Sensitivity analysis of a time-delayed thermo-acoustic system via an adjoint-based approach

We apply adjoint-based sensitivity analysis to a time-delayed thermo-acoustic system: a Rijke tube containing a hot wire. We calculate how the growth rate and frequency of small oscillations about a base state are affected either by a generic passive control element in the system (the structural sensitivity analysis) or by a generic change to its base state (the base-state sensitivity analysis). We illustrate the structural sensitivity by calculating the effect of a second hot wire with a small heat-release parameter. In a single calculation, this shows how the second hot wire changes the growth rate and frequency of the small oscillations, as a function of its position in the tube. We then examine the components of the structural sensitivity in order to determine the passive control mechanism that has the strongest influence on the growth rate. We find that a force applied to the acoustic momentum equation in the opposite direction to the instantaneous velocity is the most stabilizing feedback mechanism. We also find that its effect is maximized when it is placed at the downstream end of the tube. This feedback mechanism could be supplied, for example, by an adiabatic mesh. We illustrate the base-state sensitivity by calculating the effects of small variations in the damping factor, the heat-release time-delay coefficient, the heat-release parameter, and the hot-wire location. The successful application of sensitivity analysis to thermo-acoustics opens up new possibilities for the passive control of thermo-acoustic oscillations by providing gradient information that can be combined with constrained optimization algorithms in order to reduce linear growth rates. © Cambridge University Press 2013.

Finite element analysis of the ring rolling process with integrated closed-loop control

In FEA of ring rolling processes the tools' motions usually are defined prior to simulation. This procedure neglects the closed-loop control, which is used in industrial processes to control up to eight degrees of freedom (rotations, feed rates, guide rolls) in real time, taking into account the machine's performance limits as well as the process evolution. In order to close this gap in the new simulation approach all motions of the tools are controlled according to sensor values which are calculated within the FE simulation. This procedure leads to more realistic simulation results in comparison to the machine behaviour. © 2012 CIRP.

Modelling of equipment loaded panels for robust control investigations

This paper develops a modelling technique for equipment load panels which directly produces (adequate) models of the underlying dynamics on which to base robust controller design/evaluations. This technique is based on the use of the Lagrange's equations of motion and the resulting models are verified against those produced by a finite Element Method Model.

Optimal control with stochastic PDE constraints and uncertain controls

The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with the control function possibly decomposed into an unknown deterministic component and a known zero-mean stochastic component. The extra freedom provided by the stochastic dimension in defining cost functionals is explored, demonstrating the scope for controlling statistical aspects of the system response. One-shot stochastic finite element methods are used to find approximate solutions to control problems. It is shown that applying the stochastic collocation finite element method to the formulated problem leads to a coupling between stochastic collocation points when a deterministic optimal control is considered or when moments are included in the cost functional, thereby forgoing the primary advantage of the collocation method over the stochastic Galerkin method for the considered problem. The application of the presented methods is demonstrated through a number of numerical examples. The presented framework is sufficiently general to also consider a class of inverse problems, and numerical examples of this type are also presented. © 2011 Elsevier B.V.

Active control of high-frequency vibration: Optimisation using the hybrid modelling method

This work presents active control of high-frequency vibration using skyhook dampers. The choice of the damper gain and its optimal location is crucial for the effective implementation of active vibration control. In vibration control, certain sensor/actuator locations are preferable for reducing structural vibration while using minimum control effort. In order to perform optimisation on a general built-up structure to control vibration, it is necessary to have a good modelling technique to predict the performance of the controller. The present work exploits the hybrid modelling approach, which combines the finite element method (FEM) and statistical energy analysis (SEA) to provide efficient response predictions at medium to high frequencies. The hybrid method is implemented here for a general network of plates, coupled via springs, to allow study of a variety of generic control design problems. By combining the hybrid method with numerical optimisation using a genetic algorithm, optimal skyhook damper gains and locations are obtained. The optimal controller gain and location found from the hybrid method are compared with results from a deterministic modelling method. Good agreement between the results is observed, whereas results from the hybrid method are found in a significantly reduced amount of time. © 2012 Elsevier Ltd. All rights reserved.

Implementation of a PI phase angle controller for finite element analysis of the BDFM

Time-stepping finite element analysis of the BDFM for a specific load condition is shown to be a challenging problem because the excitation required cannot be predetermined and the BDFM is not open loops stable for all operating conditions. A simulation approach using feedback control to set the torque and stabilise the BDFM is presented together with implementation details. The performance of the simulation approach is demonstrated with an example and computed results are compared with measurements.

Stability control of a railway vehicle using absolute stiffness and inerters

Work presented in this paper studies the potential of employing inerters -a novel mechanical device used successfully in racing cars- in active suspension configurations with the aim to enhance railway vehicle system performance. The particular element of research in this paper concerns railway wheelset lateral stability control. Controlled torques are applied to the wheelsets using the concept of absolute stiffness. The effects of a reduced set of arbitrary passive structures using springs, dampers and inerters integrated to the active solution are discussed. A multi-objective optimisation problem is defined for tuning the parameters of the proposed configurations. Finally, time domain simulations are assessed for the railway vehicle while negotiating a curved track. A simplification of the design problem for stability is attained with the integration of inerters to the active solutions. © 2012 IEEE.