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

Abstract

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. The importance of controlling pressures in water distribution systems is widely recognized. This study delves into the analysis of a pressure-reducing valve, beginning with its mathematical model and culminating in its control mechanism. Two secondary (solenoid) valves serve to operate the pressure-reducing valve, acting as the system’s control inputs. The research showcases that the achieved control operates effectively across a broader range of operating conditions, a notable distinction from other pressure-reducing valve controls. Furthermore, it demonstrates the feasibility of utilizing only one control input while keeping the other fixed. Additionally, a strategy is proposed to maximize the operational range of the pressure-reducing valve within the constraints of the inputs. Finally, considering implementation in the field using validated hardware, and acknowledging the complexity of the obtained control, this study substitutes the original control with a well-established (PI) control, ensuring the desired properties. Experimental results validate the effectiveness of the proposed control strategy.