what do i need for a pid output

amgathering the materials to build a 15 gallon BIAB Kettle . what are the output parameters needed by the pid to controll an 5500 watt element this unit work

dual display universal digital programmable temperature controller that supports many type of thermocouple sensor. It can be powered by 80-265V AC/DC or 12-30V AC/DC, Comsumption5VA. DIN 1/16.

3 build-in Auto-Tuning Time proportion PID Algorithms to choose for different applications or environments to be controlled. (for variety of industries or home projects heating or cooling applications.)

Specifications:
Display: Dual display for Fahrenheit(F) and Celsius(C)
Range: -1999 to 9999 (depends on the thermocouple)
Relay Output: Mechanical (3A) and SSR
Accuracy: 0.3%
Thermo Resistor: PT100, Cu50
Thermocouple Support: K,J,E,S,T,B,R


Dimension: DIN 1/16 (48mmX48mmX80mm)

Individually programmable PID control parameters. P, I, d, controlling period, digital filter coefficient, and more¡* (for control theory experts only)

7 different Dual Output combinations with: 1 relayed output and 1 SSR control voltage output

SSR control ready to connect external Solid State Relay to handle High current. Applications.

Compact design:
DIN 1/16, great form-factor to be included/build-in to your product.

Apply with step control, 2 independent PID control for heating/cooling over temperature,pressure,level,flowm,etc

Since I just went through this exercise the cheap route, I can say that spending a few extra dollars up front will go a long ways in the end. The Auber Instruments unit is probably the best budget unit out there according to those that use them regularly.

1/16 DIN PID Temperature Controller (SSR control output) [SYL-2352] - $45.50 : auberins.com, Temperature control solutions for home and industry

There is a slightly cheaper version out of the far east on ebay. (Make sure you get the "VR" version with SSR output)

Digital PID Temperature Controller D1S-VR-220 10%OFF | eBay

And there is an even cheaper one imported from the far East by USA sellers. This cheapest one does not appear to have a manual setpoint PWM controller built in like the previous two. I ordered this one (I'm just about ready to power up my panel for the first time) so I ended up building a separate PWM to control my boil strength with. In the end I'm up to about $40-$50 and could have just bought the more expensive ones I listed first. This unit would work great for a RIMS or HERMS system, but not that great for a single vessel eBIAB setup like I am building.

New Digital PID Temperature Controller SNR Alarm SSR Thermocouple K,J,S,E,T,R,B | eBay