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Use digital control, it is much easier to build and to tune. Not just that, the interface can be very helpful for user. Some ease if you use digital control:
1. you can set the level of tolerance in any precise number as you wish depend on your data acquisition accuracy.
2. Other post design implementation can be adapted easily by reprogramming.
3. PID controlling is much easier in digital system.
and many more advantage...
Good luck...try to build pre-design, submit here and we will suggest improvement for you.
I agree with rikie_rizza; if one needs high sensivity, accuracy and to include some control algorithms (such as PID for example) it is better to build digital control.
However, digital ones (with microcontroller) have some drawbacks. The microcontroller may hung-up or software may go out of control if there is an error that has not been detected during programming phase. Such failure may, for example, cause the heater (if one is controlled by the microcontroller) to be turned on permanently regardless of the temperaure properly measured by the sensor used in the circuit. There are some good temperature sensors on the market. I often use DS18S20 sensor which has factory calibrated accuracy of +/- 0,5C and 0,0625 C resolution. It is ideally suited for digital controlling systems.
When higher accuracy is needed it is necessary to use other temperature sensors such as platinium Pt100 thermometer. I worked in a company that produced very accurate industrial thermometers based on the Pt100 sensor. The thermometers had accuracy of 0.04C. The thermometer was equipped with microcontroller to control calibrating process. There was also analog circuit (AD8574 op-amp) which was basically very precise current source that powers the Pt100. Also an A/C converter was utilized in the system. So, in some cases, analog and digtital ciruits are used both.