A new method of controlling nonlinear processes with actuator saturation nonlinearities is presented. Two nonlinear control laws are derived for single-input, single-output nonlinear processes. Whether input constraints are present or not, each of these dynamic control laws can minimize the mismatch between the closed-loop output response and the nominal linear output response that the same control law induces when there are no constraints. The control laws offer great flexibility to obtain a desirable closed-loop output response in the presence of active input constraints, and they inherently compensate for windup. They allow one to adjust the time period during which an input constraint is active and the decay rate of the mismatch between the constrained output response and the nominal linear unconstrained output response. Conditions under which the constrained closed-loop system is asymptotically stable are given. The connections between the developed control laws and the modified internal model control are established. The performance of the control laws is demonstrated by numerical simulations of chemical and biochemical reactor examples.