discuss the basics of system theory, and it will offer a
brief refresher on integral transforms. Section 2 will contain a brief
primer on digital information, for students who are not necessarily
familiar with them. This is done so that digital and analog signals can
be considered in parallel throughout the rest of the book. Next, this
book will introduce the state-space method of system description and
control. After section 3, topics in the book will use state-space and
transform methods interchangeably (and occasionally simultaneously). It
is important, therefore, that these three chapters be well read and
understood before venturing into the later parts of the book.

After the \"basic\" sections of the book, we will delve into specific
methods of analyzing and designing control systems. First we will
discuss Laplace-domain stability analysis techniques (Routh-Hurwitz,
root-locus), and then frequency methods (Nyquist Criteria, Bode Plots).
After the classical methods are discussed, this book will then discuss
Modern methods of stability analysis. Finally, a number of advanced
topics will be touched upon, depending on the knowledge level of the
various contributors.

As the subject matter of this book expands, so too will the
prerequisites. For instance, when this book is expanded to cover
**nonlinear systems**, a basic background knowledge of nonlinear
mathematics will be required.

### Versions

This wikibook has been expanded to include multiple
versions of its text,
differentiated by the material covered, and the order in which the
material is presented. Each different version is composed of the
chapters of this book, included in a different order. This book covers a
wide range of information, so if you don\'t need all the information
that this book has to offer, perhaps one of the other versions would be
right for you and your educational needs.

Each separate version has a table of contents outlining the different
chapters that are included in that version. Also, each separate version
comes complete with a printable version, and some even come with PDF
versions as well.

Take a look at the **All Versions Listing
Page** to find the version of
the book that is right for you and your needs.

## Differential Equations Review

Implicit in the study of control systems is the underlying use of
differential equations. Even if they aren\'t visible on the surface, all
of the continuous-time systems that we will be looking at are described
in the time domain by ordinary differential equations (ODE), some of
which are relatively high-order.

Differential equations are particularly difficult to manipulate,
especially once we get to higher-orders of equations. Luckily, several
methods of abstraction have been created that allow us to work with
ODEs, but at the same time, not have to worry about the complexities of
them. The classical method, as described above, uses the Laplace,
Fourier, and Z Transforms to convert ODEs in the time domain into
polynomials in a complex domain. These complex polynomials are
significantly easier to solve than the ODE counterparts. The Modern
method instead breaks differential equations into systems of low-order
equations, and expresses this system in terms of matrices. It is a
common precept in ODE theory that an ODE of order N can be broken down
into N equations of order 1.

Readers who are unfamiliar with differential equations might be able to
read and understand the material in this book reasonably well. However,
all readers are encouraged to read the related sections in
**Calculus**.

## History

The field of control systems started essentially in the ancient world.
Early civilizations, notably the Greeks and the Arabs were heavily
preoccupied with the accurate measurement of time, the result of which
were several \"water clocks\" that were designed and implemented.

However, there was very little in the way of actual progress made in the
field of engineering until the beginning of the renaissance in Europe.
Leonhard Euler (for whom **Euler\'s Formula** is named) discovered a
powerful integral transform, but Pierre-Simon Laplace used the transform
(later called the **Laplace Transform**) to solve complex problems in
probability theory.

Joseph Fourier was a court mathematician in France under Napoleon I. He
created a special function decomposition called the **Fourier Series**,
that was later generalized into an integral transform, and named in his
honor (the **Fourier Transform**). {{-}}

+----------------------------------+----------------------------------+
| ![](Pierre-Simon-Laplace_(174    | ![](Joseph_Fourier.jpg "J        |
| 9-1827).jpg "Pierre-Simon-Laplac | oseph_Fourier.jpg"){width="150"} |
| e_(1749-1827).jpg"){width="150"} |                                  |
+----------------------------------+----------------------------------+
| Pierre-Simon Laplace\            | Joseph Fourier\                  |
| 1749-1827                        | 1768-1840                        |
+----------------------------------+----------------------------------+

The \"golden age\" of control engineering occurred between 1910-1945,
where mass communication methods were being created and two world wars
were being fought. During this period, some of the most famous names in
controls engineering were doing their work: Nyquist and Bode.

**Hendrik Wade Bode** and **Harry Nyquist**, especially in the 1930\'s
while working with Bell Laboratories, created the bulk of what we now
call \"Classical Control Methods\". These methods were based off the
results of the Laplace and Fourier Transforms, which had been previously
known, but were made popular by **Oliver Heaviside** around the turn of
the century. Previous to Heaviside, the transforms were not widely used,
nor respected mathematical tools.

Bode is credited with the \"discovery\" of the closed-loop feedback
system, and the logarithmic plotting technique that still bears his name
(**bode plots**). Harry Nyquist did extensive research in the field of
system stability and information theory. He created a powerful stability
criteria that has been named for him (**The Nyquist Criteria**).

Modern control methods were introduced in the early 1950\'s, as a way to
bypass some of the shortcomings of the classical methods. **Rudolf
Kalman** is famous for his work in modern control theory, and an
adaptive controller called the **Kalman Filter** was named in his honor.
Modern control methods became increasingly popular after 1957 with the
invention of the computer, and the start of the space program. Computers
created the need for digital control methodologies, and the space
program required the creation of some \"advanced\" control techniques,
such as \"optimal control\", \"robust control\", and \"nonlinear
control\". These last subjects, and several more, are still active areas
of study among research engineers. {{-}}

## Branches of Control Engineering

Here we are going to give a brief listing of the various different
methodologies within the sphere of control engineering. Oftentimes, the
lines between these methodologies are blurred, or even erased
completely.

Classical Controls:Control methodologies where the ODEs that describe a system are transformed using the Laplace, Fourier, or Z Transforms, and manipulated in the transform domain.\
Modern Controls:Methods where high-order differential equations are broken into a system of first-order equations. The input, output, and internal states of the system are described by vectors called \"state variables\".\
Robust Control:Control methodologies where arbitrary outside noise/disturbances are accounted for, as well as internal inaccuracies caused by the heat of the system itself, and the environment.\
Optimal Control:In a system, performance metrics are identified, and arranged into a \"cost function\". The cost function is minimized to create an operational system with the lowest cost.\
Adaptive Control:In adaptive control, the control changes its response characteristics over time to better control the system.\
Nonlinear Control:The youngest branch of control engineering, nonlinear control encompasses systems that cannot be described by linear equations or ODEs, and for which there is often very little supporting theory available.\
Game Theory:Game Theory is a close relative of control theory, and especially robust control and optimal control theories. In game theory, the external disturbances are not considered to be random noise processes, but instead are considered to be \"opponents\". Each player has a cost function that they attempt to minimize, and that their opponents attempt to maximize.

This book will definitely cover the first two branches, and will
hopefully be expanded to cover some of the later branches, if time
allows.

## MATLAB

**MATLAB** ® is a programming tool that is commonly used in the field of
control engineering. We will discuss MATLAB in specific sections of this
book devoted to that purpose. MATLAB will not appear in discussions
outside these specific sections, although MATLAB may be used in some
example problems. An overview of the use of MATLAB in control
engineering can be found in the **appendix** at: Control
Systems/MATLAB.

For more information on MATLAB in general, see: MATLAB
Programming.

Nearly all textbooks on the subject of control systems, linear systems,
and system analysis will use MATLAB as an integral part of the text.
Students who are learning this subject at an accredited university will
certainly have seen this material in their textbooks, and are likely to
have had MATLAB work as part of their classes. It is from this
perspective that the MATLAB appendix is written.

In the future, this book may be expanded to include information on
**Simulink** ®, as well as MATLAB.

There are a number of other software tools that are useful in the
analysis and design of control systems. Additional information can be
added in the appendix of this book, depending on the experience and
prior knowledge of contributors.

## About Formatting

This book will use some simple conventions throughout.

### Mathematical Conventions

Mathematical equations will be labeled with the
template, to give them names. Equations that are labeled in such a
manner are important, and should be taken special note of. For instance,
notice the label to the right of this equation:

$$f(t)
        = \mathcal{L}^{-1} \left\{F(s)\right\}
        = {1 \over {2\pi i}}\int_{c-i\infty}^{c+i\infty} e^{st} F(s)\,ds$$

Equations that are named in this manner will also be copied into the
List of Equations
Glossary in the end of
the book, for an easy reference.

Italics will be used for English variables, functions, and equations
that appear in the main text. For example *e*, *j*, *f(t)* and *X(s)*
are all italicized. Wikibooks contains a LaTeX mathematics formatting
engine, although an attempt will be made not to employ formatted
mathematical equations inline with other text because of the difference
in size and font. Greek letters, and other non-English characters will
not be italicized in the text unless they appear in the midst of
multiple variables which are italicized (as a convenience to the
editor).

Scalar time-domain functions and variables will be denoted with
lower-case letters, along with a *t* in parenthesis, such as: *x(t)*,
*y(t)*, and *h(t)*. Discrete-time functions will be written in a similar
manner, except with an *\[n\]* instead of a *(t)*.

Fourier, Laplace, Z, and Star transformed functions will be denoted with
capital letters followed by the appropriate variable in parenthesis. For
example: *F(s)*, *X(jω)*, *Y(z)*, and *F\*(s)*.

Matrices will be denoted with capital letters. Matrices which are
functions of time will be denoted with a capital letter followed by a
*t* in parenthesis. For example: *A(t)* is a matrix, *a(t)* is a scalar
function of time.

Transforms of time-variant matrices will be displayed in uppercase bold
letters, such as **H***(s)*.

Math equations rendered using LaTeX will appear on separate lines, and
will be indented from the rest of the text.

### Text Conventions


# Control Systems/System Identification

## Systems

Systems, in one sense, are devices that take input and produce an
output. A system can be thought to **operate** on the input to produce
the output. The output is related to the input by a certain relationship
known as the **system response**. The system response usually can be
modeled with a mathematical relationship between the system input and
the system output.

## System Properties

Physical systems can be divided up into a number of different
categories, depending on particular properties that the system exhibits.
Some of these system classifications are very easy to work with and have
a large theory base for analysis. Some system classifications are very
complex and have still not been investigated with any degree of success.
By properly identifying the properties of a system, certain analysis and
design tools can be selected for use with the system.

The early sections of this book will focus primarily on **linear
time-invariant** (LTI) systems. LTI systems are the easiest class of
system to work with, and have a number of properties that make them
ideal to study. This chapter discusses some properties of systems.

Later chapters in this book will look at time variant systems and
nonlinear systems. Both time variant and nonlinear systems are very
complex areas of current research, and both can be difficult to analyze
properly. Unfortunately, most physical real-world systems are
time-variant, nonlinear, or both.

An introduction to system identification and least squares techniques
can be found
here.
An introduction to parameter identification techniques can be found
here.

## Initial Time

The **initial time** of a system is the time before which there is no
input. Typically, the initial time of a system is defined to be zero,
which will simplify the analysis significantly. Some techniques, such as
the **Laplace Transform** require that the initial time of the system be
zero. The initial time of a system is typically denoted by t~0~.

The value of any variable at the initial time t~0~ will be denoted with
a 0 subscript. For instance, the value of variable x at time t~0~ is
given by:

$$x(t_0) = x_0$$

Likewise, any time t with a positive subscript are points in time *after
t~0~*, in ascending order:

$$t_0 \le t_1 \le t_2 \le \cdots \le t_n$$

So t~1~ occurs after t~0~, and t~2~ occurs after both points. In a
similar fashion above, a variable with a positive subscript (unless
specifying an index into a vector) also occurs at that point in time:

$$x(t_1) = x_1$$

$$x(t_2) = x_2$$

This is valid for all points in time t.

## Additivity

A system satisfies the property of **additivity** if a sum of inputs
results in a sum of outputs. By definition: an input of
$x_3(t) = x_1(t) + x_2(t)$ results in an output of
$y_3(t) = y_1(t) + y_2(t)$. To determine whether a system is additive,
use the following test:

Given a system f that takes an input x and outputs a value y, assume two
inputs (x~1~ and x~2~) produce two outputs:

$$y_1 = f(x_1)$$

$$y_2 = f(x_2)$$

Now, create a composite input that is the sum of the previous inputs:

$$x_3 = x_1 + x_2$$ Then the system is additive if the following
equation is true:

$$y_3 = f(x_3) = f(x_1 + x_2) = f(x_1) + f(x_2) = y_1 + y_2$$

Systems that satisfy this property are called **additive**. Additive
systems are useful because a sum of simple inputs can be used to analyze
the system response to a more complex input.

### Example: Sinusoids

## Homogeneity

A system satisfies the condition of **homogeneity** if an input scaled
by a certain factor produces an output scaled by that same factor. By
definition: an input of $ax_1$ results in an output of $ay_1$. In other
words, to see if function *f()* is **homogeneous**, perform the
following test:

Stimulate the system *f* with an arbitrary input *x* to produce an
output *y*:

$$y = f(x)$$

Now, create a second input *x~1~*, scale it by a multiplicative factor
*C* (*C* is an arbitrary constant value), and produce a corresponding
output *y~1~*:

$$y_1 = f(Cx_1)$$

Now, assign x to be equal to *x~1~*:

$$x_1 = x$$

Then, for the system to be homogeneous, the following equation must be
true:

$$y_1 = f(Cx) = Cf(x) = Cy$$

Systems that are homogeneous are useful in many applications, especially
applications with gain or amplification.

### Example: Straight-Line

## Linearity

A system is considered **linear** if it satisfies the conditions of
Additivity and Homogeneity. In short, a system is linear if the
following is true:

Take two arbitrary inputs, and produce two arbitrary outputs:

$$y_1 = f(x_1)$$

$$y_2 = f(x_2)$$

Now, a linear combination of the inputs should produce a linear
combination of the outputs:

$$f(Ax_1 + Bx_2) = f(Ax_1) + f(Bx_2) = Af(x_1) + Bf(x_2) = Ay_1 + By_2$$

This condition of additivity and homogeneity is called
**superposition**. A system is linear if it satisfies the condition of
superposition.

### Example: Linear Differential Equations

## Memory

A system is said to have **memory** if the output from the system is
dependent on past inputs (or future inputs!) to the system. A system is
called **memoryless** if the output is only dependent on the current
input. Memoryless systems are easier to work with, but systems with
memory are more common in digital signal processing applications.

Systems that have memory are called **dynamic** systems, and systems
that do not have memory are **static** systems.

## Causality

Causality is a property that is very similar to memory. A system is
called **causal** if it is only dependent on past and/or current inputs.
A system is called **anti-causal** if the output of the system is
dependent only on future inputs. A system is called **non-causal** if
the output depends on past and/or current and future inputs.

## Time-Invariance

A system is called **time-invariant** if the system relationship between
the input and output signals is not dependent on the passage of time. If
the input signal $x(t)$ produces an output $y(t)$ then any time shifted
input, $x(t + \delta)$, results in a time-shifted output $y(t + \delta)$
This property can be satisfied if the transfer function of the system is
not a function of time except expressed by the input and output. If a
system is time-invariant then the system block is commutative with an
arbitrary delay. This facet of time-invariant systems will be discussed
later.

To determine if a system f is time-invariant, perform the following
test:

Apply an arbitrary input x to a system and produce an arbitrary output
y:

$$y(t) = f(x(t))$$

Apply a second input x~1~ to the system, and produce a second output:

$$y_1(t) = f(x_1(t))$$

Now, assign x~1~ to be equal to the first input x, time-shifted by a
given constant value δ:

$$x_1(t) = x(t - \delta)$$

Finally, a system is time-invariant if y~1~ is equal to y shifted by the
same value δ:

$$y_1(t) = y(t - \delta)$$

## LTI Systems

A system is considered to be a **Linear Time-Invariant** (LTI) system if
it satisfies the requirements of time-invariance and linearity. LTI
systems are one of the most important types of systems, and they will be
considered almost exclusively in the beginning chapters of this book.

Systems which are not LTI are more common in practice, but are much more
difficult to analyze.

## Lumpedness

A system is said to be **lumped** if one of the two following conditions
are satisfied:

1.  There are a finite number of states that the system can be in.
2.  There are a finite number of state variables.

The concept of \"states\" and \"state variables\" are relatively
advanced, and they will be discussed in more detail in the discussion
about **modern controls**.

Systems which are not lumped are called **distributed**. A simple
example of a distributed system is a system with delay, that is,
$A(s)y(t)=B(s)u(t-\tau)$, which has an infinite number of state
variables (Here we use $s$ to denote the Laplace variable). However,
although distributed systems are quite common, they are very difficult
to analyze in practice, and there are few tools available to work with
such systems. Fortunately, in most cases, a delay can be sufficiently
modeled with the Pade approximation. This book will not discuss
distributed systems much.

## Relaxed

A system is said to be **relaxed** if the system is causal and at the
initial time t~0~ the output of the system is zero, i.e., there is no
stored energy in the system. The output is excited solely and uniquely
by input applied thereafter.

$$y(t_0) = f(x(t_0)) = 0$$

In terms of differential equations, a relaxed system is said to have
\"zero initial states\". Systems without an initial state are easier to
work with, but systems that are not relaxed can frequently be modified
to approximate relaxed systems.

## Stability

**Stability** is a very important concept in systems, but it is also one
of the hardest function properties to prove. There are several different
criteria for system stability, but the most common requirement is that
the system must produce a finite output when subjected to a finite
input. For instance, if 5 volts is applied to the input terminals of a
given circuit, it would be best if the circuit output didn\'t approach
infinity, and the circuit itself didn\'t melt or explode. This type of
stability is often known as \"**Bounded Input, Bounded Output**\"
stability, or **BIBO**.

There are a number of other types of stability, most of which are based
on the concept of BIBO stability. Because stability is such an important
and complicated topic, an entire section of this text is devoted to its
study.

## Inputs and Outputs

Systems can also be categorized by the number of inputs and the number
of outputs the system has. Consider a television as a system, for
instance. The system has two inputs: the power wire and the signal
cable. It has one output: the video display. A system with one input and
one output is called **single-input, single output**, or SISO. a system
with multiple inputs and multiple outputs is called **multi-input,
multi-output**, or MIMO.

These systems will be discussed in more detail later.


# Control Systems/Digital and Analog

## Digital and Analog

There is a significant distinction between an **analog system** and a
**digital system**, in the same way that there is a significant
difference between analog and digital data. This book is going to
consider both analog and digital topics, so it is worth taking some time
to discuss the differences, and to display the different notations that
will be used with each.

### Continuous Time

A signal is called **continuous-time** if it is defined at every time t.

A system is a continuous-time system if it takes a continuous-time input
signal, and outputs a continuous-time output signal. Here is an example
of an analog waveform:

{{-}}

![](Analog_Waveform.svg "Analog_Waveform.svg"){width="400"}

### Discrete Time

A signal is called **discrete-time** if it is only defined for
particular points in time. A discrete-time system takes discrete-time
input signals, and produces discrete-time output signals. The following
image shows the difference between an analog waveform and the sampled
discrete time equivalent: {{-}}

![](Sampled_Waveform.svg "Sampled_Waveform.svg"){width="400"}

### Quantized

A signal is called **Quantized** if it can only be certain values, and
cannot be other values. This concept is best illustrated with examples:

1.  Students with a strong background in physics will recognize this
    concept as being the root word in \"Quantum Mechanics\". In quantum
    mechanics, it is known that energy comes only in discrete packets.
    An electron bound to an atom, for example, may occupy one of several
    discrete energy levels, but not intermediate levels.
2.  Another common example is population statistics. For instance, a
    common statistic is that a household in a particular country may
    have an average of \"3.5 children\", or some other fractional
    number. Actual households may have 3 children, or they may have 4
    children, but no household has 3.5 children.
3.  People with a computer science background will recognize that
    integer variables are quantized because they can only hold certain
    integer values, not fractions or decimal points.

The last example concerning computers is the most relevant, because
quantized systems are frequently computer-based. Systems that are
implemented with computer software and hardware will typically be
quantized.

Here is an example waveform of a quantized signal. Notice how the
magnitude of the wave can only take certain values, and that creates a
step-like appearance. This image is discrete in magnitude, but is
continuous in time:

![](Quantized_Waveform.svg "Quantized_Waveform.svg"){width="400"}

## Analog

By definition:

An analog system is a system that represents data using a direct
conversion from one form to another. In other words, an analog system is
a system that is continuous in both time and magnitude.

### Example: Motor

### Example: Analog Clock

## Digital

Digital data is represented by discrete number values. By definition:

Digital data always have a certain granularity, and therefore there will
almost always be an error associated with using such data, especially if
we want to account for all real numbers. The tradeoff, of course, to
using a digital system is that our powerful computers with our powerful,
Moore\'s law microprocessor units, can be instructed to operate on
digital data only. This benefit more than makes up for the shortcomings
of a digital representation system.

Discrete systems will be denoted inside square brackets, as is a common
notation in texts that deal with discrete values. For instance, we can
denote a discrete data set of ascending numbers, starting at 1, with the
following notation:

:   x\[n\] = \[1 2 3 4 5 6 \...\]

**n**, or other letters from the central area of the alphabet (m, i, j,
k, l, for instance) are commonly used to denote discrete time values.
Analog, or \"non-discrete\" values are denoted in regular expression
syntax, using parenthesis. Here is an example of an analog waveform and
the digital equivalent. Notice that the digital waveform is discrete in
both time and magnitude:

+----------------------------------+----------------------------------+
| ![](Analog_Waveform.svg "An      | ![](Digital_Waveform.svg "Dig    |
| alog_Waveform.svg"){width="400"} | ital_Waveform.svg"){width="400"} |
+----------------------------------+----------------------------------+
| ```{=html}                       | ```{=html}                       |
| <center>                         | <center>                         |
| ```                              | ```                              |
| **Analog Waveform**              | **Digital Waveform**             |
|                                  |                                  |
| ```{=html}                       | ```{=html}                       |
| </center>                        | </center>                        |
| ```                              | ```                              |
+----------------------------------+----------------------------------+

### Example: Digital Clock

:   {\| class=\"wikitable\"

!Minute !! Binary Representation \|- \|1 \|\| 1 \|- \|10 \|\| 1010 \|-
\|30 \|\| 11110 \|- \|59 \|\| 111011 \|}

## Hybrid Systems

**Hybrid Systems** are systems that have both analog and digital
components. Devices called **samplers** are used to convert analog
signals into digital signals, and Devices called **reconstructors** are
used to convert digital signals into analog signals. Because of the use
of samplers, hybrid systems are frequently called **sampled-data
systems**.

### Example: Automobile Computer

## Continuous and Discrete

A system is considered **continuous-time** if the signal exists for all
time. Frequently, the terms \"analog\" and \"continuous\" will be used
interchangeably, although they are not strictly the same.

Discrete systems can come in three flavors:

1.  Discrete time (sampled)
2.  Discrete magnitude (quantized)
3.  Discrete time and magnitude (digital)

**Discrete magnitude** systems are systems where the signal value can
only have certain values.**Discrete time** systems are systems where
signals are only available (or valid) at particular times. Computer
systems are discrete in the sense of (3), in that data is only read at
specific discrete time intervals, and the data can have only a limited
number of discrete values.

A discrete-time system has a **sampling time** value associated with it,
such that each discrete value occurs at multiples of the given sampling
time. We will denote the sampling time of a system as T. We can equate
the square-brackets notation of a system with the continuous definition
of the system as follows:

$$x[n] = x(nT)$$

Notice that the two notations show the same thing, but the first one is
typically easier to write, *and* it shows that the system in question is
a discrete system. This book will use the square brackets to denote
discrete systems by the sample number n, and parenthesis to denote
continuous time functions.

## Sampling and Reconstruction

The process of converting analog information into digital data is called
\"Sampling\". The process of converting digital data into an analog
signal is called \"Reconstruction\". We will talk about both processes
in a later chapter. For more information on the topic than is available
in this book, see the Analog and Digital
Conversion wikibook. Here is
an example of a reconstructed waveform. Notice that the reconstructed
waveform here is quantized because it is constructed from a digital
signal:

![](Reconstructed_Waveform.svg "Reconstructed_Waveform.svg"){width="400"}