Question

A paper machine has the transfer function G(s) = e⁻²ˢ/3s+ 1 where the input is stock flow onto the wire and the output is basis weight or thickness. Find the PID-controller parameters using the Zeigler-Nichols tuning rules.

Answer 1

To find the PID-controller parameters using Zeigler-Nichols tuning rules, identify the ultimate gain and period from the system's response, and then apply the rules to compute Kp, Ti, and Td.

Step-by-step explanation:

To find the parameters for a PID-controller using the Zeigler-Nichols tuning rules for a paper machine with a given transfer function. The transfer function provides a mathematical expression showing the relation between the input and output of the system. Zeigler-Nichols tuning rules are a heuristic method of tuning a PID controller. While the supplied text does not directly provide an answer, the solution would involve determining the ultimate gain and ultimate period of the system by applying a proportional control (P-control) and increasing the gain until a sustained oscillation (constant amplitude) occurs. These values would then be used with the Zeigler-Nichols tuning rules to compute the specific parameters for the PID controller: the proportional gain (Kp), the integral time (Ti), and the derivative time (Td).