Chapter 2 PID Algorithms
LabWindows/CVI PID Control Toolkit User Manual 2-6 ni.com
Figure 2-2 illustrates the autotuning procedure excited by the setpoint relay experiment,
which connects a relay and an extra feedback signal with the SP. Notice that the PID Library
autotuning functions directly implement this process. The existing controller remains in
the loop.
Figure 2-2. Process under PID Control with Setpoint Relay
For most systems, the nonlinear relay characteristic generates a limiting cycle from which the
autotuning algorithm identifies the relevant information needed for PID tuning. If the existing
controller is proportional only, the autotuning algorithm identifies the ultimate gain Ku and
ultimate period Tu. If the existing model is PI or PID, the autotuning algorithm identifies the
dead time and time constant Tp, which are two parameters in the integral-plus-deadtime
model, as follows:
Tuning FormulasThis package uses Ziegler and Nichols’ heuristic methods for determining the parameters of
a PID controller. When you autotune, select one of the following types of loop performance:
fast (1/4 damping ratio), normal (some overshoot), or slow (little overshoot). Refer to the
following tuning formula tables for each type of loop performance.
Table 2-1. Tuning Formula under P-Only Control (Fast)
Controller KcTiTd
P0.5Ku— —
PI 0.4Ku0.8Tu—
PID 0.6Ku0.5Tu0.12Tu
SP e
+
–P(I) Controller Process
PV
Relay
+
–
τ
GPs() = eτs–
Tps
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