this lectures on open-loop versus closed-loop control systems
control system as a mechanism that alters the future behavior
or state of assistant
now in order to be considered a control system
and not simply change the state system
the behavior or the outcome must tend towards the state that is desired
control theory is a branch of mathematics that is concerned with the
strategy to select the appropriate input
or were to put it another way
it deals with
howell
to go about generating that outcome
without control theory
the designer is relegated to selecting appropriate actions to trial and error
naal control systems have to basic parts
the system to be controlled usually called the plant
and input into the plant
the input acts on the planet which responds overtime to produce a system
output
this type of control system is called in open-loop system
because the input does not depend on the system output
open-loop control systems are typically reserved for simple processes that have
well-defined input-output behaviors
for example
dishwasher isn't open-loop control system
the goal of a dishwasher which is the plant
is clean dishes
which is the output
once the user sets the wash time which controls the time to clean the dishes
the dishwasher will run for that set time
now this is true regardless of the cleanliness of the dishes
if the dishes looted were clean to begin with the dishwasher would still run for
the prescribed time
further if you look at the dishwasher with templates full of cake
the set i might not be enough to clean up
another coming sample alderman control
izzy sprinkler system for your life
in this control system
the system i'll put it is the moisture content of the soil
again the user sets the timer which controls the amount of time to run the
sprinklers
and while the sprinklers are running the plant which is the grass in this case is
being watered
again and open-loop sprinkler system which still run even if it was raining
outside
far more complicated example imagine trying to tane
a constant speed in your car without the benefit of the built-in automatic cruise
control
to do this you were derived between the front of your cv gas pedal to the press
it halfway down
the output of control system is the speed of the car
and the input
is the position of the gas pedal
again the car itself is the plant
the cardigan street celery tonic flat road angela force applied to the system
is balanced by the force of friction
at this point the car stops exhilarated maintains a constant speed
but what happens when the car counters appeal or a valley
without tearing the input
that isn't just in the capital
the car will slow down or speed up in the desired constant speed will not be
maintained
this is the primary drawback to control
the input to the system has no way to compensate for variations in the system
that would come through these changes you must be really input your system
with respect to the output
in this type of control system is called a closed-loop control system
now in addition to calling it closed-loop control this can also be
referred to as
feedback control negative feedback controller automatic control
the time being we use these terms interchangeably although there are
slight variations between some of them that we won't address this lecture
includes loop controlled you measure the output of the system with a sensor
and compare the result against a reference signal
often this is referred to as the desired state of the commanded state
in error term is generated and then fed through a controller
where the air is converted into a system input value
went on a block diagram orbits easy to see where this is referred to as a
control
the negative part of the negative feedback control term is based on the
comparator juncture
where the feedback is subtracted
so how does feedback control work in practice
ballistic a case of the dishwasher
there could be a sensor
that measures the cleanliness of the plates
the reference it would be some sort of desired cleanliness level that would be
sent you to buy the manufacturer or by the user
this desired cleanliness level would be compared to do the measured level
in a return would be generated
which would be fed through a controller
which would monitor when to shut off the dishwasher
the sprinkler system could also benefit from closed-loop control
the center can be a device clinton in the soil and measures the moisture
content of the planet
remember that in this case the plant is both the grass
in the soil
the reference it would be a designer ex-royal moisture content
the error signal would be generated
which would then be fed through a controller
and the controller
would adjust the amount of time
that the sprinklers ram
the sprinklers would be run until the moisture level
reached a specified value
and then they would be shot off
for the car with cruise control
closed-loop control would work something like this
the sensor
is a speedometer which measures the speed of the car
the reference pete would be the speed of the car was going
when the cruise control set
now assume that the car starts in the steady-state position on flat wrote
and what i mean by that is that the speed is constant at your desired speed
and also that the gas pedal is depressed the amount needed
to generate that speed
for this example let's say that the desired speed as a hundred miles per
hour
therefore the speedometer would also be hundred miles per hour
and since the measured speed exactly matches the reference p_b_a_ return zero
the gas that was the exactly where it is
was the car counters that hill espy starts to slow
now the reference feeders greater than the measured speed here term becomes
positive which signals the controller to speed up
if the car comes a downhill the speed will increase now the reference pete is
less than the measured speed in the air term will be negative
the beauty of the feedback control systems that is kingwood reacting
changes to the plans are medically by constantly driving the a return to zero
only he was one more thought regarding closed-loop control
if we take a block diagram in the signed letters that abstractly represent the
various parts of the control system
we can gain new insight into how feedback control is manipulating a
system
for example if we're able to reference signal v
and we call the controller some abstract processed d
through the plain ji which produces an output will calm quiet which can be then
back to the sensor h two generating a return
weekend then reduce this block diagram even further
for example we can multiply detained cheated combined into a single block
to reduce further however takes a small amount of algebra
the air a signal is the referencing movie
minus the output why times centered process h
yelper why is the a return times detainees cheat
that's all this equation brigade which will give you why over teaching
now you can set both equations equal to each other
andrew a few more algebraic steps you can solve for the variable
y_ with respect to the
reasons why is the output npi has the input
the rest of that equation is what we refer to as transfer function of the
system
in this case the transfer function is d times g
over one plus deje h
and for those who are paying attention your most effort at a rate of the at the
end of that equation there
we can now rewrite this back and block diagram for
these two block diagram representations are equivalent of each other
but doesn't this new process look a lot like unopened and control system
only with the marquai plant
the feedback path has altered the original plan to be something new and
furthermore the open-loop behavior if this new plant companies act
characteristics we wanted from the original plant
namely that follows our input
that has something to ponder until the next video
one of the limitations of feedback control
in other words can we make any plant g_p_a_'s like anything we'd choose
just by adding a feedback control system
which is made up of a controller deanna sensor h
one other thing
do you think in our car example from up above
but using feedback control we can turn it pinto
into a ferrari just by applying more gas