National Instruments 371685C-01

Chapter 2 PID Algorithms

The actual controller output is limited to the range specified for control output, as follows:

and

The following formula shows the practical model of the PID controller.

The PID functions use an integral sum correction algorithm that facilitates anti-windup and

bumpless manual-to-automatic transfers. Windup occurs at the upper limit of the controller

output, for example, 100%. When the error (e) decreases, the controller output decreases,

moving out of the windup area. The integral sum correction algorithm prevents abrupt

controller output changes when you switch from manual to automatic mode or change any

other parameters.

The default ranges for the SP, PV, and output parameters correspond to percentage values;

however, you can use actual engineering units. If you use engineering units, you must adjust

the corresponding ranges accordingly. The Ti and Td parameters are specified in minutes.

In manual mode, you can change the manual input to increase or decrease the output.

All the PID control functions are reentrant. Multiple calls from high-level functions use

separate and distinct data.

Note As a general rule, manually drive the PV until it meets or comes close to the SP

before you perform the manual-to-automatic transfer.

Gain scheduling refers to a system in which you change controller parameters based on

measured operating conditions. For example, the scheduling variable can be the SP, the PV,

aco ntroller output, or an external signal. For historical reasons, the term gain scheduling is

used even if other parameters, such as the derivative time or integral time parameters, change.

Gain scheduling effectively controls a system whose dynamics change with the operating

conditions.

if uk() umax then uk() umax

=≥

if uk() uminthen uk() umin

=≤

ut() KcSP PV–() 1

---- (SP PV)dt Td

dPVf

------------

––

∫