This Faculty Early Career Development (CAREER) grant will provide viable solutions to control combined river-dam-reservoir systems in an era of unceasing growing demand for water and energy. Global warming is drastically altering rainfall patterns, increasing the risk of water scarcity. The rapid conversion of natural landscapes to urbanized areas that are continually growing in population further accentuates this issue. Sustainable management strategies are becoming critical to ensure the optimum use of essential but limited water resources on the planet. Often, river infrastructures such as dams, gates, and reservoirs are built to satisfy human societies' water and energy demands. However, the maintenance of costly engineered river infrastructures is still posing crucial problems related to reservoir sedimentation and ecosystem preservation. First, estimation methodologies that allow real-time quantification and monitoring of distributed profiles of sediments transported in a water channel from the measurement of appropriate quantities at gate locations will be developed. Second, flow control strategies for hydraulic systems governed by continuum models of density gradient induced by moving sediment will be exploited to ensure stable operation when gates release high discharges in the channel or reservoir, generating turbulence during sediment flushing or venting operations. An experimental setup that supports the feasibility and efficiency of the control/estimation methodologies will be designed. While advancing the science through the development of innovative real-time control and estimation approaches, the research program will be consolidated with an integrated educational plan with the introduction of a graduate course related to the research topic. This project will create opportunities for the participation of students in research and development in water management systems at the K-12, undergraduate, and graduate levels.
The key idea of the research is to exploit PDE (Partial Differential Equation) boundary control techniques towards efficient water and sediment dynamics management. Fundamental balance equations reflecting the dynamics of coupled water and sediment waves, namely, the bilayer Saint-Venant model, which describes a multiphase flow with a density gradient, will be exploited to achieve the objective. The main difficulties to overcome involve the real-time monitoring of distributed sediment bed profiles and disturbances arising from flushing processes such as shock-waves and hydraulic jumps generated by significant gate discharges over channels. Strongly coupled nonlinear hyperbolic PDEs and mixed systems consisting of cascading hyperbolic PDEs and ODE (Ordinary Differential Equations) are relevant to the flow physics problems. The backstepping control technique combined with Lyapunov analysis will be employed to derive high-performance observers and controllers that solely use gate actuation dynamics and output measurements to enable fast and exponential stabilization at a prescribed setpoint. Various extensions of the theoretical outcomes of the research can essentially solve decisive challenges related to the control of traffic dynamics, networks of sewer systems, and pollutant transport in water flow, to name a few.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
