SIMC Tuning Rules for Slow Processes

… more less SIMC, short for Skogestad's simple IMC rules, is a small change to lambda tuning. With lambda tuning, the integral time equals the process time constant. On a slow process with a long time constant, that makes the integral very weak. A load change then leaves an error that creeps back for a long time. SIMC fixes this. It keeps the same gain, Kc = τ / (K (τc + θ)). Here τc is the closed-loop time you choose, the same idea as lambda, K is the process gain, τ is the time constant and θ is the dead time. But it sets the integral time to the smaller of two numbers: τ, or 4 times (τc + θ). On a fast process, τ is smaller, so nothing changes from lambda tuning. On a slow process, the second number wins, and the integral works harder. There is one knob, τc. A common choice is τc equal to the dead time θ, for a tight loop that still has good margin. A larger τc gives a softer, more robust loop. The cost of the shorter integral time is a little overshoot on setpoint steps. Use SIMC over plain lambda tuning when the loop must recover fast from loads and the time constant is long next to the dead time. After this Concept you can compute SIMC PI gains and tell when they beat plain lambda tuning.