this lecture is on open-loop versus closed-loop control systems a control
system is a mechanism that alters the future behavior or state of a system now
in order to be considered a control system and not simply a change the state
system the behavior or the outcome must tend towards a state that is desired
control theory is a branch of mathematics that is concerned with the
strategy to select the appropriate input or to put it another way it deals with
how to go about generating that outcome without control Theory the designer is
relegated to selecting appropriate actions through trial and error
now all control systems have two basic parts the system to be controlled
usually called the plant and an input into the plant the input acts on the
plant which responds over time to produce a system output this type of
control system is called an 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 a
dishwasher is an 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 dish is loaded were clean to begin with
the dishwasher would still run for the prescribed time further if you loaded
the dishwasher with ten plates full of cake the set time might not be enough to
clean them another common example of open-loop control is a sprinkler system
for your lawn in this control system the system output 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 water'd again an open-loop sprinkler
system would still run even if it was raining outside for a more complicated
example imagine trying to obtain a constant speed in your car without the
benefit of the built-in automatic cruise control to do this you went to Rod
between the front of your seat and the gas pedal to depress it halfway down the output of the 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 car begins to accelerate down a flat road until the
force applied to the system is balanced by the force of friction at this point
the car stops accelerating and maintains a constant speed but what happens when
the car encounters a hill or a Valley without varying the input that is
adjusting the gas pedal the car will slow down or speed up and the desired
constant speed will not be maintained this is the primary drawback to
open-loop control the input to the system has no way to compensate for variations in the system now to account
for these changes you must vary the input to your system with respect to the
output and this type of control system is called a closed loop control system
now in addition to calling a closed loop control this can also be referred to as
feedback control negative feedback control or automatic control for the
time being we'll use these terms interchangeably although there are
slight variations between some of them that we won't address in this lecture in
closed loop control 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 or the commanded state an error term is generated and then fed
through a controller where the error is converted into a system input value when
drawn in block diagram form it's easy to see why this is referred to as a control
loop 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 well let's take the case of the dishwasher
there could be a sensor that measures the cleanliness of the plates the
reference signal would be some sort of desired cleanliness level that would be
set either by the manufacturer or by the user
this desired cleanliness level would be compared to the measured level an error
term would be generated which would be fed through a controller which would monitor when to shut off the dishwasher
a sprinkler system could also benefit from closed-loop control the sensor could be a device planted in the soil
that measures the moisture content of the plant remember that in this case the
plant is both the grass and the soil the reference signal would be a desired soil
moisture content and again 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 ran the sprinklers would then run until the moisture level reached a specified value
and then they would be shut 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 speed would be the speed that the car was going when the cruise
control was set now assume that the car starts in a steady-state position on
flat road 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 the desired speed is a hundred miles per hour
therefore the speedometer would also read a hundred miles per hour and since
the measured speed exactly matches the reference be the error term is zero the
gas pedal would stay exactly where it is once the car encounters the hill the
speed starts to slow now the reference speed is greater than
the measured speed and the error term becomes positive which signals the
controller to speed up if the car encounters are downhill the speed will
increase now the reference speed is less than the measured speed and the error
term will be negative the beauty of the feedback control system is that it is
capable of reacting to changes to the plant automatically by constantly
driving the error term to zero I want to leave you with one more thought
regarding closed-loop control if we take a block diagram and assign letters that
abstractly represent the various parts of a control system we can gain new
insight into how feedback control is manipulating a system for example if we
label the reference signal V and we call the controller some abstract process D
through the plant G which produces an output we'll call Y which can be fed
back through the sensor H to generate an error term e we can then reduce this block diagram even further for example
we can multiply D and G to combine into a single block to reduce further however
takes a small amount of algebra the error signal is the reference signal V
minus the output Y times the sensor process H the output Y is the error term
times D times G now solve this equation for e which will give you Y over DG
now you can set both equations equal to each other and through a few more algebraic steps you can solve for the
variable Y with respect to V and since Y is the output and V is the input the
rest of that equation is what we refer to as a transfer function of the system in this case the transfer function is d
times G over 1 plus DGH and for those who are paying attention you'll notice that I forgot to write the V at the end
of that equation there we can now rewrite this back in block diagram form
these two block diagram representations are equivalent of each other now doesn't
this new process look a lot like an open-loop control system only with a
modified plant the feedback path has altered the original plant to be something new and furthermore the
open-loop behavior of this new plant has the exact characteristics we wanted from
the original plant namely that it follows our input now here's something
to ponder until the next video what are the limitations of feedback control in
other words can we make any plant G behave like anything we choose just by
adding a feedback control system which is made up of a controller D and a
sensor H one other thing do you think in our car example from up above by using
feedback control we can turn a Pinto into a Ferrari just by applying more gas
we'll discuss that in a future video