PID CONTROL
Apart from sluggish performance to avoid oscillations, another
problem with proportional-only control is that power application is
always in direct proportion to the error. In the example above we
assumed that the set temperature could be maintained with 50% power.
What happens if the furnace is required in a different application where
a higher set temperature will require 80% power to maintain it? If the
gain was finally set to a 50° PB, then 80% power will not be applied
unless the furnace is 15° below setpoint, so for this other application
the operators will have to remember always to set the setpoint
temperature 15° higher than actually needed. This 15° figure is not
completely constant either: it will depend on the surrounding ambient
temperature, as well as other factors that affect heat loss from or
absorption within the furnace.
To resolve these two problems, many feedback control schemes include
mathematical extensions to improve performance. The most common
extensions lead to proportional-integral-derivative control, or PID control (pronounced pee-eye-dee).
DDERIVATIVE ACTION
The derivative
part is concerned with the rate-of-change of the error with time: If
the measured variable approaches the setpoint rapidly, then the actuator
is backed off early to allow it to coast to the required level;
conversely if the measured value begins to move rapidly away from the
setpoint, extra effort is applied—in proportion to that rapidity—to try
to maintain it.
Derivative action makes a control system behave much more
intelligently. On control systems like the tuning of the temperature of a
furnace, or perhaps the motion-control of a heavy item like a gun or
camera on a moving vehicle, the derivative action of a well-tuned PID
controller can allow it to reach and maintain a setpoint better than
most skilled human operators could.
If derivative action is over-applied, it can lead to oscillations
too. An example would be a PV that increased rapidly towards SP, then
halted early and seemed to "shy away" from the setpoint before rising
towards it again.
INTEGRAL ACTION
The integral term magnifies the effect of long-term steady-state
errors, applying ever-increasing effort until they reduce to zero. In
the example of the furnace above working at various temperatures, if the
heat being applied does not bring the furnace up to setpoint, for
whatever reason,integral action increasingly moves
the proportional band relative to the setpoint until the PV error is
reduced to zero and the setpoint is achieved.In the furnace example,
suppose the temperature is increasing towards a set point at which, say,
50% of the available power will be required for steady-state. At low
temperatures, 100% of available power is applied
When the PV is within,
say 10° of the SP the heat input begins to be reduced by the
proportional controller. (Note that this implies a 20° "proportional
band" (PB) from full to no power input, evenly spread around the
set point value). At the set point the controller will be applying 50%
power as required, but stray stored heat within the heater sub-system
and in the walls of the furnace will keep the measured temperature
rising beyond what is required. At 10° above SP, we reach the top of the
proportional band (PB) and no power is applied, but the temperature may
continue to rise even further before beginning to fall back. Eventually
as the PV falls back into the PB, heat is applied again, but now the
heater and the furnace walls are too cool and the temperature falls too
low before its fall is arrested, so that the oscillations continue.
OTHER TECHNIQUES
It is possible to filter
the PV or error signal. Doing so can reduce the response of the system
to undesirable frequencies, to help reduce instability or oscillations.
Some feedback systems will oscillate at just one frequency. By filtering
out that frequency, more "stiff" feedback can be applied, making the
system more responsive without shaking itself apart.
Feedback systems can be combined. In cascade control,
one control loop applies control algorithms to a measured variable
against a setpoint, but then provides a varying setpoint to another
control loop rather than affecting process variables directly. If a
system has several different measured variables to be controlled,
separate control systems will be present for each of them.
Control Engineering in many applications produces control systems that are more complex than PID control. Examples of such fields include fly-by-wire aircraft control systems, chemical plants, and oil refineries. Model predictive control
systems are designed using specialized computer-aided-design software
and empirical mathematical models of the system to be controlled.