pid control basics

1. PID CONTROLLERS

3. ▪ A sensor measures and transmits the current value
of the process variable, PV, back to the controller (the
'controller wire in')
▪ Controller error at current time t is computed as set
point minus measured process variable, or e(t) = SP – PV
▪ The controller uses this e(t) in a control algorithm
to compute a new controller output signal, CO
▪ The CO signal is sent to the final control element
(e.g. valve, pump, heater, fan) causing it to change (the
'controller wire out')
▪ The change in the final control element (FCE) causes
a change in a manipulated variable
▪ The change in the manipulated variable (e.g. flow
rate of liquid or gas) causes a change in the PV

4. PROPORTIONAL ONLY MODE
The P-Only Algorithm -
The P-Only controller computes a CO action every loop
sample time T as:
CO = CObias + Kc∙e(t)
Where:
• CObias = controller bias or null value
• Kc = controller gain, a tuning parameter
• e(t) = controller error = SP – PV
• SP = set point
• PV = measured process variable

7. DEFINITIONS –
CObias is the value of the CO that, in manual mode, causes the
PV to steady at the DLO while the major disturbances are quiet
and at their normal or expected values.
Control loop sample time specifies how often the controller
samples the measured process variable (PV) and computes and
transmits a new controller output (CO) signal.
OFFSET – The difference between process value (PV) and set
point (SP) when the controller output has already settled.
Proportional Band –
PB = (COmax – COmin)/Kc
When CO and PV have units of percent and both range from 0%
to 100%, the much published conversion between controller
gain and proportional band results:
PB = 100/Kc

8. ADVANTAGES–
1. Only one variable, gain Kc has to be controlled to
control the response of the system
2. Relatively simple to design
3. Works well for systems where set point doesn’t
change
DISADVANTAGES –
1. Offset is produced if set point is changed from
design value.
2. If proportional gain is increased to reduce the
offset, the system becomes unstable.

9. THE PI MODE
• The PI Algorithm
• While different vendors cast what is essentially the same algorithm in
different forms, here we explore what is variously described as the
dependent, ideal, continuous, position form:
Where:
• CO = controller output signal (the wire out)
• CObias = controller bias or null value; set by bump-less transfer as
explained below
• e(t) = current controller error, defined as SP – PV
• SP = set point
• PV = measured process variable (the wire in)
• Kc = controller gain, a tuning parameter
• Ti = reset time, a tuning parameter

12. • ADVANTAGES –
1. It eliminates offset produced due to proportional
control
2. Accelerates the response towards steady state
DISADVANTAGES –
1. It may lead to sustained oscillations about the set
point
2. The two tuning parameters interact with each
other and their influence must be balanced by the
designer which is more complex than p only.
3. The integral term tends to increase the oscillatory
or rolling behavior of the process response.

13. PID CONTROL
The Dependent, Ideal PID Form
A popular way vendors express the dependent, ideal PID controller is:
Where:
CO = controller output signal (the wire out)
CObias = controller bias; set by bump-less transfer
e(t) = current controller error, defined as SP – PV
SP = set point
PV = measured process variable (the wire in)
Kc = controller gain, a tuning parameter
Ti = reset time, a tuning parameter
Td = derivative time, a tuning parameter

14. • The proportional term considers how far PV is from
SP at any instant in time. Its contribution to the CO
is based on the size of e(t) only at time t.
• The integral term addresses how long and how far
PV has been away from SP. The integral term is
continually summing e(t).
• A derivative describes how steep a curve is. More
properly, a derivative describes the slope or the rate
of change of a signal trace at a particular point in
time.

15. DERIVATIVE ACTION

17. DERIVATIVE KICK
• When the controller begins operation, the
slope of the controller response is almost 90
degrees and thus the derivative term
produces a huge output (theoretically
infinity).This is known as a Derivative kick and
is mostly undesirable.
• To overcome this, instead of taking derivative
of error voltage, we take the derivative of the
process value(PV).

18. • When set point is constant, its derivative is
zero. So we can write the differential term as –
So we can write the PID control equation as –