Sum-of-Squares approach to feedback control of laminar wake flows

A novel nonlinear feedback control design methodology for incompressible fluid flows aiming at the optimisation of long-time averages of flow quantities is presented. It applies to reduced-order finite-dimensional models of fluid flows, expressed as a set of first-order nonlinear ordinary differential equations with the right-hand side being a polynomial function in the state variables and in the controls. The key idea, first discussed in Chernyshenko et al. 2014, Philos. T. Roy. Soc. 372(2020), is that the difficulties of treating and optimising long-time averages of a cost are relaxed by using the upper/lower bounds of such averages as the objective function. In this setting, control design reduces to finding a feedback controller that optimises the bound, subject to a polynomial inequality constraint involving the cost function, the nonlinear system, the controller itself and a tunable polynomial function. A numerically tractable approach to the solution of such optimisation problems, based on Sum-of-Squares techniques and semidefinite programming, is proposed. To showcase the methodology, the mitigation of the fluctuation kinetic energy in the unsteady wake behind a circular cylinder in the laminar regime at Re=100, via controlled angular motions of the surface, is numerically investigated. A compact reduced-order model that resolves the long-term behaviour of the fluid flow and the effects of actuation, is derived using Proper Orthogonal Decomposition and Galerkin projection. In a full-information setting, feedback controllers are then designed to reduce the long-time average of the kinetic energy associated with the limit cycle. These controllers are then implemented in direct numerical simulations of the actuated flow. Control performance, energy efficiency, and physical control mechanisms identified are analysed. Key elements, implications and future work are discussed

Active vibration control of transverse vibrating segmented marine riser

Vortex induced vibration (VIV) could be regarded as a fluid-structure interaction vibration type where the bluff structure vibrates due to fluid flowing around the body. The separation of boundary layer has created vortex layer that staggers the structure in cross-flow direction. VIV suppression work has attracted numerous researchers to build a passive device that could reduce the vibration. However, such device requires an intricate design which incurs high expense and indirectly contributes to higher chance of VIV occurrence due to the additional mass to the system. This research proposed a method to overcome those shortcomings by introducing an active flow control concept to the system. Since the vibration originates from unhindered flowing fluid, the approach is to avoid the development of the vortex by attaching a single control rod to the system as an actuator. The actuator injects momentum to the boundary layer thus preventing the VIV phenomenon. Both simulation and experimental works were implemented in this study. The input-output data of the system were measured directly from the experimental rig. For system identification, three methods were employed which were least square (LS), recursive least square (RLS) and differential evolutionary (DE) algorithms. It was found that the DE methods were stable, had considerably lower mean squared error (MSE) and the transfer function itself represented the natural frequency of the system. The study was continued by tuning the proportionalintegral- derivative (PID) based controllers to the simulated system plant in offline mode. The PID based controllers were tuned using heuristic and Ziegler-Nichols (ZN) methods. The best performance was recorded. However, it was observed that once the disturbance of the system changed, the performance of the PID tuned using heuristic and ZN were deteriorated. To overcome this drawback, adaptive tuning algorithms were introduced, namely ZN-Fuzzy-PID and ZN-Fuzzy-Iterative Learning Algorithm-PID (ZN-Fuzzy-ILA-PID) based controllers. In simulation, it was found that the ZN-Fuzzy-ILA-PD controller outperformed other controllers with 57.82 dB of attenuation level. In experimental works, dynamic response comparison was made between the bare pipe, fixed single and double control rods. It was observed that the fixed single and double control rods could not effectively attenuate the system, but amplified the vibration instead. Further experimental work was conducted by varying the rotating speed of the actuator at various disturbances. The result shows that at 100 % actuator rotating speed with 33 Hz disturbance flow to the system, the vibration was successfully reduced with attenuation level of 20.71 dB. However, by changing the disturbance, the actuator performance was reduced. Therefore, the controller was adaptively tuned using the fuzzy and iterative learning (ILA) schemes. It was observed that the maximum vibration attenuation was achieved by ZN-Fuzzy-ILA-PD controller with 13.8 dB of attenuation level at changing disturbance. Overall results show that by adopting the single rotating control rod, the vibration of VIV could be successfully attenuated

Model-Guided Data-Driven Optimization and Control for Internal Combustion Engine Systems

The incorporation of electronic components into modern Internal Combustion, IC, engine systems have facilitated the reduction of fuel consumption and emission from IC engine operations. As more mechanical functions are being replaced by electric or electronic devices, the IC engine systems are becoming more complex in structure. Sophisticated control strategies are called in to help the engine systems meet the drivability demands and to comply with the emission regulations. Different model-based or data-driven algorithms have been applied to the optimization and control of IC engine systems. For the conventional model-based algorithms, the accuracy of the applied system models has a crucial impact on the quality of the feedback system performance. With computable analytic solutions and a good estimation of the real physical processes, the model-based control embedded systems are able to achieve good transient performances. However, the analytic solutions of some nonlinear models are difficult to obtain. Even if the solutions are available, because of the presence of unavoidable modeling uncertainties, the model-based controllers are designed conservatively

Design of a mechatronic system for postural control analysis

L'abstract è presente nell'allegato / the abstract is in the attachmen

Summary of research in applied mathematics, numerical analysis and computer science at the Institute for Computer Applications in Science and Engineering

Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science during the period October 1, 1983 through March 31, 1984 is summarized

Design and simulation of a distortion masking control algorithm for a pneumatic cylinder

Low energy efficiency is one of the main detractors of fluid power technology. To ensure the availability and sustainability of energy sources, fluid power technology needs to meet high energy-efficiency and cost standards. This study aims to design, simulate and test a control algorithm that attenuates the detrimental effects of air compressibility on the performance and efficiency of a pneumatic cylinder. The transmission of power over long distances makes it more difficult for fluid power technology to meet energy-efficiency and cost requirements. Transmitting power over long distances represents a challenge particularly for pneumatics due to the compressibility of air. The compressibility of air transmitted through lengthy tubing decreases the performance and efficiency of pneumatic actuators, mainly affecting their time response and velocity. The system under analysis was composed of a pneumatic cylinder, two proportional control valves, and connective tubing. The dynamics of the individual components were characterized through experimentation. Nonlinear and linear models for the system were validated through the comparison of simulated and experimental data. The models predicted the system behavior more accurately at 2.5 Hz, when friction effects became negligible, as compared to 1.0 and 0.5 Hz. A controller was designed using pole/zero cancellation, a control strategy able to mask undesirable dynamics of the system being controlled. Pole/zero cancellation had superior performance in the attenuation of air compressibility effects in comparison to proportional and proportional-derivative (PD) control. System performance and efficiency were assessed in terms of the variation of the length of tubing connecting the pneumatic cylinder and the control valves. Pole/zero cancellation enabled the cylinder to achieve similar levels of performance for long (3.0 m) tubing as with short (0.55 m) tubing. With a 1.0-Hz sinusoidal input and equal control gains, pole/zero cancellation reduced the tracking error by approximately 30% and 23% in comparison to proportional and PD control, respectively. In terms of efficiency, with the system tracking a 2.5-Hz sinusoidal command, and using equal control gains, pole/zero cancellation increased the cylinder efficiency by approximately 36% and 54% in comparison to proportional and PD control, respectively. In general, pole/zero cancellation increased the system performance and efficiency in comparison to the other control schemes applied

A generalised immersed boundary method for flows of dense suspension of solid particles

Immersed boundary method (IBM) provides computational advantages in approximating moving solid surfaces on fixed numerical meshes. It has been widely used for fully-resolved simulations of particulate flows. This thesis proposes a generalised formulation of IBM with improved applicability to flows with dense concentrations of particles and unstructured meshes. The new IBM formulation, which is based on the smooth-interface direct forcing approach, directly uses the algebraic discretised terms of the momentum equations in the evaluation of the forces on Lagrangian immersed boundary (IB) points, and evaluate the integral Lagrangian volumes based on these forces. Appropriate reconstructions of the boundary forces are adopted to ensure the compatibility with the momentum-weighted interpolation used for the finite-volume discretisation with a collocated mesh arrangement. A modified direct forcing formulation is also proposed, which results in an efficiency gain of a devised segregated flow-particle coupling scheme. The novel framework is applied to flows with stationary and moving IBs on both Cartesian and arbitrary triangular/tetrahedral meshes, and the results are similar or better than other related methods that are mostly developed for Cartesian meshes. Accurate and stable enforcement of the no-slip condition on the IB at every time-step is demonstrated, even for flows with strong transient behaviour and high velocity and pressure gradients. Local continuity in the vicinity of the IB is also preserved, ensuring local and global mass conservation alongside the local no-slip condition. Adaptations devised for unstructured meshes results in an accuracy close to that obtained on Cartesian meshes. The framework is successfully applied in the simulations of fluidisation of dense particle bed and a rising pack of light particles, showing robust stability. The issues related to the interfering regularised forces of different particle surfaces are not significant using the present formulation, hence eliminate unphysical flow patterns between aggregated particles.Open Acces