Model-free adaptive control (MFAC) has four model parameters

and existing studies consider it to be uncorrelated and conserved throughout. The relationship among 4 parameters is found out in this paper by assuming an initial state of the controlled system at the initial moment

based on the rule of the first moment output value should be close to the target value with genetic algorithm (GA)

making the issue of 4 parameters to be simplified into the one of single parameter. Further

an automatic estimation method on step-length factor is suggested according to whether the absolute value of difference between output value and target value is less than a default value

thus it is regarded as a parameter with characteristic of time-variable and its maximum value is also enlarged into positive infinity from 1. The proposed two changes improve the present MFAC greatly

resulting in a faster calculation speed at the early control stage as well as avoiding overshoot and vibration at the convergence stage. A case application in a unit of oil refinery shows that the improved MFAC only needs 14 iterations for reaching the optimal target

and the system’s maximum added-benefit (MAD) can reach 5.43 million CNY/a. The number of parameter adjustments for the maximum gain of the system is reduced from 33 to 14 times

and the maximum gain is increased from 4.134 million CNY/a to 5.429 million CNY/a.