Process Control Q11

Front 1

As frequency increases:
Amplitude ratio decreases
Phase angle is negative if ys lags c

Back 1

.

Front 2

_

Back 2

_

Front 3

ωco - crossover frequency

PM - phase margin

Back 3

.

Front 4

Time difference between peaks can be converted into the

Back 4

Phase angle of response

Front 5

Time difference between peaks is assumed positive in phase angle equation when

Back 5

c lags ys

Front 6

Bode plot of a process is a plot of _____ and the logarithm of _______ vs. the logarithm of _______

Back 6

plot of phase angle and
logarithm of amplitude ratio vs. logarithm of frequency (rad/time)

Front 7

System with greater gain margin

Back 7

Can withstand greater changes in system parameters before becoming unstable in closed loop

Front 8

Phase Margin

Measures the system's

Back 8

Determines the phase angle at the crossover frequency

Tolerance to time delay

Front 9

A system is stable if

Back 9

Ar is less than 1.0 at the frequency where phase angle = -180˚ (critical frequency)

GM > 1
PM > 0

Front 10

Critical frequency

Back 10

Frequency (w) at which the phase angle = -180º

If Ar < 1 at wc, system is stable

Front 11

Gain Margin =

Back 11

1/Ar*
Where Ar* is the amplitude ratio at the critical frequency.

Front 12

Controllers are typically designed with gain margins in the range of ___ which implies that ___ at the critical frequency varies between ______

Back 12

1.4 to 1.8
Ar
0.7 and 0.55

Front 13

System is stable when A*r is

Back 13

Less than 1, GM > 1

Front 14

When GM = 1

When PM = 0

Back 14

Sustained Oscillations

Front 15

Gain Margin is to ____ as Phase Margin is to

Back 15

GM = 1/A*r
PM = f* - (-180

Front 16

Phase margin is the difference between

Back 16

The phase angle corresponding to Ar = 1 and a phase angle of –180˚

PM = f* + 180˚
where f* is the phase angle corresponding to Ar=1

Front 17

Crossover frequency

Back 17

ωco
Frequency that corresponds to Ar = 1

Front 18

Typical values used for tuning:
GM
PM

Back 18

GM: 1.4 - 1.8
PM: 30˚ - 45˚

Front 19

GM and PM for tuning similar to ______ in that

Back 19

Decay ratio
The more nonlinear a process and the larger the magnitude of disturbance, the larger the values of PM or GM used.