J
jeremy
28 minutes
Cohen-Coon Tuning Rules from a Step Test
Cohen-Coon is another table that turns the same three step-test numbers into gains. You need the process gain K, the dead time θ (theta), and the time constant τ (tau). It dates from 1953 and was built for loops where the dead time is a larger share of the response, where Ziegler-Nichols does poorly. Like Ziegler-Nichols, the controller gain grows with τ divided by K times θ. So a longer dead time or a larger process gain both call for a lower gain. Cohen-Coon then adds correction terms that depend on the ratio θ/τ. The integral and derivative times also change with that ratio. The formulas are longer, so most people use a printed table or a small spreadsheet. Copy them from a trusted controls text, and note which PID form the table uses. Cohen-Coon also aims for a quarter amplitude decay. So its gains are aggressive too, with large overshoot. It is also touchy: if your step-test numbers are a bit off, the loop can cycle. Treat its answer as a starting point. Then detune, for example by cutting the gain, and test with a setpoint step and a load change. If the loop rings, the gain is too high. A slow sway can also mean too much integral. After this Concept you can compute Cohen-Coon gains from a step test and decide how much to detune them.