Some chemical processes, such as a distillation column, can be modeled as a series of first-order processes with the same time constant. For the process with transfer function
design a digital proportional controller with a sampling period T = 0.1 by applying the tangent method and the Ziegler-Nichols rules (see Sections 5.5 and 6.3.4). Use the circle criterion to show that the closed-loop system with actuator saturation nonlinearity of slope unity is asymptotically stable. Obtain the step response of the closed-loop system to verify the stability of the closed-loop system with actuator saturation.