Robust operation of fed batch fermenters

This paper deals with uncertain model structures, model validation and robust performance analysis of active magnetic bearings. The dynamics of active magnetic bearing systems are characterized by their instability and complex dynamics of rotor and electromagnets. The feedback control is indispensable to stabilize the system, further the closed-loop systems of magnetic bearings should have robustness for stability and performance against model uncertainties. First we derive a nominal mathematical model of AMBs as a linear state-space model under some assumption and idealization, then we consider the discrepancy between the real physical systems and the obtained nominal design model. This discrepancy can be expressed as the structured uncertainties by Linear Fractional Transformation. These uncertainties include linearization error, parametric uncertainties, unmodeled dynamics, and gyroscopic effect. Then we set the interconnection structure which contains the above structurally represented uncertainties. Next we design a robust controller which achieves robust performance condition. Finally, we validate the interconnection structure with the nominal model and uncertainties, and analyze the robustness of stability and performance of the closed-loop system via the mixed structured singular value.

Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as nonlinear optimization problems. Increasing the number of scenarios improves robustness, while increasing the size of the optimization problems. Mitigating the size of the problem by reducing the number of scenarios requires knowledge about how the uncertainty affects the system. This paper draws from local reduction methods used in semi-infinite optimization to solve robust optimal control problems with parametric uncertainty. We show that nonlinear robust optimal control problems are equivalent to semi-infinite optimization problems and can be solved by local reduction. By iteratively adding interim globally worst-case scenarios to the problem, methods based on local reduction provide a way to manage the total number of scenarios. In particular, we show that local reduction methods find worst case scenarios that are not on the boundary of the uncertainty set. The proposed approach is illustrated with a case study with both parametric and additive time-varying uncertainty. The number of scenarios obtained from local reduction is 101, smaller than in the case when all 214+3x192 boundary scenarios are considered. A validation with randomly drawn scenarios shows that our proposed approach reduces the number of scenarios and ensures robustness even if local solvers are used.

Detecting genetic variants for extreme aging using multiple data sources

Preface. Securitisation deals have come into focus during the recent years due to the challenges in their assessments and their role in the recent credit crises. These deals are created by the pooling of assets and the tranching of liabilities. The later are backed by the collateral pools. Tranching makes it possible to create liabilities of a variety of seniorities and risk-return profiles. The assessment of a securitisation deal is based on qualitative and quantitative assessments of the risks inherent in the transaction and how well the structure manages to mitigate these risks. Example of risks related to the performance of a transaction are credit risk, prepayment risk, market risk, liquidity risk, counterparty risk, operational risk and legal risk. In the light of the recent credit crisis, model risk and parameter uncertainty have come in focus. Model risk refers to the fact that the outcome of the assessment of a securitisation transaction can be influenced by the choice of the model used to derive defaults and prepayments. The uncertainties in the parameter values used as input to these models add to the uncertainty of the output of the assessment. The aim of this report is to give an overview of recent performed research on model risk and parameter sensitivity of asset backed securities ratings. The outline of the text is as follows.3 In Chapter 1, an introduction to asset-backed securities (ABSs) is given. We describe, for example, key securitisation parties, structural characteristics and credit enhancements. The cashflow modelling of ABS deals can be divided into two parts: (1) the modelling of the cash collections from the asset pool and the distribution of these collections to the note holders, discussed in Chapter 2, and (2) the modelling of defaults and prepayments. Deterministic models to generate default and prepayment scenarios are presented in Chapter 3; a collection of stochastic models is presented in Chapter 4. In Chapter 5, two of the major rating agencies quantitative methodologies for ABS rating are discussed. Next, the model risk in rating ABSs is discussed and we elaborate on the parameter sensitivity of ABS ratings. More precisely, in Chapter 6 we look at how the choice of default model influences the ratings of an ABS structure. We illustrate this using a two tranche ABS. Furthermore, we also investigate the influence of changing some of the input parameters one at a time. A more systematic parameter sensitivity analysis is presented in Chapter 7. In this chapter we introduce global sensitivity analysis techniques, which allow us to systematically analyse how the uncertainty in each input parameter’s value contributes to the uncertainty of the expected loss and the expected average life of the notes and hence the rating. The report concludes with an summary of the findings in Chapter 8.

Control of whole-body vibration (WBV) via a seat suspension in off-road vehicles is a challenging task due to the presence of severe external disturbances and parametric uncertainties. In this paper, a novel optimal robust (mixed ${\boldsymbol{H}_\infty }/{\boldsymbol{H}_2})$ controller is proposed to achieve enhanced vibration attenuation performance of seat suspensions considering the parametric uncertainties due to variations in driver mass and external disturbances encountered at the cabin floor including occasional shocks. A direct Lyapunov based LMI approach is employed to prove stability of the closed-loop system. In search of an optimal solution for the designed robust controller, a ${\boldsymbol{H}_\infty }$ disturbance attenuation performance together with the weighted ${\boldsymbol{H}_2}$ norm for minimizing the mean disturbance rejection, are considered using the Chaos-enhanced Accelerated Particle Swarm Optimization (CAPSO). The optimization problem for the proposed controller is formulated to minimize the frequency-weighted vibration dose value (VDV) due to acceleration response at the seat, while constraining the relative displacement between the seat and the seat base. The effectiveness of the proposed controller is illustrated through comparisons with performance achieved through some of the reported other seat suspension robust controllers in addition to a passive suspension. Results show that the proposed optimal robust controller could provide substantial reductions in the frequency-weighted acceleration at the seat and the VDV, measures of the force applied to the driver due to terrain induced vibration and shock, while limiting the relative displacement between the seat and the seat base.

Parameter uncertainty in hydrologic modeling is commonly evaluated, but assessing the impact of spatial input data uncertainty in spatially descriptive ‘distributed’ models is not common. This study compares the significance of uncertainty in spatial input data and model parameters on the output uncertainty of a distributed hydrology and sediment transport model, HYdrology Simulation using Time-ARea method (HYSTAR). The Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm was used to quantify parameter uncertainty of the model. Errors in elevation and land cover layers were simulated using the Sequential Gaussian/Indicator Simulation (SGS/SIS) techniques and then incorporated into the model to evaluate their impact on the outputs relative to those of the parameter uncertainty. This study demonstrated that parameter uncertainty had a greater impact on model output than did errors in the spatial input data. In addition, errors in elevation data had a greater impact on model output than did errors in land cover data. Thus, for the HYSTAR distributed hydrologic model, accuracy and reliability can be improved more effectively by refining parameters rather than further improving the accuracy of spatial input data and by emphasizing the topographic data over the land cover data.

The hazard and increased risk associated with slope failures in the natural habitat are attributed to uncertainty in soil parameters. These soil parameters, that is, cohesion, internal friction angle, and shear modulus, are estimated using the back-analysis method. The method incorporates machine learning algorithms such as particle swarm optimization and support vector machine. However, to capture the uncertainties in the soil parameters, probabilistic analysis is required. This study implements support vector machine for estimating soil parameters as the function of displacement in the soil. The Bayesian method is used to account for uncertainty in soil parameters. The Noto Hanto earthquake in 2007 and the consequent slope failure at Noto Yuryo Road, Japan, is considered as the case study for the proposed model. The finite-element method is used to simulate this slope failure. The soil parameters are treated as random variables to account for uncertainties in these parameters. The predicted displacement is comparable with the measured displacement in the field, which validates the application of the proposed model. The proposed method can efficiently predict experiment soil parameters by capturing uncertainty in soil parameters through a probabilistic approach.

LQG optimal control of discrete stochastic systems under parametric and noise uncertainties

Some robust control methods have been developed in the past in order to increase tracking performance in the presence of parametric uncertainties. In the presence of parametric uncertainty, unmodelled dynamics and other sources of uncertainties, robust control laws are used. Corless-Leitmann [1] approach is a popular approach used for designing robust controllers for robot manipulators. In early application of Corless-Leitmann [1] approach to robot manipulators [2, 3], it is difficult to compute uncertainty bound precisely. Because, uncertainty bound on parameters depends on the inertia parameters, the reference trajectory and manipulator state vector. Spong [4] proposed a new robust controller for robot manipulators using the Lyapunov theory that guaranties stability of uncertain systems. In this approach, Leithmann [5] or Corless-Leithman [1] approach is used for designing the robust controller. One of the advantage of Spong’s approach [4] is that uncertainty on parameter is needed to derive robust controller and uncertainty bound parameters depends only on the inertia parameters of the robots. Yaz [6] proposed a robust control law based on Spong’s study [4] and global exponential stability of uncertain system is guaranteed. However, disturbance and unmodelled dynamics are not considered in algorithm of [4, 6]. Danesh at al [7] develop Spong’s approach [4] in such a manner that control scheme is made robust not only to uncertain inertia parameters but also to robust unmodelled dynamics and disturbances. Koo and Kim [8] introduce adaptive scheme of uncertainty bound on parameters for robust control of robot manipulators. In [8], upper uncertainty bound is not known as would be in robust controller [4] and uncertainty bound is estimated with estimation law in order to control the uncertain system. A new robust control approach is proposed by Liu and Goldenerg [9] for robot manipulators based on a decomposition of model uncertainty. Parameterized uncertainty is distinguished from unparameterized uncertainty and a compensator is designed for parameterized and unparameterized uncertainty. A decomposition-based control design framework for mechanical systems with model uncertainties is proposed by Liu [10]. In order to increases tracking performance of uncertain systems, design of uncertainty bound estimation functions are considered. For this purpose, some uncertainty bound estimation functions are developed [11-15] based on a Lyapunov function, thus, stability of

Robust tracking control for vehicle electronic throttle using adaptive dynamic sliding mode and extended state observer

Acoustic Wavenumber Spectroscopy (AWS) is a technique for nondestructive testing and evaluation capable of identifying local damage in thin plates through the estimation of the characteristic wavenumber of propagating elastic waves. Current state of the art in AWS estimates wavenumber based on the maximum data fit of the wavenumber dispersion curve and derives thickness deterministically through the Lamb wave equations. Successful determination of thickness from the measurements through inverse analysis is dependent upon two aspects: uncertainties regarding material properties of the system (parametric uncertainty) and uncertainties regarding data collected in the field under less than ideal conditions (experimental uncertainty). Thus, the deterministic approach may lead to large false positives in the presence of parametric and experimental uncertainties. The focus of this paper is to develop a stochastic approach for inferring thickness from the measurements in which both parametric and experimental uncertainties are accounted for. Herein, parametric uncertainty is managed by calibrating material-dependent properties using wavenumber measurements. Experimental uncertainty is controlled through incorporation of expert judgment by means of an elicited prior uncertainty of thickness. The technological advancement produced in this study is demonstrated on a case study application of an aluminum plate with imposed thinning.

The aim of this presentation is to construct a robust optimal PID feedback controller, taking into account stochastic uncertainties in the initial conditions. Usually, a precomputed feedback control is based on exactly known model parameters. However, in practice, often exact information about model parameters and initial values is not given. Hence, having an inital point, which differs from the nominal values, a standard precomputed controller may produce bad results. Supposing now that the probability distribution of the random parameter variations is known, in the following stochastic optimisation methods will be applied in order to obtain robust optimal feedback controls. Taking into account stochastic parameter variations at the initial point, the method works with expected total costs arising from the primary control expenses and the tracking error. Furthermore, the free regulator parameters are selected then such that the expected total costs are minimized. After Taylor expansion to calculate expected cost functions and a few transformations an approximate deterministic substitute control problem follows. Here, retaining only linear terms, approximation of expectations and variances of the expected cost functions can be calculated explicitly. By means of splines, numerical approximations of the objective function and the differential equations are obtained then. Using stochastic optimization methods, random parameter variations are incorporated into the optimal control process. Hence, robust optimal feedback controls are obtained. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The optimal placement of sensors for the estimation of turbulence model parameters in computational fluid dynamics is presented. The information entropy (IE), applied on the posterior uncertainty of the model parameters inferred from Bayesian analysis, is used as a scalar measure of uncertainty. Using an asymptotic approximation, the IE depends on nominal values of the CFD model and prediction error model parameters. It is derived from the sensitivities of the flow quantities predicted by the flow model with respect to the model parameters. A stochastic optimization algorithm is used to perform the minimization of the IE in the continuous design space. Robustness to uncertainties in the nominal model parameters and flow conditions is addressed. Information redundancy due to sensor clustering is addressed by introducing spatially correlated prediction error models. The algorithm is applied to the turbulent flow through a backward-facing step where the optimal locations of velocity and Reynolds shear stress profiles of sensors are sought for the estimation of the parameters of the Spalart-Allmaras turbulence model. © 2015 by Begell House, Inc.

Optimal placement of voltage measurements for wide area fault location observability considering the uncertainty of network parameters

In this article, the practical problem of current tracking for Brushless Direct Current motors is approached. The main feature of the contribution lies in the fact that uncertainty in the parameters of the motor's model is considered. This lack of knowledge is compensated by proposing an adaptive control scheme that directly deals with the uncertainty in the electrical parameters without requiring any knowledge, neither of the mechanical parameters nor the load torque, as long as this external disturbance remains bounded. The strength of the proposed control scheme appears from the passivity‐based decomposition of the motor's model allowing robust control of the electrical subsystem without requiring mechanical information, providing the rotor speed remains bounded. Moreover, achievement of the control objective does not rely on estimated parameter convergence to the real values. The stability properties of the proposed scheme are mathematically proved using classical results from the passivity and the adaptive control theories, which makes it attractive from a practical perspective. Moreover, it exhibits a simple structure and is easy to tune. The usefulness of the contribution is validated in an experimental setting using the BLY344S‐240V‐3000 motor manufactured by Anaheim Automation.