“…Ignoring the slight influence of RT on the quadratic and quartic flatness, and the cascade controllers adopt proportional control, the quadratic and quartic flatness decoupling PI-adaptive Smith predictive control system shown in Figure 6 2 and ∆a * 4 are the quadratic and quartic flatness changes of the Smith predictors, and e y2 and e y4 are the deviation between the actual and predicted outputs of the quadratic and quartic flatness control loops respectively. Referring to the adaptive algorithm of primary flatness control, the adaptive algorithm of quadratic and quartic flatness control loops is obtained as shown in Equation (17) and Equation (18), respectively, in which K 2 (0) and K 4 (0) are the initial values of K 2 (t) and K 4 (t), respectively, and λ 2 , λ * 2 , λ 4 and λ * 4 are four constants greater than zero. 17) and Equation (18), respectively, in which K2(0) and K4(0) are the initial values of K2(t) and K4(t), respectively, and λ2, λ…”