Finite Energy Disturbances Research Articles

New Safety Feedback Control Design to Guarantee Adequate Frequency Performance in Microgrids

ABSTRACTSafety analysis of power systems is concerned with the system's ability to maintain critical variables within specified limits following a disturbance. Frequency control adequacy has become increasingly important as the system inertia decreases due to the increase in renewable energy penetration. Various controllers for inverters have been proposed to improve the system frequency response and few are capable to ensure the safety of the response. In this article, a diesel‐wind energy system is considered and modeled as a switching system between normal, faulted, and post‐fault modes. A safety feedback controller is designed as a supplementary signal for a wind turbine generator such that the speed of the diesel generator stays within a permissible range in the presence of a finite energy disturbance. Numerical results on the modified 33‐bus microgrid system obtained of the proposed novel approach indicate that the suggested control configuration can guarantee adequate frequency response without excessive conservativeness.

The H∞‐optimal control problem of CSVIU systems

AbstractThe article devises an ‐norm theory for the CSVIU (control and state variations increase uncertainty) class of stochastic systems. This system model appeals to stochastic control problems to express the state evolution of a possibly nonlinear dynamic system restraint to poor modeling. It introduces the control with infinity energy disturbance signals, contrary to usual stochastic formulations, which mimic deterministic models dealing with finite energy disturbances. The reason is to portray the persistent perturbations due to the environment more naturally. In this regard, it develops a refined connection between a notion of stability and the system's power finiteness. It delves into the control solution employing the relations between optimization and differential games, connecting the worst‐case stability analysis of CSVIU systems with a perturbed Lyapunov type of equation. The norm characterization relies on the optimal cost induced by the min–max control strategy. The solvability of a generalized game‐type Riccati equation couples to the rise of a pure saddle point, yielding the global solution of the CSVIU dynamic game. In the way to the optimal stabilizing compensator, the article finds it based on linear feedback stabilizing gain from solving the Riccati equation together with a spectral radius test of an ensuing matrix. The optimal disturbance compensator produces inaction regions in the sense that, for sufficiently minor deviations from the model, the optimal action is constant or null in the face of the uncertainty involved. Finally, an explicit solution approximation developed by a Monte Carlo method appears, and a numerical example illustrates the synthesis.

Fault Tolerant Control of Sensor Faults in Microgrid Inverter Control System

Aiming at sensor drift fault, the design problem of active fault tolerant controller for island-AC microgrid inverter system is studied. The controller has good ability to suppress external finite energy disturbance. Firstly, a closed-loop system state space model is constructed for an isolated AC microgrid inverter system with external finite energy disturbance. Then, when the sensor fault occurs in the control system, the fault information is taken as an auxiliary state vector, and the estimated value of the sensor fault and the system state variable is obtained simultaneously through the proposed extended observer. A fault tolerant controller is designed based on the idea of fault compensation. Finally, the correctness and effectiveness of this method are verified by programming simulation in MATLAB.

Hybrid Robust H2/H∞ Fault-Tolerant Control with Random Delay NCS

In this paper, a hybrid fault-tolerant control method with off-line design and online scheduling is proposed for NCS with actuator faults, random delay, and external finite energy disturbance. The problem of less conservatism of robust generalized H2/H∞ hybrid fault-tolerant control is studied. Firstly, a closed-loop fault model of the system with random delay parameters was established according to the Bernoulli 0-1 distribution; all possible prior faults are divided into a few intervals according to certain rules, and then an interval fault-tolerant controller is designed off-line according to the prior faults of each interval. Secondly, when the fault is estimated online, the corresponding interval fault-tolerant controller is called through the scheduling mechanism to achieve rapid fault tolerance of prior faults within the interval and mitigate the impact of other faults within the interval, which provides a guarantee for subsequent safe reconstruction control. Finally, the effectiveness of the proposed method is verified by Matlab simulation.

Fault estimation and optimization for uncertain disturbed singularly perturbed systems with time-delay

This paper presents a observer-based fault estimation method for a class of singularly perturbed systems subjected to parameter uncertainties and time-delay in state and disturbance signal with finite energy. To solve the estimation problem involving actuator fault and sensor fault for the uncertain disturbed singularly perturbed systems with time-delay, the problem we studied is firstly transformed into a standard $ H_\infty $ control problem, in which the performance index $ \gamma $ represents the attenuation of finite energy disturbance. By adopting Lyapunov function with the $ \varepsilon $-dependence, a sufficient condition can be derived which enables the designed observer to estimate different kinds of fault signals stably and accurately, and the result obtained by dealing with small perturbation parameter in this way is less conservative. A novel multi-objective optimization scheme is then proposed to optimal disturbance attenuation index $ \gamma $ and system stable upper bound $ \varepsilon^* $, in this case, the designed observer can estimate the fault signals better in the presence of interference when the systems guarantee maximum stability bound. In the end, the validity and correctness of proposed scheme is verified by comparing the error between the estimated faults and the actual faults.

On the <inline-formula> <tex-math notation="LaTeX">$l_2$ </tex-math> </inline-formula>-<inline-formula> <tex-math notation="LaTeX">$l_\infty$ </tex-math> </inline-formula> and <inline-formula> <tex-math notation="LaTeX">$H_\infty$ </tex-math> </inline-formula> Performances of the Continuous-Time Deadbeat <inline-formula> <tex-math notation="LaTeX">$H_2$ </tex-math> </inline-formula> FIR Filter

The continuous-time deadbeat $ H_{ 2}$ finite impulse response filter (CTDH2FF) was originally designed by Ahn to diminish the effect of external disturbances. In this brief, we provide an in-depth investigation of the CTDH2FF and show that it also obeys the $ l_{ 2}$ – $ l_{ \infty }$ filtering performance to capture the peak value of the filter error for finite energy disturbances. We also prove that the CTDH2FF satisfies the robust $ H_{ \infty }$ filtering performance criterion to consider the filter error energy for finite energy external disturbances. Finally, the determination of the horizon size for the CTDH2FF considering both the $ l_{ 2}$ – $ l_{ \infty }$ and $ H_{ \infty }$ filtering performance bounds based on a numerical example of the F-404 engine model is discussed.

Lyapunov-based design of resilient mixed MSE-dissipative-type state observers for a class of nonlinear systems and general performance criteria

A class of continuous-time nonlinear system and measurement equations having locally incrementally conic nonlinearities and finite energy disturbances is considered. A Lyapunov-based resilient mixed mean square error (MSE)-dissipative-type state observer design approach is presented, which guarantees the satisfaction of MSE-type estimation error performance together with a variety of dissipative performance criteria ranging from H∞ to passivity of various types. Linear matrix inequalities are used in the feasibility study of the solution. Some simulation examples are included to illustrate and provide support to the effectiveness of the proposed design methodology.

A robust state-space kinetics-guided framework for dynamic PET image reconstruction

Dynamic PET image reconstruction is a challenging issue due to the low SNR and the large quantity of spatio-temporal data. We propose a robust state-space image reconstruction (SSIR) framework for activity reconstruction in dynamic PET. Unlike statistically-based frame-by-frame methods, tracer kinetic modeling is incorporated to provide physiological guidance for the reconstruction, harnessing the temporal information of the dynamic data. Dynamic reconstruction is formulated in a state-space representation, where a compartmental model describes the kinetic processes in a continuous-time system equation, and the imaging data are expressed in a discrete measurement equation. Tracer activity concentrations are treated as the state variables, and are estimated from the dynamic data. Sampled-data H∞ filtering is adopted for robust estimation. H∞ filtering makes no assumptions on the system and measurement statistics, and guarantees bounded estimation error for finite-energy disturbances, leading to robust performance for dynamic data with low SNR and/or errors. This alternative reconstruction approach could help us to deal with unpredictable situations in imaging (e.g. data corruption from failed detector blocks) or inaccurate noise models. Experiments on synthetic phantom and patient PET data are performed to demonstrate feasibility of the SSIR framework, and to explore its potential advantages over frame-by-frame statistical reconstruction approaches.

Design of mixed H2-dissipative observers with stochastic resilience for discrete-time nonlinear systems

Abstract A linear matrix inequality based mixed H2-dissipative type state observer design approach is presented for smooth discrete time nonlinear systems with finite energy disturbances. This observer is designed to maintain H2 type estimation error performance together with either H∞ or a passivity type disturbance reduction performance in case of randomly varying perturbations in its gain. A linear matrix inequality is used at each time instant to find the time-varying gain of the observer. Simulation studies are included to explore the performance in comparison to the extended Kalman filter and a previously proposed constant gain observer counterpart.

On reference model tracking for Markov jump systems

This article deals with the tracking problem for the Markov Jump systems with external finite energy disturbance. A state feedback controller that makes the state vector of the system track precisely a given state vector of a reference model is proposed. The tracking problem is formulated as an ℋ∞ control problem and an approach to synthesise the state feedback controller that quadratically stabilises the augmented dynamics and at the same time rejects the external disturbance that is developed. This approach is based on the solution of some linear matrix inequalities. A numerical example is provided to show the usefulness of the developed results.

Mixed H2/H∞ residual generator design via Heuristic Kalman Algorithm

This paper presents a simple but effective synthesis strategy for observers based faults detection in linear time-invariant (LTI) systems which are simultaneously affected by two classes of unknown inputs: Noises having fixed spectral densities and unknown finite energy disturbances. The problem of designing such an observer, also called a residual generator, is formulated as a mixed H2/H∞ optimization problem. This is done to obtain an optimal residual generator, i.e. with minimal sensitivity to unknown inputs. Unfortunately, there is no known solution to this difficult optimization problem. Finding such a residual generator is known to be computationally intractable via the conventional techniques. This is mainly due to the non-convexity of the resulting optimization problem. To solve this kind of problem easily and directly, without using any complicated mathematical manipulations, we utilize the Heuristic Kalman Algorithm (HKA) for the resolution of the underlying constrained non-convex optimization problem. A numerical example is given to illustrate the advantage of the mixed H2/H∞ optimization approach against techniques based on optimization of H2 or H∞ criteria.

State Feedback Controller Design for a Class of Nonlinear Systems with General Criteria

In this work, we provide a framework for the design of linear state feedback controllers for a class of continuous-time conic nonlinear systems driven by finite energy disturbances. This controller design is presented for various performance criteria in a unified framework using linear matrix inequalities in the formulation. Illustrative examples are included.

Stochastically Resilient Design of Mixed H2-Dissipative Observers for Discrete-Time Nonlinear Systems

A linear matrix inequality based mixed H2-Dissipative type state observer design approach is presented for smooth discrete time nonlinear systems with finite energy disturbances. This observer is designed to maintain H2 type estimation error performance together with either H∞ or a passivity type disturbance reduction performance in case of randomly varying perturbations in its gain. A linear matrix inequality is used at each time instant to find the time-varying gain of the observer. Simulation studies are included to explore the performance in comparison to the extended Kalman filter.

Discrete-time nonlinear observer design with general criteria

A class of discrete-time nonlinear system and measurement equations having incrementally conic nonlinearities and finite energy disturbances is considered. A linear matrix inequality-based design approach is presented, which guarantees the satisfaction of a variety of performance criteria ranging from simple estimation error boundedness to dissipativity. Some simulation examples are included to illustrate and provide support to the proposed design methodology.

Fault detection in a mixed H/sub 2//H/sub /spl infin// setting

In this note, we study the problem of fault detection in linear time-invariant (LTI) systems which are simultaneously effected by two classes of unknown inputs: Noises having fixed spectral densities and unknown finite energy disturbances. This problem is formulated as a mixed H/sub 2//H/sub /spl infin// filtering problem. Necessary and sufficient conditions for local optimality are presented. Moreover, it is shown that suboptimal solutions can be computed by solving a convex minimization problem with a set of linear matrix inequality (LMI) constrains. A numerical example is given to illustrate the advantage of the mixed H/sub 2//H/sub /spl infin// approach as compared to existing techniques which are based on optimization of H/sub 2/ and H/sub /spl infin// criteria.

State estimation of uncertain nonlinear stochastic systems with general criteria

A general class of discrete-time uncertain nonlinear stochastic systems corrupted by finite energy disturbances and estimation performance criteria are considered. These performance criteria include guaranteed-cost suboptimal versions of estimation objectives like H 2, H ∞, stochastic passivity, etc. Linear state estimators that satisfy these criteria are presented. A common matrix inequality formulation is used in characterization of estimator design equations.

LMI Approach to Mixed H-2 and H-infinity Performance Objective Controller Design

The problem of synthesizing controllers for plants subject to arbitrary, finite energy disturbances and white noise disturbances via Linear Matrix Inequalities (LMIs) is presented. This is achieved by considering white noise disturbances as belonging to a constrained set in l2. In the case where only white noise disturbances are present, the procedure reduces to standard H2 synthesis. When arbitrary, finite energy disturbances are also present, the procedure may be used to synthesize general mixed performance objective controllers, and for certain cases. Robust H2 controllers.

Optimum guidance with a single uncertain time lag

A disturbance attenuation problem that corresponds to optimal target interception is considered. In this problem the target's jerk is modeled as a finite energy disturbance, and the commanded acceleration of the interceptor is the control variable, to which the actual acceleration is assumed to be related via a single uncertain tune lag. The interceptor's optimal strategy is obtained by considering an auxiliary disturbance attenuation problem in which an additional fictitious disturbance of finite energy, which corresponds to the uncertainty, is introduced. The resulting robust guidance law is compared to proportional navigation and minimum effort guidance (with zero miss constraint) for situations with and without uncertainty and in the presence of heading error and various target maneuvers. The robust guidance law turns out to be the best choice in the setup we have worked with, which is linear, continuous time, and assumes perfect measurements of relative position, velocity, and accelerations of the interceptor and the target. Nomenclature N' = navigation constant rgo = time to go until intercept Vc = closing velocity y = relative interceptor-target separation ()r = transpose I. Introduction