Temperature and Pressure Controllers form a large part of Process control Instrumentation. Then you have Flow, Humidity and many more custom parameters.
All Real Life Physical Phenomena are reduced to Analog Numbers by Sensors and Transducers. This analog value is amplified and linearized and brought into standardized windows like 1-5 Volts or 4-20mA and more.
These Analog Values go to Analog Closed Loop Controllers or Meters for Measurement and Control. In Embedded Controllers, the Analog is converted to Digital ( At least 12 bit, 8 bits are cheap not used for industrial automation, more than 16 bits is not required as sensor accuracy/linearity never transgress such precision )
Embedded Process Controllers may use Microcontrollers with Floating Point Arithmetic, Lookup Table, Logic and Basic Math. Advanced Controllers may use DSP and Complex Algorithms for Adaptive control. (self learn, fuzzy logic.).
There is a instruction sheet for a 3 wire transmitter. It Amplifies the uV signals from a K type Thermocouple, Chromel-Alumel. The output is a strong 4-20mA which is fit for looping and driving a Controller an Alarm and an Analog Recorder too.
8 Bits D/A may be used when a control signal is needed, like 4-20 mA Control Output driving a Thyristor PWM bank. Here 8 Bit is enough when the thyristor bank drives large heaters. The thermal inertia and delay makes very precise control nearly impossible.
When a parameter needs to be controlled in a tiny area, precision control is possible. A 16 Bit control signal is required. The system/thermal design here is more important than the controller, they have to be tandem for obtaining repeatable precision control.
Read More about this here – Electronics Theory – Industrial Control Panels