Linear controls

Linear controls use negative feedback to keep some desired process within an acceptable
range. For example, a thermostat is a simple negative feedback control: when the
temperature goes below a threshold, a heater is switched on. Another example is a
refrigerator, where the mechanism is switched on when the internal temperature rises.
However, a simple logic control like a home thermostat doesn’t respond smoothly. In
industrial furnaces, it’s often better to turn the fuel valve open proportionally to the
coldness of the furnace. This avoids sudden shocks to the furnace and applies heat more
smoothly.


A simple proportional feedback system can either be slow to respond, or can tend to
oscillate. In the furnace example, the valve may open and shut indefinitely in a cycle as
the furnace heats, and then overruns the target temperature. This is bad because it stresses
the system. In a furnace, the constantly turning valve will quickly wear out. More
expensively, the fluctuating temperature causes expansion and contraction all through the
furnace, causing unnecessary, very expensive mechanical wear. Most systems have
similar problems.


To resolve this problem, the most common feedback control scheme has mathematical
extensions to cope with the future and the past. This type of control is called a
proportional-integral-derivative control, or PID control (pronounced pee-eye-dee). The
derivative part is concerned with the rate-of-change of the error: If the measured variable
is approaching the setpoint rapidly, then the actuator is backed off to allow it to coast to
the required level; conversely if the measured value begins to fall away rapidly, extra
effort is applied in proportion to that rapidity to try to maintain it. The integral term
magnifies the effect of long-term steady-state errors, applying ever-increasing effort until
these reduce to zero. When correctly tuned to the time-constants of the controlled system,
a PID control loop can be surprisingly effective at maintaining effortless control.


In many real cases, control system designers have to be concerned about practicalities
like wearing out control machinery such as valves, by adjusting them too frequently.
Therefore, control systems may have a “deadband,” a region around the current value in
which no control action occurs. In commercial controls, the deadband is programmable.
Another common technique is to filter the feedback loop. A filter may reduce the
response of the system to undesirable frequencies, to help eliminate instability or
oscillations. Most feedback systems will oscillate at just one frequency. By filtering out
that frequency, one can use very “stiff” feedback and the system can be very responsive
without shaking itself apart.