Chapter 6 Flashcards
which of the following is true about MIMO systems?
a. their dynamics can be simplified using laplace transforms
b. transfer function matrices contain individual SISO systems
c. time delay has no effect on interaction
D. they always require nonlinear modeling
b
interaction in MIMO systems makes controller design:
a. simpler
b. more difficult
c. unnecessary
d. faster
b. more difficult
which of the following statements about poles and system stability is true?
a. a system is always stable regardless of pole location
b. a zero in the left half plane causes instability
c. a system is stable if all poles lie on the imaginary axis
d. a system is unstable if it has a pole in the right half plane
d. a system is unstable if it has a pole in the right half plane
in state-space form, system dynamics are expressed using:
a. algebraic gain equations
b. first-order differential equations
c. transfer functions only
d. second-order polynomials
b. first-order differential equations
time delay in a process can cause:
a. reduced process gain
b. faster settling time
c. instability in a feedback loop
d. improved disturbance rejection
c. instability in a feedback loop
what effect does a zero have on a system’s time response?
a. it always stabilizes the system
b. it may introduce an initial inverse response
c. it reduces the number of poles
d. it slows down the rise time
b. it may introduce an initial inverse response
decoupling in MIMO systems aims to:
a. lower control cost
b. eliminate time delay
c. combine feedback and feedforward
d. reduce loop interactions
d. reduce loop interactions
the main difficulty of dead time in control is that it:
a. increases controller gain
b. makes sensors inaccurate
c. prevents zero error
d. delays corrective action
d. delays corrective action
a noninteracting system is easier to analyze because:
a. the subsystems can be analyzed independently
b. it is always linear
c. it has no zeros
d. it has fewer poles
a. the subsystems can be analyzed independently
in noninteracting two-tank systems, the output of the first bank:
a. directly affects the input of the second
b. is zero at steady state
c. is oscillatory
d. has no dynamic effect on the second tank
a. directly affects the input of the second
The dynamic behavior of a transfer function model can be characterized by the numerical value of its
poles and zeros.
Time delays occur due to:
- Fluid flow in a pipe
- Transport of solid material (e.g., conveyor belt)
- Chemical analysis
- Sampling line delay
- Time required to do the analysis (e.g., on-line gas chromatograph)
has proposed an approximation method for higher-order models that contain multiple time constants.
Skogestad (2002)
Skogestad (2002) approximates the largest neglected time constant in the following manner:
- One half of its value is added to the existing time delay (if any) and the other half is added to the smallest retained time constant.
- Time constants that are smaller than the “largest neglected time constant” are approximated as time delays
What indicates an unstable system in pole locations?
A pole to the right of the imaginary axis
What is the effect of complex conjugate poles?
Indicate oscillatory modes in the response
What is Skogestad’s method used for?
To approximate higher-order transfer functions
What indicates stability in a state-space model?
All eigenvalues have negative real parts
How can state-space models be converted?
To transfer function models
An inverse response occurs when
The initial response to a step input is in one direction, but the final steady state is in the opposite direction.
Changes in a downstream unit have no effect on upstream units.
Noninteracting Process
Downstream units affect upstream units and vice versa.
Interacting Process
Zeros significantly affect:
The coefficients of the response modes (how they are weighted)
The presence or absence of system zeros does not affect:
- The number and location of the poles.
- Their associated response modes unless there is an exact cancellation of a pole by a zero with the same numerical value.
Instantaneous step response occurs when:
The numerator and denominator polynomials have the same order.
