Proportional-Integral Control of Pressure-Reducing Valves Using Control Lyapunov Functions

This work presents nonlinear and linear controls ensuring the global stability of a pressure-reducing valve. The global property using both nonlinear and linear controls is very important to guarantee stability even though the pressure-reducing valve operates far from its nominal working point. To this goal, this work develops the mathematical description of a pressure-reducing valve. It is a second-order model, nonlinear, and nonaffine in control implemented with two secondary (solenoid) valves. Due to the nonlinear nature of the system, the Lyapunov theory allows developing the control, which ensures the global stability of the system using one input. In addition, the second control input is modified to enlarge the operating range of the pressure-reducing valve. To implement the control in (nowadays) industrial controllers, a linear proportional-integral (PI) control, ensuring all the stabilizing properties of the nonlinear control, is included as a subset of the nonlinear law. Experimental results demonstrate the good performance of the proposed PI.