User manual

PID Loop Operation
(DL450 Only)
Maintenance
8--9
PID Loop Operation (DL450 only)
DL405 User Manual, 4th Edition, Rev. A
PID Loop Operation
The Proportional--Integral--Derivative (PID) algorithm is widely used in process
control. The PID method of control adapts well to electronic solutions, whether
implemented in analog or digital (CPU) components. The DL450 CPU implements
the PID equations digitally by solving the basic equations in software. I/O modules
serve only to convert electronic signals into digital form (or vice v ersa).
The DL450 uses two types of PID controls: “position“ and “velocity“. These terms
usually refer to motion control situations, but here we use them in a different sense:
S PID Position Algorithm -- The control output is calculated so it responds
to the displacement (position) of the PV from the SP (error term).
S PID Velocity Algorithm -- The control output is calculated to represent
the rate of change (velocity) for the PV to become equal to the SP.
Referring to the control output equation on page 8--6, the DL450 CPU approximates
the output M(t) using a discrete position form of the PID equation.
Let:
Ts = Sample rate
Kc = Proportional gain
Ki = Kc * (Ts/Ti) = Coefficient of integral term
Kr = Kc * (Td/Ts) = Coefficient of derivative term
Ti = Reset or integral time
Td = Derivative time or rate
SP = Setpoint
PV
n
= Process variable at n
th
sample
en = SP -- PV
n
= Error at n
th
sample
Mo = Value to which the controller output has been initialized
Then:
M
n
= Control output at n
th
sample
Σ
M
n
= Kc £ e
n
+ Ki ei +Kr (en -- e n--1)+Mo
i=1
n
This form of the PID equation is referred to as the position form since the actual
actuator position is computed. The velocity form of the PID equation computes the
change in actuator position. The CPU modifies the standard equation slightly to use
the derivative of the process variable instead of the error as follows:
Σ
Mn = Kc £ en + Ki ei +Kr (PVn -- P V n--1)+Mo
i=1
n
These two forms are equivalent unless the setpoint is changed. In the original
equation, a large step change in the setpoint will cause a correspondingly large
change in the error resulting in a bump to the process due to derivative action. This
bump is not present in the second form of the equation.
PID Position
Algorithm