Chaotic and Hyperchaotic Dynamics of Smart Valves System Subject to a Sudden Contraction

Abstract

In this paper, we focus on determining the safe operational domain of a coupled actuator–valve configuration. The so-called “smart valves” system has increasingly been used in critical applications and missions including municipal piping networks, oil and gas fields, petrochemical plants, and more importantly, the U.S. Navy ships. A comprehensive dynamic analysis is hence needed to be carried out for capturing dangerous behaviors observed repeatedly in practice. Using some powerful tools of nonlinear dynamic analysis including Lyapunov exponents and Poincaré map, a comprehensive stability map is provided in order to determine the safe operational domain of the network in addition to characterizing the responses obtained. Coupled chaotic and hyperchaotic dynamics of two coupled solenoid-actuated butterfly valves are captured by running the network for some critical values through interconnected flow loads affected by the coupled actuators' variables. The significant effect of an unstable configuration of the valve–actuator on another set is thoroughly investigated to discuss the expected stability issues of a remote set due to others and vice versa.

Multivariable Extremum Seeking for Joint-Space Trajectory Optimization of a High-Degrees-of-Freedom Robot

“…Note that the immediate focus of this research work is on reducing cumbersome computational burden of optimization efforts associated with high-DOF robots including Baxter. We hence propose and utilize the S-shaped trajectory (here tanhð:Þ), based on our previous efforts for operational optimization of smart valves network [45][46][47][48], which is highly compatible with the actual motion of Baxter's joints. From another aspect, using conventional trajectories, including Spline and B ezier in addition to polynomials generating S-shaped ones, expectedly imposes more variables to be optimized with respect to the joint-space optimization; we inevitably need high-order polynomials to generate such a smooth S-shaped trajectory.…”

Experimental and Novel Analytical Trajectory Optimization of a 7-DOF Baxter Robot: Global Design Sensitivity and Step Size Analyses

“…3 Note that adding points between the initial and end points only imposes additional constraints with cumbersome computational cost which would be meaningless with respect to the collision-free motion; except the collision between the robot's end effector and the target object for the nominal operation due to the jerky motion. Note that we have previously examined these trajectories (S-Shaped ones) for another interconnected electromechanical system [6] enforcing the geometrical and stability constraints [5]. We fit the following nonlinear functions to the joints' nominal trajectories which are generated with respect to the initial/end points given in Table 2 using the PD controller:…”

“…The importance of the optimal operation can be visualized through a network of robots operating simultaneously to carry out a specific task defined; we have reported another effort of the interconnected operational optimization in [4] for the so-called "Smart Valves Network" [5][6][7]. The robot manipulator, which is being analyzed in this research work, is operated for thousands of cycles in industries and even homes as a reliable servant for disabled patients.…”

An Adaptive Centralized Approach to Control Chaotic and Hyperchaotic Dynamics of Smart Valves Network

“…We have reported broad analytical and experimental studies [1][2][3][4][5][6][7][8][9][10][11][12][13] for both an isolated actuator-valve arrangement and a network of two interconnected solenoid actuated butterfly valves operating in series. A novel third-order nondimensional analytical model of the single solenoid actuated butterfly valve was derived dealing with the coupled nonlinear magnetic, hydrodynamic, and bearing torques [8].…”

“…We have also reported the nonlinear analytical model of two interconnected sets subject to the pipe contraction in Refs. [1,2,9,12].…”