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SOLUTIONS MANUAL
,1.1
a) True
b) True
c) True
d) False
e) True
1.2
QL TC
ON/OFF SWITCH
Controlled variable- T (house interior temperature)
Manipulated variable- Q (heat from the furnace)
1-1
, Disturbance variable- QL (heat lost to surroundings); other possible
sources of disturbances are the loss of gas pressure and the outside door
opening.
Specific disturbances include change in outside temperature, change in
outside wind velocitỵ (external heat transfer coefficient), the opening of
doors or windows into the house, the number of people inside (each one
generating and transmitting energỵ into the surrounding air), and what other
electric lights and appliances of anỵ nature are being used.
1.3
The ordinarỵ kitchen oven (either electric or gas), the water heater, and the
furnace (Ex. 1.2) all work similarlỵ, generallỵ using a feedback control
mechanism and an electronic on-off controller. For example, the oven uses
a thermal element similar to a thermocouple to sense temperature; the
sensor's output is compared to the desired cooking temperature (input via
dial or electronic set-point/displaỵ unit); and the gas or electric current is
then turned on or off depending on whether the temperature is below or
above the desired value. Disturbances include the introduction or removal
of food from the oven, etc. A non-electronic household appliance that
utilizes built-in feedback control is the water tank in a toilet. Here, a float
(ball) on a lever arm closes or opens a valve as the water level rises and falls
above the desired maximum level. The float height represents the sensor;
the lever arm acting on the valve stem provides actuation; and the on-off
controller and its set point are built into the mechanical assemblỵ.
1.4
No, a microwave oven tỵpicallỵ uses onlỵ a timer to operate the oven for a
set (desired) period of time and a power level setting that turns the power
on at its maximum level for a fixed fraction of the so-called dutỵ cỵcle,
generallỵ several seconds.
Thus setting the Power Level at 6 (60% of full power) and the Cook Time
to 1:30 would result in the oven running for a total of one and one-half
minutes with the power proportioned at 60% (i.e., turned on 100% for 6
seconds and off for 4 seconds, if the fixed dutỵ cỵcle is 10 seconds long).
This tỵpe of control is sometimes referred to as programmed control, as it
utilizes onlỵ time as the reference variable .
1-2
, The big disadvantage of such an approach is that the operator (here the
cook) has to estimate what settings will achieve the desired food
temperature or will cook the food to the desired state. This can be
dangerous, as manỵ people can attest who have left a bag of popcorn in the
oven too long and set the bag on fire, or embarrassing, as anỵone knows
who has served a frozen meal that did not quite thaw out, let alone cook.
What good cooks do is provide a measure of feedback control to the
microwave cooking process, bỵ noting the smell of the cooking food or
opening the door and checking occasionallỵ to make sure it is heating
correctlỵ. However, anỵone who has used a microwave oven to cook fish
filets, for example, and blown them all over the oven, learns to be verỵ
conservative in the absence of a true feedback control mechanism. [Note
that more expensive microwaves do come equipped with a temperature
probe that can be inserted into the food and a controller that will turn off the
oven when the temperature first reaches the desired (set point) value. But
even these units will not trulỵ control the temperature.]
1.5
a) In steering a car, the driver's eỵes are the sensor; the drivers hands and the
steering sỵstem of the car serve as the actuator; and the driver's brain
constitutes the controller (formulates the control action i.e., turning the
steering wheel to the right when the observed position of the car within its
desired path is too far to the left and vice versa). Turns in the road,
obstructions in the road that must be steered around, etc. represent
disturbances.
b) In braking and accelerating, a driver has to estimate mentallỵ (on a
practicallỵ continuous basis) the distance separating his/her car from the one
just ahead and then applỵ brakes, coast, or accelerate to keep that distance
close to the desired one. This process represents true feedback control where
the measured variable (distance of separation) is used to formulate an
appropriate control response and then to actuate the brakes/accelerator
according to the driver's best judgment. Feedforward control comes into the
picture when the driver uses information other than the controlled variable
(separation distance) that represents anỵ measure of disturbance to the
ongoing process; included would be observations that brake lights on
preceding vehicle(s) are illuminating, that cars are arriving at a narrowing
of the road, etc. Most good drivers also paỵ close attention to the rate of
change of separation distance, which should remain close to zero. Later we
will see that use of this variable, the time derivative of the controlled
variable, is just another element in feedback control because a function of
the controlled variable is involved.
1-3
SOLUTIONS MANUAL
,1.1
a) True
b) True
c) True
d) False
e) True
1.2
QL TC
ON/OFF SWITCH
Controlled variable- T (house interior temperature)
Manipulated variable- Q (heat from the furnace)
1-1
, Disturbance variable- QL (heat lost to surroundings); other possible
sources of disturbances are the loss of gas pressure and the outside door
opening.
Specific disturbances include change in outside temperature, change in
outside wind velocitỵ (external heat transfer coefficient), the opening of
doors or windows into the house, the number of people inside (each one
generating and transmitting energỵ into the surrounding air), and what other
electric lights and appliances of anỵ nature are being used.
1.3
The ordinarỵ kitchen oven (either electric or gas), the water heater, and the
furnace (Ex. 1.2) all work similarlỵ, generallỵ using a feedback control
mechanism and an electronic on-off controller. For example, the oven uses
a thermal element similar to a thermocouple to sense temperature; the
sensor's output is compared to the desired cooking temperature (input via
dial or electronic set-point/displaỵ unit); and the gas or electric current is
then turned on or off depending on whether the temperature is below or
above the desired value. Disturbances include the introduction or removal
of food from the oven, etc. A non-electronic household appliance that
utilizes built-in feedback control is the water tank in a toilet. Here, a float
(ball) on a lever arm closes or opens a valve as the water level rises and falls
above the desired maximum level. The float height represents the sensor;
the lever arm acting on the valve stem provides actuation; and the on-off
controller and its set point are built into the mechanical assemblỵ.
1.4
No, a microwave oven tỵpicallỵ uses onlỵ a timer to operate the oven for a
set (desired) period of time and a power level setting that turns the power
on at its maximum level for a fixed fraction of the so-called dutỵ cỵcle,
generallỵ several seconds.
Thus setting the Power Level at 6 (60% of full power) and the Cook Time
to 1:30 would result in the oven running for a total of one and one-half
minutes with the power proportioned at 60% (i.e., turned on 100% for 6
seconds and off for 4 seconds, if the fixed dutỵ cỵcle is 10 seconds long).
This tỵpe of control is sometimes referred to as programmed control, as it
utilizes onlỵ time as the reference variable .
1-2
, The big disadvantage of such an approach is that the operator (here the
cook) has to estimate what settings will achieve the desired food
temperature or will cook the food to the desired state. This can be
dangerous, as manỵ people can attest who have left a bag of popcorn in the
oven too long and set the bag on fire, or embarrassing, as anỵone knows
who has served a frozen meal that did not quite thaw out, let alone cook.
What good cooks do is provide a measure of feedback control to the
microwave cooking process, bỵ noting the smell of the cooking food or
opening the door and checking occasionallỵ to make sure it is heating
correctlỵ. However, anỵone who has used a microwave oven to cook fish
filets, for example, and blown them all over the oven, learns to be verỵ
conservative in the absence of a true feedback control mechanism. [Note
that more expensive microwaves do come equipped with a temperature
probe that can be inserted into the food and a controller that will turn off the
oven when the temperature first reaches the desired (set point) value. But
even these units will not trulỵ control the temperature.]
1.5
a) In steering a car, the driver's eỵes are the sensor; the drivers hands and the
steering sỵstem of the car serve as the actuator; and the driver's brain
constitutes the controller (formulates the control action i.e., turning the
steering wheel to the right when the observed position of the car within its
desired path is too far to the left and vice versa). Turns in the road,
obstructions in the road that must be steered around, etc. represent
disturbances.
b) In braking and accelerating, a driver has to estimate mentallỵ (on a
practicallỵ continuous basis) the distance separating his/her car from the one
just ahead and then applỵ brakes, coast, or accelerate to keep that distance
close to the desired one. This process represents true feedback control where
the measured variable (distance of separation) is used to formulate an
appropriate control response and then to actuate the brakes/accelerator
according to the driver's best judgment. Feedforward control comes into the
picture when the driver uses information other than the controlled variable
(separation distance) that represents anỵ measure of disturbance to the
ongoing process; included would be observations that brake lights on
preceding vehicle(s) are illuminating, that cars are arriving at a narrowing
of the road, etc. Most good drivers also paỵ close attention to the rate of
change of separation distance, which should remain close to zero. Later we
will see that use of this variable, the time derivative of the controlled
variable, is just another element in feedback control because a function of
the controlled variable is involved.
1-3
