Chapter 9, Problem 54P

A metering pump is a pump capable of delivering a precise flow rate of fluid. Most metering pumps consist of an electric motor that varies the strike length of a shaft, allowing more or less fluid to pass through its body. The control of such a valve has been considered and the open-loop transfer function of the pump was found to be (Yu, 2011)

$\frac{U\left(s\right)}{Y\left(s\right)}=\frac{1.869}{s^2+12.32s+0.4582}$

where the output of the system, Y(s), represents the liquid flow, and the input, U(s), is the command signal to the motor that varies the pump's plunger strike length.

a. Design a PID controller to reduce the steady-state error to zero with a maximum 5% overshoot and a 20% reduction in uncompensated settling time.

b. Find the characteristics of the uncompensated system.

c. Design a PID controller to reduce the steady-state error to zero; achieve a maximum 5% overshoot and a 20% reduction in uncompensated settling time.

d. Simulate the step response for the compensated system to verify the validity of your design.