Chp. 3 Review Questions Flashcards
What is the definition of “transfer function”?
The Laplace transform of the output of a linear, time-invariant system, Y(s), is proportional to the transform of its
input, U(s). The function of proportionality is the transfer function F(s), so that Y(s) = F(s)U(s). It is assumed that
all initial conditions are zero.
What are the properties of systems whose responses can be described by transferfunctions?
The system must be both linear (superposition applies) and time invariant (the parameters do not vary with time).
What is the most common use of the Final Value Theorem in control?
A standard test of a control system is the step response, and the FVT is used to determine the steady-state error to
such an input.
Given a second-order transfer function with damping ratio ζ, and natural frequency ωn, what is the estimate of the
step response rise time? What is the estimate of the percent overshoot in the step response? What is the estimate
of the settling time?
These are given by tr ≅ 1.8/ωn, Mp is set by the damping ratio and ts ≅ 4.6/σ.
What is the major effect of an extra zero in the LHP on the second-order step response?
Such a zero causes additional overshoot, and the closer the zero is to the imaginary axis, the higher the overshoot.
If the zero is more than six times the real part of the complex poles, the effect is negligible.
What is the most noticeable effect of a zero in the RHP on the step response of the second-order system?
Such a zero often causes an initial undershoot of the response.
What is the main effect of an extra real pole on the second-order step response?
A pole slows down the response and makes the rise time longer. The closer the pole is to the imaginary axis, the
more pronounced is the effect. If the pole is more than six times the real part of the complex poles, the effect is
negligible.
Why is stability an important consideration in control system design?
Almost any useful dynamic system must be stable to perform its function. Feedback around a system that is
normally stable can actually introduce instability, so control designers must be able to assure the stability of their
designs.
What is the main use of Routh’s criterion?
With this method, we can find (symbolically) the range of a parameter such as the loop gain for which the system
will be stable.
Under what conditions might it be important to know how to estimate a transfer function from experimental
data?
In many cases, the equations of motion are either extremely complex or not known at all. Chemical processes such as a paper-making machine are often of this kind. In these cases, if one wishes to build a good control, it is very useful to be able to take transient data or steady-state frequency-response data and to estimate a transfer function from these.
