National-instruments PID Control Toolkit 371685C-01 Instrukcja Użytkownika Strona 10
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© National Instruments Corporation 2-1 LabWindows/CVI PID Control Toolkit User Manual
2
PID Algorithms
This chapter explains the fast PID, precise PID, and autotuning algorithms.
The PID Algorithm
The PID controller compares the setpoint (SP) to the process variable (PV) to obtain the error
(e), as follows:
e = SP – PV
Then the PID controller calculates the controller action, u(t), as follows. In this equation, K
c
is the controller gain.
If the error and the controller output have the same range, –100% to 100%, controller gain is
the reciprocal of proportional band. T
i
is the integral time in minutes, also called the reset
time, and T
d
is the derivative time in minutes, also called the rate time. The following formula
represents the proportional action.
The following formula represents the integral action.
The following formula represents the derivative action.
ut() K
c
e
1
T
i
----
etd
0
t
∫
T
d
de
dt
------
++
⎝⎠
⎜⎟
⎜⎟
⎛⎞
=
u
p
t() K
c
e=
u
I
t() =
K
c
T
i
-------
etd
0
t
∫
u
D
t() K
c
T
d
de
dt
-------
=
- LabWindows 1
- Important Information 3
- Contents 4
- About This Manual 6
- Overview of the PID Control 7
- Activation Instructions 8
- PID Control 9
- PID Algorithms 10
- Error Calculation 11
- Proportional Action 11
- Trapezoidal Integration 11
- Partial Derivative Action 11
- Controller Output 11
- Gain Scheduling 12
- The Precise PID Algorithm 13
- The Autotuning Algorithm 14
- Tuning Formulas 15
- Chapter 2 PID Algorithms 16
- Using the PID Control Toolkit 18
- Tuning Controllers Manually 19
- Using the PID Library 21
- Control Input Filter 22
- Output Rate Limiting 22
- Using PID with Autotuning 23
- Using PID with Lead-Lag 25
- Using Ramp Generators 26
- Using PID with DAQ Devices 27
- References 29
- Technical Support and 30
- Professional Services 30
- Glossary 32
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