National Instruments NI MATRIXx Xmath, User Manual

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© National Instruments Corporation 4-1 Xmath Interactive Control Design Module
4
PID Synthesis
This chapter discusses the PID Synthesis window. This window is used to
synthesize various types of standard classical SISO controllers such as P,
PI, PD, PID, lead-lag, and lag-lead. However, the controller that is
designed by the PID Synthesis window will be referred to as a PID
controller even if it has some other form such as PI. Multivariable (MIMO)
PID controllers can be synthesized using the Multiloop Synthesis
window.
Refer to Chapter 13, Multi-Loop Synthesis .
Window Anatomy
The PID Synthesis window is shown in Figure 4-1. It consists of the
following, from top to bottom:
• A menu bar with entries Special , Edit , View , and Help .
• A text area that displays the transfer function of the current PID
controller.
• A control panel with five rows, each of which corresponds to one
design parameter. A Bode plot of the controller transfer function with
handles for graphically manipulating the design.
PID Controller Terms
The overall controller transfer function is given by the product of up to five
terms, each of which depends on one parameter. The five parameters and
corresponding terms in the controller are shown in Table 4-1, from top to
bottom.
Table 4-1. PID Controller Terms and Parameters
Term Parameter Symbol Controller
Proportional (P) Gain K
p
K
p
Integral (I) Integral time constant
T
int
1 + 1/( sT
int
)
Derivative (D) Derivative time constant
T
diff
1 + sT
diff