Learn how Cohen–Coon uses process gain, time constant and dead time to tune an FOPDT model.
G(s)=τs+1Ke−θs
Cohen–Coon tuning starts from a first-order-plus-dead-time model and adjusts its recommendation according to the ratio between delay and time constant.
01
The model behind the rule
The plant is summarized by process gain K, time constant τ and apparent delay θ. Identification quality matters as much as the arithmetic of the tuning rule.
MODEL VIEW 01
FOPDT compresses a process into three numbers
Process gain K sets the final change, dead time θ postpones motion, and time constant τ sets the speed after motion begins.
Measured plantFOPDT fit
READ THE PLOTSeparate the silent delay from the dynamic rise
02
When it is useful
The rule is intended for self-regulating processes and accounts for delay more explicitly than simple no-delay heuristics. It can still be aggressive when uncertainty or actuator constraints are large.
RATIO VIEW 02
The delay-to-time-constant ratio changes the problem
Plants with the same final gain can be easy or difficult to control depending on how much of the response is pure delay.
θ/τ = 0.1θ/τ = 0.5θ/τ = 1.0
READ THE PLOTA large θ/τ ratio means less feedback information
03
Validation after tuning
Use the proposed gains in a closed-loop simulation, then increase delay and vary process gain to see whether acceptable behavior survives model error.
ROBUSTNESS VIEW 03
A nominal fit can hide delay uncertainty
The Cohen–Coon recommendation may look good on the fitted model and ring when the real plant has more dead time than expected.
SetpointNominal model+20% delay+40% delay
READ THE PLOTStress-test delay before trusting nominal performance