Effect Of Stochastic Disturbances Research Articles

A model-based tracking control scheme for nonlinear industrial processes involving joint unscented Kalman filter

This paper proposes a model-based reference tracking scheme for stable, MIMO, nonlinear processes. A Joint Unscented Kalman Filtering technique is exploited here to develop a stochastic model of the physical process via simultaneous estimation of the process states and the time-varying/uncertain parameters. Unlike the existing nonlinear model predictive controllers, the proposed scheme does not involve any dynamic optimisation process, which helps to reduce the overall complexity, computation overburden and execution time. Furthermore, the proposed methodology offers robustness to process model-mismatch and considers the effects of stochastic disturbances. A nonlinear two-tank liquid-level control problem and a nonlinear coupled level-temperature control process are studied to demonstrate the usefulness of the proposed scheme.

Modeling and simulation of stochastic transients in power systems based on frequency shifting theory

The increasing uncertainties in power systems have brought non-negligible influences on the dynamic behaviors. An accurate and efficient simulation method considering the effects of stochastic disturbances is of critical importance for the analysis of the dynamic performance of power systems. In this paper, a methodology for the simulation of stochastic transients in power systems is developed based on frequency shifting theory. The stochastic differential equations describing the stochastic process of parameter migration are represented through analytic signals. The frequency shifting operation is introduced. The Fourier spectra of analytic signals are shifted to reduce their maximum frequency contents, thereby permitting a larger time-step in time-domain simulation in accordance with Shannon’s sampling theory. Through the trapezoidal Milstein scheme, the stochastic differential equations with shifted analytic signals are discretized. Branch companion models that process analytic signals for the simulation of stochastic transients are formulated. The numerical properties of branch models are further examined. The analysis of test cases demonstrates that the proposed method can be used to represent stochastic transients caused by parameter migrations accurately and efficiently.

Ellipsoidal Design of Robust Stabilization for Markov Jump Power Systems under Normal and Contingency Conditions

The essential prerequisites for secure customer service are power system stability and reliability. This work shows how to construct a robust switching control for studying power system load changes using an invariant ellipsoid method. Furthermore, the suggested control ensures stability when the system is subjected to random stochastic external disturbances, and functions randomly in two conditions: normal and contingency. The extreme (least) reliability state is chosen as the most severe scenario (corresponding to a transmission line outage). As a two-state Markov random chain, the transition probabilities are utilized to simulate the switching between normal and contingency modes (or processes). To characterize the dynamics of the studied system, a stochastic mathematical model is developed. The effect of stochastic disturbances and random normal/contingency operations is taken into account during the design stage. For a stochastic power system, a novel excitation control is designed. The attractive ellipsoid approach and linear matrix inequalities (LMIs) optimization are used to build the best two-controller gains. Therefore, the proposed modeling/design technique can be employed for the power system under load changes, stochastic topological changes, and random disturbances. Finally, the system’s random dynamics simulation indicates the effectiveness of the designed control law.

An investigation of the response characteristics of a system of coupled resonant circuits to stochastic disturbance

The solution to the problem of searching for the reaction of multi-frequency oscillatory systems to random action based on the residual method is proposed. The mathematical foundations of the proposed approach are presented and justified. The regularity of the reaction is demonstrated for various exposure and system parameters. The effect of stochastic disturbance on the behavior of the system is studied. The proposed theoretical foundations for solving the problem of searching for the response of multi-frequency oscillatory systems to random action based on the residual method are confirmed by the results of the simulation. Table: 1. Refs.: 13 titlesKeywords: system of coupled oscillatory circuits; multi-frequency oscillatory system; system response; residual method.

Bayesian approach to identify Hammerstein–Wiener non‐linear model in presence of noise and disturbance

In this study, a recursive algorithm is presented for identification of both linear and non-linear blocks of the Hammerstein–Wiener (H–W) models. An iterative sampling schema is used, along with non-parametric describing of non-linear functions by Gaussian processes, to consider the Gaussian distributed noise and disturbances. Different aspects of solving the H–W problem are discussed, covering the formulation of the non-linear functions, uniqueness assumptions and the effect of stochastic disturbances on the solution. The proposed method is used to identify an H–W model for the systems encounter all possible disturbances consists of input and output measurement noise, disturbances in the linear block and the additive disturbances to the interconnecting signals of the linear and non-linear blocks. Effectiveness and simplicity of the method are shown by an example. The results show that the accuracy of the proposed method is acceptable in presence of noise and disturbances.

Dynamic Collection Strategy and Coordination of a Remanufacturing Closed-Loop Supply Chain under Uncertainty

This paper aims to investigate the uncertainty factors that impact the collection strategy of a remanufacturing closed-loop supply chain. The basis of this type of supply chain is the collection of used products, without which the remanufacturing of new products would be out of the question. In this paper, we considered the effect of stochastic disturbance on the collection process in a closed-loop supply chain consisting of a manufacturer and a retailer, in which the manufacturer is responsible for collecting the used products. Considering stochastic disturbance, in this research, we proposed a stochastic collection model, and derived the feedback control strategies for both the manufacturer and retailer. Next, we investigated the evolutionary path and probability distribution of the stochastic return rate. Finally, we proposed a contract to coordinate the decentralized closed-loop supply chain. The results showed that the manufacturer would improve the level of return effort as the intensity of stochastic disturbance increases. However, the disturbance would not affect the pricing strategies of the supply chain members. As a result of the stochastic disturbance, the return rate always hovered around the expected return rate, while the expectation and variance of the return rate remained stable from a long-term perspective. The expected value and variance of the return rate could decrease or increase with time, depending on the value of the initial return rate of the system.

Solution of the discrete-time stochastic optimal control problem in the 2-domain

The design of discrete-time optimal multivariate systems is considered in the z-domain. The constant plant can be non-square, unstable and/or non-minimum phase and feedback system dynamics can be modelled. The stationary coloured noise processes are assumed to be represented by discrete rational spectral densities. The system can contain transport delay elements and the effects of plant saturation can be limited by the choice of performance criterion. The system inputs are assumed to contain both stochastic and deterministic components. The two-stage design procedure is original and it enables the stochastic and deterministic control functions to be separated, A performance criterion is first defined which is insensitive to the deterministic signals and this defines the closed-loop optimal controller. The resulting closed-loop system acts as an optimum regulator to minimize the effects of stochastic disturbances. A second tracking error performance criterion is then specified which determines the optimal ...

Design of stochastic optimal feedback control systems

The design of stochastic, linear, multivaribale feedback systems is considered where the plant is constant and the noise processes are stationary. The plant can be unstable and nonminimum-phase and feedback-system dynamics can be modelled. Approximate methods are described for limiting the effects of plant saturation and for modelling transport delays. The closed-loop system is assumed, to have a coloured process, disturbance and measurement noise inputs and a coloured reference input. The plant disturbance and the closed-loop-system reference inputs are also assumed to contain deterministic components, e.g. step or ramp signals. The design procedure is original and involves two stages. A performance criterion is defined first that is not sensitive to the deterministic signals, and this defines the closed-loop controller. The resulting closed-loop system acts as an optimum regulator to minimise the effects of stochastic disturbances. A second tracking-error performance criterion is then specified that determines the optimal reference input to the closed-loop system. This reference signal is generated by two optimal open-loop controllers. One controller ensures the plant output is following a desired trajectory, and the second acts as a feedforward controller to offset plant disturbances.