Exam I Flashcards
Why is process control important?
Guarantee Safety Meet product specifications Control emissions Meet operational constraints Optimize process economics
What should process controls do?
Suppress the influence of external disturbances
Ensure process stability
Optimize the process performance
When is a process defined as linear?
If a positive or negative input change produces a proportional change in the output, although the sign of the output change can be different.
How are inputs defined in controls?
The effect of the surroundings on the system.
How are outputs defined in controls?
The effect of the process on the surroundings.
What are two types of inputs?
Manipulated and disturbances
What are two types of disturbances?
Measured and unmeasured
What variable that is part of a process does control act on?
Manipulated variable
What is the principle of feed back control?
Feedback control is corrective
What is the principle of Feedforward control?
Feed forward control is predictive
If feed can be controlled by a valve it is a ________.
If feed can not be controlled it is a ________.
Manipulated variable; output
Outputs are measurable if we have appropriate what?
Instrumentation.
If the error signal equals zero, what control action is required?
None
If the error signal is greater than zero than the measured variable is _______ than expected.
Lower
If the error signal is less than zero the measured variable is _____ than expected.
Higher.
Step 1 the control does what?
Measures variable
Step two the controller does what?
Compare the variable (v) with the set variable (vs)
What describes a system, a process apparatus, a device, a chemical plant, etc, with one ore more equations?
mathematical model
We use mathematical models to predict what?
For a given change in the input, what is the corresponding change in the output
what is the dynamic behavior of a system, before it reaches steady state
what is the new steady state
What are models based on?
The principles of conservation (mass, energy, momentum) + constitutive equations
With lumped parameter models process variables are not a function of what?
spatial coordinates
What are some examples in which you would use a lumped parameter model
CSTR reactor, where composition and temperature distributions are uniform
Generally lumped parameter models are what?
macroscopic
With distributed parameter models process variables are a function of what?
spatial coordinates (and time)
What are some examples in which you would use a distributed parameter model?
PFR reactor, where properties change along the coordinate z.
Generally distributed parameter models can be what?
microscopic
You need to make sure that the number of equations matches the number of what?
unknowns
What is an example of an EOS
Pv=nRT
What is an example of a transport equation?
Q=UA(Tinf - T)
What is an example of a reaction rate?
R=(koe^(E/RT)Ca
A mathematical model is a system of what?
equations
If you have one independent variables what kind of equations do you use?
ODE
If you have two or more independent variables what kind of equations do you use?
PDE
Models can be linear or what?
nonlinear
Differential equations describe what?
the time evolution of a given system
A mathematical model has to be what?
flexible
A mathematical model should be able to describe what?
the dynamic state of a process, as well as its steady state
At steady state, time derivatives are what?
0
At steady state, derivatives with respect to the spatial coordinates may not be what?
0
ODEs contain derivatives with respect to what?
one independent variable
What is the control law with respect to heat flow?
Q=Qs - alpha e
As alpha increases it never goes to what?
zero (this logic does not work! have to run experiments!)
f’(xo) represents what in a Taylor series?
the slope of the line
before time 0 we should assume that xo equals what?
xs
What is the physical meaning of the deviation variable?
the departure of that variable from steady state
The Laplace transform is what kind of operator?
linear
The Laplace exists if what?
the integral above takes a finite value
What is a Laplace transform?
a transformation of the function f from the time domain to the s-domain, where s is a generic complex variable
Laplace transforms help develop what?
input/output models
Laplace transforms help predict what?
how a process reacts to external disturbances
What is the mathematical representation of a step input?
F(s)= a/s
In a unit impulse, what does F(s) equal?
1
a unit impulse can be defined mathematically as what?
d(step)/dt
a ramp can be defined mathematically as what?
the integral (step) dt
What kind of step is defined by F(s) = (a/s)(1-e^(-deltats))
rectangular
What kind of pulse is define as F(s) = (aw/(s^2+ w^2))
sinusoidal pulse
For systems that are not perfectly mixed describe the translated functions
if f is advanced f(t+to) —-> Laplace e^(sto)F(s)
if f is normal f(t)—–> Laplace F(s)
if f is delayed f(t-to)—–> Laplace e^(-sto)F(s)
what is td?
the time delay or dead time
With Laplace what disappears?
derivatives and integrals
We can compute f(t) at t = infinity if we know what?
its Laplace transform at t=0 (final value theorem)
We can compute f(t) at t=0 if we know its Laplace at t equals what?
infinity (Initial value theorem)
What is the patch to solving differential equations using the Laplace transform?
linearize differential equations in the time domain
algebraic equations in the s domain
solution (expressed in the time domain)
the zeroes of the numerator are called what?
zeros
the zeroes of the denominator are called what?
poles
Which Heaviside Theorem do you use if your poles are real and distinct?
1
For denominators of a polynomial 3 how many terms would you expect?
3
What theorem do you use if your poles are real but repeated with a multiplicity of q?
Heaviside 2
What theorem would you use if your poles are complex?
Heaviside 3
What are the generalized equations used in Heaviside Theorem 3?
F(s) = N(s)/D(s) = N(s)/(Q(s)[((s-a)^2)+b^2] f(t) = (e^(at)/b)(Psi(i) cos (bt)+ Psi(r) sin (bt))
where b is the positive imaginary part of the pole.
When the system is initially at steady-state at t=0 what are y and its derivatives equal to?
zero
G(s) is equal to what mathematically?
Y(s)/F(s)
What is the physical meaning of the transfer function?
The laplace transform of the output in the deviation form / The Laplace transform of the input in deviation form
Systems with multiple inputs and 1 output are the sum of what?
The transfer functions
Gi is the transfer function that does what?
relates the output of the process to each of the inputs
The order of the denominator has to be what of the numerator?
greater or equal
Distinct real poles give rise to what?
exponential factors that decay over time if p < 0 or grow grow exponentially if p > 0.
If one pole is positive the system is what?
unstable
based on the 2nd Heaviside Theorem, the polynomial term goes to what with time?
infinity
The exponential terms in the 2nd heaviside theorem depend on what?
the pole being positive, negative, or zero
If the pole is positive in the exponential term the term goes to what?
infinity
if the pole equals zero in the exponential term the term goes to what?
1
If the pole is negative in the exponential term the term goes to what?
zero
For the third Heaviside Theorem, the behavior of the function is what and what does it depend on?
oscillating, the real part
If the real part of a complex pole is greater than zero what happens?
you have exponentially growing sinusoidal behavior
If the real part of a complex pole is less than zero what happens?
you have damped sinusoidal behavior( amplitude of oscillation decreases continuously)
If the real part of a complex pole is equal to zero what happens?
Harmonic oscillation (constant amplitude)
Poles located on the right side of the imaginary axis give rise to terms that do what?
grow to infinity with time
if terms grow to infinity with time, the system is defined as what?
unstable
Poles located on the left side of the imaginary axis give rise to terms that do what?
terms that decay to zero with time
terms that decay to zero give rise to systems that are defined how?
stable
If any of the coefficients are negative, there is at least one positive pole, the system is defined as what?
unstable
If all coefficients are positive then you can test the system using what?
Routh Array
The Routh array contains n+1 row, where n is the order of what?
the transfer function G(s)
If any number in the first column of the Routh array are negative the system is what?
unstable
The input/output relationship for any of the TF in the sequence is what?
G1 * G2 * G3 *….
So the overall TF of a sequence is what?
The product of the TFs in the sequence
The order of the denominator of a transfer function is the same as what?
the order of the differential equation from which it was derived
What is Kp defined as?
steady-state gain
What is tau p defined as?
time constant
at steady state, what does Kp equal?
delta y/ delta f = change in the output/ change in the input at steady state
What systems behave like first order systems?
tanks, mixers, isothermal CSTR with a 1 st order reaction
What is the Laplace definition of an impulse of magnitude A?
A
What is the Laplace definition of a step size of A?
A/s
The smaller the tau p the system reaches a new steady state _______.
faster
The larger the Kp the larger the what?
the final steady-state value of the output
experimentally impose what kind of change because it is much easier to realize?
step
The slope of the experimental dynamic data is what?
-t/tau p
a ramp disturbance with a slope of a has an input transfer function defined how?
F(s) = a / (s^2)
Are ramp systems self regulating?
No!
What is an example of a system that exhibits a ramp disturbance?
membrane system
tau decreases with increasing what?
h (heat transfer)
what is one way you can increase h?
Use better material with higher heat transfer
What is another way to decrease the time constant involved in heat transfer?
increase the area of thermocouple
In heat transfer how is tau defined?
the capability to store energy times the resistance to transfer energy
For volume level how is tau defined?
A/alpha where A is the capability to store liquid and 1/alpha is the resistance to flow
In second order systems how many terms define the system?
3
What are the terms that define a second order system?
tau, episilon, and K
In a second order system what is the definition of tau
natural period of oscillation tau = 1/w w is the frequency of the oscillations
In a second order system what is the definition of epsilon?
the damping factor, determines the shape of the dynamic response (oscillating, non oscillating)
In a second order system what is the definition of Kp?
steady-state gain (how sensitive a system is to a stimulus)
What processes can be described as 2nd order systems?
a series of two first order systems,
inherently second order systems that exhibit resistance to motion
controlled processes
if epsilon is greater than one how can the poles be described and what is the system defined as?
2 distinct real poles, both negative; overdamped
if epsilon is equal to one than how can the poles be described and what is the system defined as?
2 repeated poles, both negative; critically damped
if epsilon is less than one how can the poles be described and what is the system defined as?
2 complex conjugate poles with negative real part; underdamped
Critically damped systems respond faster than what?
overdamped systems
the higher the order of the transform function the system is more what?
sluggish
As epsilon increases the system becomes more what?
sluggish
2 complex conjugate poles implies that the system will exhibit what with underdamped systems?
oscillations
the negative real parts of an underdamped system relates how it what?
decays with time (oscillations)
The underdamped response is initially what?
faster than the overdamped or critically damped responses.
What is overshoot?
The phenomenon where an underdamped system exceeds by several times the steady state value.
Overshooting can create what?
dangerous situations
What is rise time?
The initial time to achieve steady state
what is the decay ratio?
the amplitude of the second departure divided by the amplitude of the first
What is the period of oscillation?
the time needed to complete 1 oscillation
When designing a good controller, tau and epsilon need to be selected carefully, so that what?
overshoot is small, the rise time is short, and the decay ratio is small.
A series of N first order systems gives rise to what order of system?
N-order
As N increases, the system becomes more what?
sluggish
If the system is controlled, the controller should help do what?
improve the speed of the system’s response
Dead time shows up when you consider what kind of systems?
PFR, shell-and-tube heat exchangers, and plug flow systems
A system exhibits inverse response if its transfer function has what?
any zero with positive real part (zeroes = roots of numerator)
The zeroes of the numerator determine what?
whether an inverse response takes place
the zeroes of the denominator deterime what?
the shape of the response and the stability
What systems exhibit an inverse response?
reboilers
Two first order, noninteracting systems in a series give rise to what kind of second order system?
Overdamped
