what is the one quarter decay criterion?
for tuning by mathematical optimisation, picking a decay ratio of 1/4
compromise between fast rise time and reasonable settling time (key criteria to minimise)
we can also optimise the controller by minimising some measure of the error. name three common error measurements
integral of the square error
integral of the absolute error
integral of time-weighted absolute error
NOTE: not useful for proportional only control !
in which cases is the integral of the square error best used for tuning?
to suppress LARGER errors, which are amplified
(as opposed to IAE)
in which cases is the integral of absolute error best used for controller tuning?
to suppress smaller errors
(as opposed to using ISE)
in which cases is the integral of time-weighted absolute error best used for tuning?
to suppress errors that persist for a long time – more tolerant to earlier errors
name the empirical method commonly used for controller tuning (mathematical optimisation often too difficult)
Ziegler-Nichols
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based on the 1/4 decay ratio
explain how the Ziegler-Nichols tuning procedure is carried out.
operate under P control ONLY, bring process to a steady-state at a low value of controller gain.
w closed control loop, slowly increase Kc until the system oscillates continuously after a small disturbance / sp change
= incipient instability, Kc = Ku.
here, freq of oscillations is phase crossover frequency, find P(u) ultimate period
choose settings from table.
recap: how is period calculated from frequency?
P = 2 pi / frequency
Aside from Ziegler-Nichols, what is another empirical method of tuning controller settings?
Cohen-Coon method
Cohen-Coon is a graphical method. What is the name of the curve that is examined?
the Process Reaction Curve
explain how the Process Reaction Curve for the Cohen-Coon method is found.
disconnect controller (break between Gc and Gv)
introduce step change –> measure output change: this is the process reaction curve.
G(PRC)(s) = Gv Gp Gm
what three values are of interest to obtain from a process reaction curve by the Cohen-Coon method?
K
t(d) time delay
tau
describe the key features of a process reaction curve (Cohen-Coon method)
graph is process variable vs time
s-shaped curve: from 0, asymptote up to K
tangent to inflexion of curve intersect w x-axis: t(d) for time delay (first part up to intersection), and tau (up to x-value where tangent intersects y=K)
for a small dead time, the Cohen-Coon method may be…
too robust – too close to instability.
