In order to support the advanced autonomy programs of the US Navy, predictive and adaptive shipboard machinery systems are generaly used. The objective in this effort has been to enable real time predictive capability to help achieve a much higher degree of autonomy than has been achieved so far. Advanced automation clearly lead to reduced manning and increased ship capability, ship survivability, and enhance the mission effectiveness, and is hence an important objective for the US Navy. In this project the actuator-valve systems as a critical part of the automation system are analyzed. Using physics-based high fidelity modeling, this research provides a set of tools to help understand, predict, optimize, and control the real performance of these complex systems.

**Mathematical modeling and analysis:** We derive with high fidelity the mathematical model for the behavior analysis of butterfly valves driven by solenoid actuators using multiphysics models. Based on that model, the dynamics of the valve was analyzed. The results have shown some nonlinearities responses to be considered in order to uncover harmful phenomena captured in the practice.

- The complex interplay between the electromagnetic, hydrodynamic and mechanical forces leads to a funda- mentally multiphysical, nonlinear dynamical model.
- The static onâ€“off angle linearly increases with the time constant of the electric circuit
- The critical (cut-off) angle for stability depends nonlinearly on the inlet velocity and the seating coefficient.
- The cut-off velocity decreases as the cut-off angle increases.
- The inlet velocity can sift the frequency response curve
- The system is also shown to exhibit complex nonlinear phenomena such as hysteresis, horseshoes chaos, crisis and transient chaotic responses.

The results of the optimization indicated that energy optimization is associated with the following observations.

- Lower values of the current particularly for higher rotation angles.
- Lower values of the energy is used particularly for higher rotation angles.
- Higher values of the magnetic actuation force.
- Higher values of the hydrodynamic torque.
- Higher values of the bearing torque.
- A better optimal performance would be obtained if the number of windings, N is also a design variable.

The following observations were made

- Energy can be saved by a significant amount (as much as 90%) by implementing optimal operation.
- The results showed an interesting interaction between the hydrodynamic and bearing torque.
- Lower values of the current.
- Lower values of the energy.
- Higher values of the hydrodynamic torque.
- Higher values of the bearing torque.

- Naseradinmousavi P., Nataraj C., 2013, Optimal design of solenoid actuators driving butterfly valves, ASME Journal of Mechanical Design, 135(9),094501
- Naseradinmousavi Peiman, Nataraj C., 2011, Nonlinear mathematical modeling of butterfly valves driven by solenoid actuators, Journal of Applied Mathematical Modelling, 35, 5, 2324-2335
- Kwuimy Kitio, Nataraj C., 2012, Modeling and nonlinear dynamics analysis of a magneticall y actuated butterfly valve, Nonlinear Dynamics, 70, 435-451