Presence Of Random Disturbances Research Articles

Simulation-Based Design of an Efficient Control System for the Continuous Purification and Processing of Active Pharmaceutical Ingredients

In this study, an efficient system-wide controlsystem has been designed for the integrated continuous purification and processing of the active pharmaceutical ingredient (API). The control strategy is based on the regulatory PID controller which is most widely used in the manufacturing industry because of its simplicity and robustness. The designed control system consists of single and cascade (nested) control loops. The control system has been simulated in gPROMSTM (Process System Enterprise). The ability of the control system to track the specified set point changes as well as to reject disturbances has been evaluated. Results demonstrate that the model shows an enhanced performance in the presence of random disturbances under closed-loop control compared to an open-loop operation. The control system is also able to track the set point changes effectively. This proves that closed-loop feedback control can be used in improving pharmaceutical manufacturing operations based on the Quality by Design (QbD) paradigm.

Robustness of globally exponential stability of delayed neural networks in the presence of random disturbances

This paper analyzes the robustness of globally exponential stability of time-varying delayed neural networks (NNs) subjected to random disturbances. Given a globally exponentially stable neural network, and in the presence of noise, we quantify how much noise intensity that the delayed neural network can remain to be globally exponentially stable. We characterize the upper bounds of the noise intensity for the delayed NNs to sustain globally exponential stability. The upper bounds of parameter uncertainty intensity are characterized by using transcendental equation. A numerical example is provided to illustrate the theoretical result.

Fluctuation-dissipation relationships used for calculating the response of the soil moisture content to atmospheric actions

Methods of stochastic dynamics based on the application of fluctuation theorems (FTs) are used for describing nonstationary responses of natural objects to specified finite, but not necessarily small, changes in external factors in the presence of random disturbances. Nonlinear fluctuation-dissipation relationships (FDRs) are obtained on the basis of one of the FTs. These FDRs are used for calculating the soil moisture content response to specified changes in the mean precipitation in the presence of synoptic disturbances. The model under consideration, in spite of its coarseness, includes an important nonlinear effect of the moisture excess discharge into a reservoir. An approximate analytical theory is constructed. This theory makes it possible to take into account nonlinear effects when response functions are determined.

Iteration algorithms for dynamically tuning regulators in the presence of random disturbances

Peculiarities of implementing iteration algorithms for dynamically tuning regulators in the presence of random disturbances are considered. An algorithm for dynamically tuning regulators with filtration of interference and taking into account of the combined effect of high-and low-frequency disturbances is proposed.

Optimal selection of the forgetting matrix into an iterative learning control algorithm

A recursive optimal algorithm, based on minimizing the input error covariance matrix, is derived to generate the optimal forgetting matrix and the learning gain matrix of a P-type iterative learning control (ILC) for linear discrete-time varying systems with arbitrary relative degree. This note shows that a forgetting matrix is neither needed for boundedness of trajectories nor for output tracking. In particular, it is shown that, in the presence of random disturbances, the optimal forgetting matrix is zero for all learning iterations. In addition, the resultant optimal learning gain guarantees boundedness of trajectories as well as uniform output tracking in presence of measurement noise for arbitrary relative degree.

The Quantization Property of Probability Distributions of the Characteristics of Dynamic Systems Observed in the Presence of Random Disturbances

The class of linear stochastic dynamic systems is defined, such that the laws of the probability distribution of values of output signals of a system are determined by its equations complying with the case of the absence of random disturbances. These distribution laws are found to be similar to the quantum laws of the distribution values of observable physical quantities. On this basis, a possibility of the definition of the quantum systems as systems of this class is investigated. It is shown that the theoretical proof of some axioms of quantum mechanics and new facts requiring the experimental verification follow from this definition.

Testing for hysteresis against nonlinear alternatives

A number of studies have hypothesised certain economic behaviour to be hysteretic, but few have actually been able to establish hysteretic behaviour in the data. This is because of the lack of an effective test for hysteresis. This paper compares and contrasts two new measures of hysteretic behaviour, designed explicitly for detecting hysteresis in economic systems. Using Monte Carlo techniques, we show that one has considerably more power than the other against nonlinear, cyclical or multiple equilibria alternatives in the presence of random disturbances. The key properties of this measure appear to be functional form independence and rate independence.

Stochastic adaptive control using multiple models for improved performance in the presence of random disturbances

Stochastic adaptive control using multiple models for improved performance in the presence of random disturbances

Stochastic adaptive control using multiple models for improved performance in the presence of random disturbances

AbstractThe use of multiple models for adaptively controlling an unknown continuous‐time linear system was proposed in Narendra and Balakrishnan (IEEE Transactions on Automatic Control 1994; 39(9):1861–1866). and discussed in detail in Narendra and Xiang (IEEE Transactions on Automatic Control 2000, 45(9):(1669–1686) Technical Reports 9801 and 9803, Centre for System Science, Yale University, 1998). Recently, the same concepts were extended to discrete‐time systems, both for the noise free case as well as when a stochastic disturbance is present, and the convergence of the algorithms was established. In this paper we consider structurally different estimation models, and use the multiple models approach to select, on‐line, the one that results in the best performance of the overall system for the given disturbance characteristics. The principal objective of the paper is to demonstrate that the convergence of these schemes can be treated in a unified manner. Simulations are included towards the end of the paper to indicate the improvement in performance that can be achieved using such schemes. Copyright © 2001 John Wiley & Sons, Ltd.

Iterative Learning Control for Nonlinear Nonminimum Phase Plants1

Learning control is a very effective approach for tracking control in processes occurring repetitively over a fixed interval of time. In this paper a robust learning algorithm is proposed for a generic family of nonlinear, nonminimum phase plants with disturbances and initialization error. The “stable-inversion” method of Devasia, Chen and Paden is applied to develop a learning controller for linear nonminimum phase plants. This is adapted to accommodate a more general class of nonlinear plants. The bounds on the asymptotic error for the learned input are exhibited via a concise proof. Simulation studies demonstrate that in the absence of input disturbances, perfect tracking of the desired trajectory is achieved for nonlinear nonminimum phase plants. Further, in the presence of random disturbances, the tracking error converges to a neighborhood of zero. A bound on the tracking error is derived which is a continuous function of the bound on the disturbance. It is also observed that perfect tracking of the desired trajectory is achieved if the input disturbance is the same at every iteration.

Optimal synthesis of smart measurement systems with adaptive correction of drifts and setting errors of the sensor's working point

This paper deals with a problem in optimal synthesis of smart measurement systems. A nonlinear model of the sensor is introduced, and directly applied to the derivation of optimal algorithms for processing measurement data. The analysis is performed for systems with both noncompensatory and compensatory sensors. It is assumed that a measurement is performed in the presence of random disturbances and noise. The algorithms developed take into account the limited input-output range of the sensor as well as the influence of its internal noise on measurement quality. Simultaneously, they automatically and optimally correct errors in the initial setting of the sensor's working point, as well as those caused by its random drift.

Fault Detection in Induction Motors via Parameter Estimation Techniques

This paper deals with the application of model-based fault detection in an induction motor. Two different techniques (based on the extended Kalman filter) for estimating the physical parameters of the induction motor are presented A high performing simulator is used to perform identification experiments. In order to decide whether the discrepancy between the identified parameter values and the reference ones is significant in the presence of random disturbances and modelling errors, a robust decision test is implemented

Sequence estimation in the presence of random parameters via the EM algorithm

The expectation-maximization (EM) algorithm was first introduced in the statistics literature as an iterative procedure that under some conditions produces maximum-likelihood (hit) parameter estimates. In this paper we investigate the application of the EM algorithm to sequence estimation in the presence of random disturbances and additive white Gaussian noise. As examples of the use of the EM algorithm, we look at the random-phase and fading channels, and show that a formulation of the sequence estimation problem based on the EM algorithm can provide a means of obtaining ML sequence estimates, a task that has been previously too complex to perform.

Design of Global Control Algorithm for Irrigation Canals

The problem of irrigation canal regulation under demand delivery operation was formulated as an optimal control problem. To apply the linear optimal control theory, the Saint-Venant equations of open-channel flow were linearized using the Taylor series after using a finite-difference approximation on the original nonlinear, partial differential equations. A proportional-plus-integral (PI) controller was developed using the concepts of linear optimal control theory. Since the order of the controller gain matrix was large, an optimal observer (Kalman filter) was designed to estimate values for the variables that were not measured. An example irrigation canal with five pools was considered. With the finite-difference technique used, there was a total of 45 state variables and five control variables (gates) in the problem. With two measurements per pool, values for 35 state variables were estimated using the observer. By subjecting the canal to random disturbances of up to 40% of the initial inflow rate into the canal, the simulated performance of the global feedback control algorithm along with the Kalman filter was found to be acceptable in terms of achieving either a constant-volume control or a constant-level control in the canal pools in the presence of random disturbances in lateral flow rates.

Self-tuning adaptive control of engine speed in the presence of random disturbances

This work deals with the control of engine speed systems that are subjected to unknown and time-varying external load disturbances, and have varying structural parameters due to the uncertainties of the system's performance. The conventional approach to the controller design of such system may not assure satisfactory control performance. A self-tuning adaptive control algorithm is presented and an on-line estimation strategy based on the recursive maximum likelihood method for the system parameters is developed. The estimation strategy updates the system dynamics to the adaptive controller, this enables the controller to control the engine speed system for the best transient and steady state response. Computer simulation results of the suggested estimation-adaptation algorithms, and comparative analysis of the adaptive scheme with the conventional control approach are presented.

Estimating the solutions of linear stochastic equations by the information criterion

The information criterion is applied to estimate the state of linear dynamic systems in the presence of random disturbances on the input and the output. The problem of finding the best information estimator is reduced to an optimal control problem. An expression for the maximum mean information is derived. Recursive Kalman-Bucy filters are constructed.

Risk and control of a stochastic distributed system using the level exceeding probability of an integral quadratic criterion

Here x(t) and w(t) are N-component vectors describing the system and the external white noise; N is the dimension of the system with the N • N matrix A. In order to refine the analysis of the accuracy characteristics of synthesized systems in the presence of random disturbances, we need to investigate the statistical properties of the integral quadratic criterion. While the solution of the synthesis problem requires only information about the mean value of the functional, the choice of optimal dimension for finite-dimensional models, observers, and controllers, and of various alternatives by comparison of the random values of the integral quadratic criterion requires a complete statistical description of the functional, i.e., evaluation of the distribution density of the criterion. We propose a new approach to this problem, based on construction of the generating function of the sought criterion. Consider an integral criterion of the form

Multimodel strategies under random disturbances and imperfect partial observations

Multimodel strategies in which control agents use different simplified models of the same system are studied for interconnected systems with slow and fast dynamics. The well-posedness of multimodel strategies in the presence of random disturbances and imperfect partial observations is established by studying an LQG control problem. The study reveals that for the well-posedness of multimodel strategies control agents need to communicate their observations and decisions. The need to communicate decisions does not arise when all agents use the same overall model to compute the optimal control.

Informational uniqueness of closed-loop Nash equilibria for a class of nonstandard dynamic games

This paper discusses an extension of the currently available theory of noncooperative dynamic games to game models whose state equations are of order higher than one. In a discrete-time framework, it first elucidates the reasons why the theory developed for first-order systems is not applicable to higher-order systems, and then presents a general procedure to obtain an informationally unique Nash equilibrium solution in the presence of random disturbances. A numerical example solved in the paper illustrates the general approach.

Multimodel Strategies Under Random Disturbances and Imperfect Partial Observations

Multimodel stategies in which control agents use different simplified models of the same system are studied for interconnected systems with slow and fast dynamics. The well-posedness of multimodel strategies in the presence of random disturbances and imperfect partial observations is established by studying an LOG control problem. The study reveals that for the well-posedness of multimodel strategies control agents need to communicate their observations and decisions. The need to communicate decisions does not arise when all agents use the same overall model to compute the optimal control.