It is important to precisely control the amount of organic fertilizer applied to a specific crop area in order to provide specific nutrient quantities and to avoid unnecessary environmental pollution. A precise delivery liquid manure machine has been developed for this purpose (Saeys, 2008). The system consists of a pressurized tank, a valve, and a rheological flow sensor. After simplification, the system can be modeled as a closed-loop negative feedback system with a forward path transfer function
consisting of an electrohydraulic system in cascade with the gain of the manure flow valve and a variable gain, K. The feedback path is comprised of
a. Use the SISO Design Tool in MATLAB to obtain the root locus of the system.
b. Use the SISO Design Tool to find the range of K for closed-loop stability.
c. Find the value of K that will result in the smallest settling time for this system.
d. Calculate the expected settling time for a step input with the value of K obtained in Part c.
e. Check your result through a step-response simulation.
