We determine closed-loop behavior of a P-only controller with the TCLab including oscillatory behavior and stability. We start by determining a second-order model between heater 1 (Q1) and temperature sensor 1 (TC1). With the second-order TCLab model, we determine the range of controller gains (Kc) where a P-only controller oscillates and is stable (does not diverge). Traditional stability analysis does not include information about controller output saturation (0-100% heater).
We use the P-Only simulator to test the stability and oscillation predictions. The simulator shows the stability and oscillation of a P-only controller with a TCLab second-order model with Kp=0.8473 oC/%, τs=51.08 sec, ζ=1.581 sec, and θp=0.0 sec. We use the second-order model parameters from a TCLab device for a more accurate simulation. The controller gain Kc is adjusted with a slider to compute the updated temperature response.
Source code:
Stability analysis theory:
Temperature Control Lab:
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