Nonlinear modeling of butterfly valves and flow rate control using the Circle Criterion Bode plot

Butterfly valves are widely used control components in piping systems. This paper derives the nonlinear mathematical relationship between flow rate, pressure difference, and valve angle in a butterfly valve. We use the Circle Criterion Bode plot and loop shaping to design a flow rate controller in a motor-gearbox-butterfly valve system. The design employs a complex proportional-integral-lead (CPIL) compensator, and we show the benefit of using a damping ratio less than unity. Finally, we demonstrate the effectiveness of the design through simulation.