Time-delay estimation for nonlinear systems with piecewise-constant input

We consider a general nonlinear time-delay system in which the input signal is piecewise-constant. Such systems arise in a wide range of industrial applications, including evaporation and purification processes and chromatography. We assume that the time-delays—one involving the state variables and the other involving the input variables—are unknown and need to be estimated using experimental data. We formulate the problem of estimating the unknown delays as a nonlinear optimization problem in which the cost function measures the least-squares error between predicted and measured system output. The main difficulty with this problem is that the delays are decision variables to be optimized, rather than fixed values. Thus, conventional optimization techniques are not directly applicable. We propose a new computational approach based on a novel algorithm for computing the cost function’s gradient. We then apply this approach to estimate the time-delays in two industrial chemical processes: a zinc sulphate purification process and a sodium aluminate evaporation process

Approximations for the Moments of Nonstationary and State Dependent Birth-Death Queues

In this paper we propose a new method for approximating the nonstationary moment dynamics of one dimensional Markovian birth-death processes. By expanding the transition probabilities of the Markov process in terms of Poisson-Charlier polynomials, we are able to estimate any moment of the Markov process even though the system of moment equations may not be closed. Using new weighted discrete Sobolev spaces, we derive explicit error bounds of the transition probabilities and new weak a priori estimates for approximating the moments of the Markov processs using a truncated form of the expansion. Using our error bounds and estimates, we are able to show that our approximations converge to the true stochastic process as we add more terms to the expansion and give explicit bounds on the truncation error. As a result, we are the first paper in the queueing literature to provide error bounds and estimates on the performance of a moment closure approximation. Lastly, we perform several numerical experiments for some important models in the queueing theory literature and show that our expansion techniques are accurate at estimating the moment dynamics of these Markov process with only a few terms of the expansion

Model predictive control based on LPV models with parameter-varying delays

© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This paper presents a Model Predictive Control (MPC) strategy based on Linear Parameter Varying (LPV) models with varying delays affecting states and inputs. The proposed control approach allows the controller to accommodate the scheduling parameters and delay change. By computing the prediction of the state variables and delay along a prediction time horizon, the system model can be modified according to the evaluation of the estimated state and delay at each time instant. Moreover, the solution of the optimization problem associated with the MPC design is achieved by solving a series of Quadratic Programming (QP) problem at each time instant. This iterative approach reduces the computational burden compared to the solution of a non-linear optimization problem. A pasteurization plant system is used as a case study to demonstrate the effectiveness of the proposed approach.Peer ReviewedPostprint (author's final draft

An analysis at mesospheric coherent-scatter power enhancements during solar flare events

Solar flares produce increases in coherent-scatter power from the mesosphere due to the increase in free electrons produced by X-ray photoionization. Thirteen such power enhancements were observed at Urbana. When such an enhancement occurs at an altitude containing a turbulence layer with constant strength, the relative enhancement of electon density is estimated from the enhancement in power. Such estimates of enchanced electron density are compared with estimates of the X-ray photoionization at that altitude, deduced from geostationary satellite measurements. It is found that possible types ion-chemical reaction scheme may be distinguished, and the nonflare ion-pair production function may be estimated. The type of ion-chemical scheme and the nonflare ion-production function are shown to depend on the solar zenith angle

Online Drift Compensation for Chemical Sensors Using Estimation Theory

Sensor drift from slowly changing environmental conditions and other instabilities can greatly degrade a chemical sensor\u27s performance, resulting in poor identification and analyte quantification. In the present work, estimation theory (i.e., various forms of the Kalman filter) is used for online compensation of baseline drift in the response of chemical sensors. Two different cases, which depend on the knowledge of the characteristics of the sensor system, are studied. First, an unknown input is considered, which represents the practical case of analyte detection and quantification. Then, the more general case, in which the sensor parameters and the input are both unknown, is studied. The techniques are applied to simulated sensor data, for which the true baseline and response are known, and to actual liquid-phase SH-SAW sensor data measured during the detection of organophosphates. It is shown that the technique is capable of estimating the baseline signal and recovering the true sensor signal due only to the presence of the analyte. This is true even when the baseline drift changes rate or direction during the detection process or when the analyte is not completely flushed from the system

Maximizing information on the environment by dynamically controlled qubit probes

We explore the ability of a qubit probe to characterize unknown parameters of its environment. By resorting to quantum estimation theory, we analytically find the ultimate bound on the precision of estimating key parameters of a broad class of ubiquitous environmental noises ("baths") which the qubit may probe. These include the probe-bath coupling strength, the correlation time of generic bath spectra, the power laws governing these spectra, as well as their dephasing times T2. Our central result is that by optimizing the dynamical control on the probe under realistic constraints one may attain the maximal accuracy bound on the estimation of these parameters by the least number of measurements possible. Applications of this protocol that combines dynamical control and estimation theory tools to quantum sensing are illustrated for a nitrogen-vacancy center in diamond used as a probe.Comment: 8 pages + 6 pages (appendix), 3 Figure

Performance Monitoring of Control Systems using Likelihood Methods

Evaluating deterioration in performance of control systems using closed loop operating data is addressed. A framework is proposed in which acceptable performance is expressed as constraints on the closed loop transfer function impulse response coefficients. Using likelihood methods, a hypothesis test is outlined to determine if control deterioration has occurred. The method is applied to a simulation example as well as data from an operational distillation column, and the results are compared to those obtained using minimum variance estimation approaches