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In this paper, an improved parameterized controller reduction technique via a new frequency weighted model reduction formulation is developed for the feedback control of MIMO discrete time systems particularly for non-unity feedback control system configurations which have the controller located in the feedback path. New frequency weights which are a function of a free parameter matrix are derived based on a set of equivalent block diagrams and this leads to a generalized double sided frequency weighted model reduction formulation. Solving this generalized double sided frequency weighted model reduction problem for various values of the free parameter results in obtaining controllers which correspond to each value of the free parameter. It is shown that the proposed formulation has a useful characteristic such that selecting a controller which corresponds to a large value of the free parameter results in obtaining an optimal reduced order controller and using this optimal reduced order controller in a closed loop system results in significant reduction in the infinity norm of the approximation error between the original closed loop system and the closed loop system which uses an optimal reduced order controller (when compared to existing frequency weighted model reduction methods). [ABSTRACT FROM AUTHOR]

Popular model reduction methods can easily be adapted to retain the asymptotic response to inputs with rational transform. To this purpose, the forced response of the high-order system is decomposed into a transient and a steady-state component. Then, the reduced-order model is obtained by combining the unaltered steady-state component with an approximation of the transient component. Examples show that forcing the reduced-order model to retain the steady-state component does not compromise the transient accuracy. [ABSTRACT FROM AUTHOR]

In this paper a novel model order reduction method for nonlinear models, based on decoupled multi-model, via trajectory piecewise-linearization is proposed. Through different strategies in trajectory piecewise-linear model reduction, model order reduction of a trajectory piecewise-linear model based on output weighting (TPWLOW), has been developed by authors of current work. The structure of mentioned work was founded based on Krylov subspace method, which is appropriate for high order models. Indeed the size of the Krylov subspaces may increase with the number of inputs of the system. As a result, the use of Krylov subspace method may become deficient the case for multi-input systems of order few decades. This paper aims to generalize the idea of model reduction of TPWLOW model by concentrating on balanced truncation technique which is appropriate for medium size systems. In addition, the proposed method either guarantees or provides guaranteed stability in some mentioned conditions. Finally, applicability of the reduced model, instead of high-order decoupled multi-model in weighting multi-model controllers, is investigated through the control of a nonlinear Alstom gasifier benchmark. [ABSTRACT FROM AUTHOR]

We consider model reduction for magneto-quasistatic field equations in the vector potential formulation. A finite element discretization of such equations leads to large-scale differential-algebraic equations of special structure. For model reduction of linear systems, we employ a balanced truncation approach, whereas nonlinear systems are reduced using a proper orthogonal decomposition method combined with a discrete empirical interpolation technique. We will exploit the special block structure of the underlying problem to improve the performance of the model reduction algorithms. Furthermore, we discuss an efficient evaluation of the Jacobi matrix required in nonlinear time integration of the reduced models. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A crucial part of the inference of industrial process change point detection is that once a suspected change point is detected, the statistical test needs to be carried out to ensure the significance of the change. Conventional test statistics such as Maximum-Type testing method is very sensitive to outliers as the formulation of the estimator is lack of robustness. In addition, oftentimes, evidence of larger shifts could be mistakenly downweighted or rejected stemming from these outliers and also due to the designated score function. The proposed robust individuals control chart adopting the Huber Maximum-Type (HMT) testing method is based on a well-motivated Huber score function, which appears to provide protection against this complication. Extensive numerical simulation studies were carried out to assess the performance of the proposed procedure with its counterparts. Taking a real data set from industry, we illustrate the usefulness and applicability of the proposed chart in practice. [ABSTRACT FROM AUTHOR]

In this paper, a controller order reduction method for linear parameter-varying systems is presented. The proposed method is based on the frequency-weighted balanced truncation technique, which has the advantage to reduce the order in a specific frequency range. The approach is discussed and is proved to preserve the closed-loop stability with a guaranteed upper error bound. Effectiveness and performance of the obtained reduced-order controller are investigated by applying it to an automotive semi-active suspension control. The obtained simulation results show that objectives such as the road handling and the passenger comfort realised with the reduced-order controller are kept in the same performance level as with the full-order controller. Moreover, a comparison with an other-order reduction method is shown and confirms the advantage of the developed method. [ABSTRACT FROM AUTHOR]

A finite element (FE) model simulates an unconstrained aluminum thin plate to which four macro-fiber composites are bonded. This plate model is experimentally validated for single and multiple inputs. While a single input excitation results in the frequency response functions and operational deflection shapes, two input excitations under prescribed conditions result in tailored traveling waves. The emphasis of this article is the application of projection-based model reduction techniques to scale-down the large-scale FE plate model. Four model reduction techniques are applied and their performances are studied. This article also discusses the stability issues associated with the rigid-body modes. Furthermore, the reduced-order models are utilized to simulate the steady-state frequency and time response of the plate. The results are in agreement with the experimental and the full-scale FE model results. [ABSTRACT FROM AUTHOR]

We present a time-series-based algorithm to identify structural damage in the structure. The method is in the context of non-model-based approaches; hence, it eliminates the need of any representative numerical model of the structure to be built. The method starts by partitioning the state space into a finite number of subsets which are mutually exclusive and exhaustive and each subset is identified by a distinct symbol. Partitioning is performed based on a maximum entropy approach which takes into account the sparsity and distribution of information in the time series. After constructing the symbol space, the time series data are uniquely transformed from the state space into the constructed symbol space to create the symbol sequences. Symbol sequences are the simplified abstractions of the complex system and describe the evolution of the system. Each symbol sequence is statistically characterized by its entropy which is obtained based on the probability of occurrence of the symbols in the sequence. As a consequence of damage occurrence, the entropy of the symbol sequences changes; this change is implemented to define a damage indicative feature. The method shows promising results using data from two experimental case studies subject to varying excitation. The first specimen is a reinforced concrete jack arch which replicates one of the major structural components of the Sydney Harbor Bridge and the second specimen is a three-story frame structure model which has been tested at Los Alamos National Laboratory. The method not only could successfully identify the presence of damage but also has potential to localize it. [ABSTRACT FROM AUTHOR]

To solve a stochastic linear evolution equation numerically, finite dimensional approximations are commonly used. For a good approximation, one might end up with a sequence of ordinary stochastic linear differential equations of high order. To reduce the high dimension for practical computations, model order reduction is frequently used. Balanced truncation (BT) is a well-known technique from deterministic control theory and it was already extended for controlled linear systems with Lévy noise. Recently, a new ansatz was investigated which provides an alternative way to generalize BT for stochastic systems. There, the question of the existence of an H 2 -error bound was asked which we answer in this paper. We discuss how this bound can be computed practically and how to use it to find a suitable reduced order dimension. [ABSTRACT FROM AUTHOR]

This paper proposes a procedure for designing a fast terminal sliding-mode control involving an integral filter that guarantees a finite time of convergence to zero dynamics, robustness against polynomial bounded uncertainties, and external disturbances. It reduces the chattering effect by employing a state-dependent gain and adds an integral filter to smooth the input control signal. We suggest a simplified algorithm to design the controller. To test the performance of the algorithm, we use a Van der Pol chaotic oscillator synchronization with perturbations in the states. Finally, we compare the performance of the method by using the proposed controller with the filter turned-on and turned-off. [ABSTRACT FROM PUBLISHER]

Model order reduction (MOR) methods are applied in different areas of physics in order to reduce the computational time of large scale systems. It has been an active field of research for many years, in mechanics especially, but it is quite recent for magnetoquasi-static problems. Although the most famous method, the proper orthogonal decomposition (POD) has been applied for modeling many electromagnetic devices, this method can lack accuracy for low-order magnitude output quantities, like flux associated with a probe in regions where the field is low. However, the balanced POD (BPOD) is an MOR method, which takes into account these output quantities in its reduced model to render them accurately. Even if the BPOD may lead to unstable reduced systems, this can be overcome by a stabilization procedure. Therefore, the POD and the stabilized BPOD will be compared on a 3-D linear magnetoquasi-static field problem. [ABSTRACT FROM AUTHOR]

In this paper, a fast and accurate numerical simulation method on dynamic heat transfer through building envelopes has been developed by using the Krylov subspace and the balanced truncation model order reduction (MOR) algorithms. The computational accuracy and efficiency of the two MOR algorithms are discussed through the numerical simulation on a roof heat transfer in a one-day period, and then the two verified algorithms are applied to simulate the heat transfer through a multilayer wall for a week and the two-dimensional heat transfer through an L-shape thermal bridge. The results show that the relative errors of the two algorithms to the harmonic response method or to the direct solution method are all less than 1%, and the solving time with the two MOR algorithms decreases greatly. In addition, the Krylov subspace MOR algorithm has a faster solving speed and is more suitable for solving the heat transfer through a building envelope than the balanced truncation MOR algorithm. [ABSTRACT FROM AUTHOR]

Study of transient behavior and design of control for large reactors, such as the Advanced Heavy Water Reactor (AHWR) requires accurate mathematical models. An 80th order space–time kinetics model which describes the core neutronics behavior of AHWR is available but it is nonlinear and stiff. The modern control design and analysis studies with this model are accompanied by serious numerical ill-conditioning problems. Hence, there is a strong motivation for obtaining a reduced order model which preserves the input–output behavior accurately. In this paper, we have explored the application of balanced truncation technique to obtain a reduced order model from the original high order model of the AHWR. The reduced order model thus obtained was examined from the view point of transient performance by comparing its response with that of the original model and it is found to yield a very good approximation. We also carried out the comparative study between different reduced order models of AHWR, namely, Davison’s technique, Marshall’s technique, singular perturbation analysis and balanced truncation by comparing their performances with respect to each other and with the original model. All of these methods are found to be effective, however the overall accuracy in the approximation using the balanced truncation approach is found to be far more superior. [ABSTRACT FROM AUTHOR]

We consider a p-logistic equation with equidiffusive reaction. We study the existence, nonexistence and uniqueness of positive solutions as the parameter $$\lambda >0$$ varies. In the case of a unique positive solution $$u_{\lambda }$$ , we investigate the monotonicity and continuity properties of the map $$\lambda \rightarrow u_{\lambda }$$ . [ABSTRACT FROM AUTHOR]

This paper presents the development of a new model reduction method for discrete-time bilinear systems based on the balanced truncation framework. In many model reduction applications, it is advantageous to analyze the characteristics of the system with emphasis on particular frequency intervals of interest. In order to analyze the degree of controllability and observability of discrete-time bilinear systems with emphasis on particular frequency intervals of interest, new generalized frequency interval controllability and observability gramians are introduced in this paper. These gramians are the solution to a pair of new generalized Lyapunov equations. The conditions for solvability of these new generalized Lyapunov equations are derived and a numerical solution method for solving these generalized Lyapunov equations is presented. Numerical examples which illustrate the usage of the new generalized frequency interval controllability and observability gramians as part of the balanced truncation framework are provided to demonstrate the performance of the proposed method.

This paper presents a reduced order model problem using reciprocal transformation and balanced truncation followed by low order controller design of infinite dimensional systems. The class of systems considered is that of an exponentially stable state linear systems (A, B, C), where operator A has a bounded inverse, and the operator B and C are of finite-rank and bounded. We can connect the system (A, B, C) with its reciprocal system via the solutions of the Lyapunov equations. The realization of the reciprocal system is reduced by balanced truncation. This result is further translated using reciprocal transformation as the reduced-order model for the systems (A, B, C). Then the low order controller is designed based on the reduced order model. The numerical examples are studied using simulations of Euler-Bernoulli beam to show the closed-loop performance.

In standard balanced truncation model order reduction, the initial condition is typically ignored in the reduction procedure and is assumed to be zero instead. However, such a reduced-order model may be a bad approximation to the full-order system, if the initial condition is not zero. In the literature there are several attempts for modified reduction methods at the price of having no error bound or only a posteriori error bounds which are often too expensive to evaluate. In this work we propose a new balancing procedure that is based on a shift transformation on the state. We first derive a joint projection reduced-order model in which the part of the system depending only on the input and the one depending only on the initial value are reduced at once and we prove an a priori error bound. With this result at hand, we derive a separate projection procedure in which the two parts are reduced separately. This gives the freedom to choose different reduction orders for the different subsystems. Moreover, we discuss how the reduced-order models can be constructed in practice. Since the error bounds are parameter-dependent we show how they can be optimized efficiently. We conclude this paper by comparing our results with the ones from the literature by a series of numerical experiments. [ABSTRACT FROM AUTHOR]

A model reduction technique aimed at computing efficiently Frequency Response Functions of damped structures is presented. The frequency-dependent complex moduli are approximated by a mini-oscillators model, known as the Golla–Hughes–MacTavish (GHM) model, which permits to recast the original problem as a more familiar second-order, constant-coefficient system of equations. The matrix system, although much larger, is then treated by application of the Balanced Proper Orthogonal Decomposition (BPOD) which aims at approximating the transfer function matrix, or equivalently the admittance matrix, connecting forces and displacements at a specified set of points of the vibrating structure. All the necessary ingredients of the reduction strategy as well as its efficiency measured in terms of data reduction, accuracy and computational cost are shown. Two illustrative examples of increasing complexity involving a clamped cantilever beam and a realistic windshield are presented. It is shown that the admittance matrix can be approximated by matrices of very small size which computation can be speeded up via diagonalization. It is concluded that the application of BPOD combined with the GHM decomposition of the frequency-dependent algebraic system proves extremely efficient for the modeling of vibrating structures made of different materials, either viscoelastic or purely elastic. [ABSTRACT FROM AUTHOR]

Model reduction, based on balanced truncation, of stable and of positive real systems are considered. An overview over some of the already existing techniques are given: Lyapunov balancing and stochastic balancing, which includes Riccati balancing. A novel scheme for positive real balanced truncation is then proposed, which is a combination of the already existing Lyapunov balancing and Riccati balancing. Using Riccati balancing, the solution of two Riccati equations are needed to obtain positive real reduced order systems. For the suggested method, only one Lyapunov equation and one Riccati equation are solved in order to obtain positive real reduced order systems, which is less computationally demanding. Further it is shown, that in order to get positive real reduced order systems, only one Riccati equation needs to be solved. Finally, this is used to obtain positive real frequency weighted balanced truncation.

We consider the model reduction problem for linear time-invariant dynamical systems having nonzero (but otherwise indeterminate) initial conditions. Building upon the observation that the full system response is decomposable as a superposition of the response map for an unforced system having nontrivial initial conditions and the response map for a forced system having null initial conditions, we develop a new approach that involves reducing these component responses independently and then combining the reduced responses into an aggregate reduced system response. This approach allows greater flexibility and offers better approximation properties than other comparable methods. [ABSTRACT FROM AUTHOR]

Advances in experimental techniques and the ever-increasing fidelity of numerical simulations have led to an abundance of data describing fluid flows. This review discusses a range of techniques for analyzing such data, with the aim of extracting simplified models that capture the essential features of these flows, in order to gain insight into the flow physics, and potentially identify mechanisms for controlling these flows. We review well-developed techniques, such as proper orthogonal decomposition and Galerkin projection, and discuss more recent techniques developed for linear systems, such as balanced truncation and dynamic mode decomposition (DMD). We then discuss some of the methods available for nonlinear systems, with particular attention to the Koopman operator, an infinite-dimensional linear operator that completely characterizes the dynamics of a nonlinear system and provides an extension of DMD to nonlinear systems. [ABSTRACT FROM AUTHOR]

In this paper, nonlinear model reduction for power systems is performed by the balancing of empirical controllability and observability covariances that are calculated around the operating region. Unlike existing model reduction methods, the external system does not need to be linearized but is directly dealt with as a nonlinear system. A transformation is found to balance the controllability and observability covariances in order to determine which states have the greatest contribution to the input-output behavior. The original system model is then reduced by Galerkin projection based on this transformation. The proposed method is tested and validated on a system comprised of a 16-machine 68-bus system and an IEEE 50-machine 145-bus system. The results show that by using the proposed model reduction the calculation efficiency can be greatly improved; at the same time, the obtained state trajectories are close to those for directly simulating the whole system or partitioning the system while not performing reduction. Compared with the balanced truncation method based on a linearized model, the proposed nonlinear model reduction method can guarantee higher accuracy and similar calculation efficiency. It is shown that the proposed method is not sensitive to the choice of the matrices for calculating the empirical covariances. [ABSTRACT FROM AUTHOR]

Model reduction for linear Volterra integro-diffferential equations is studied. Generalized system Gramians are introduced and characterized as solutions to delay Lyapunov equations similarly arising for finite delay systems. The usual energy interpretation of the Gramians is provided and a reduced-order model of Volterra integro-differential type is obtained by truncation of a balanced system. An error bound for the H2-norm is derived. It is further shown that particular choices for the Volterra kernel automatically yield approaches that have been studied in the literature. Additionally, the new approach allows us to also reduce time fractional systems. The method is numerically investigated by means of two spatially discretized partial differential equations. [ABSTRACT FROM AUTHOR]

This paper presents dynamic equivalence of a wind farm based on the model order reduction (MOR) methods. A doubly-fed induction generator (DFIG) with complete mechanical, electrical and control components is the basis for model development. For the purpose of wind fluctuation simulation, the dynamic model of DFIG can be seen as a linear input–output system with the incoming wind speed as the input and the generated active power as the output. Linear model reduction techniques, dominant pole based modal analysis (DPMA) and balanced truncation (BT), combined with classical aggregation skills are applied to obtain a new low-order system representing a wind farm. Simulations and comparisons are carried out in the test system to validate the ability of the reduced order model in matching the active power generated by the detailed wind farm model. [ABSTRACT FROM AUTHOR]

Nowadays, mechanical engineers heavily depend on mathematical models for simulation, optimization and controller design. In either of these tasks, reduced dimensional formulations are obligatory in order to achieve fast and accurate results. Usually, the structural mechanical systems of machine tools are described by systems of second-order differential equations. However, they become descriptor systems when extra constraints are imposed on the systems. This article discusses efficient techniques of Gramian-based model-order reduction for second-order index-1 descriptor systems. Unlike, our previous work, here we mainly focus on a second-order to second-order reduction technique for such systems, where the stability of the system is guaranteed to be preserved in contrast to the previous approaches. We show that a special choice of the first-order reformulation of the system allows us to solve only one Lyapuov equation instead of two. We also discuss improvements of the technique to solve the Lyapunov equation using low-rank alternating direction implicit methods, which further reduces the computational cost as well as memory requirement. The proposed technique is applied to a structural finite element method model of a micro-mechanical piezo-actuators-based adaptive spindle support. Numerical results illustrate the increased efficiency of the adapted method. [ABSTRACT FROM PUBLISHER]

This paper considers robust boundary control with disturbance adaptation to stabilize the vibration of a rectangular plate under disturbances with unknown upper-bounds. Disturbances are considered to be distributed both over the plate interior domain and along the boundary (in-domain and boundary distributed disturbances). Applying Hamilton's principle, the dynamics of the plate is represented in the form of a fourth-order partial differential equation subject to static and dynamic boundary conditions. The proposed model considers the membrane effect of axial force and the effect of actuator mass dynamics on the plate vibration. A robust boundary control is established that stabilizes the plate in presence of both in-domain and boundary disturbances. A rigorous Lyapunov stability analysis shows that the vibration of the plate is uniformly ultimately bounded and converges to the vicinity of zero by proper selection of control gains. For the vanishing in-domain disturbances, it is seen that exponential stability is achieved by the proposed control. Next, a disturbance adaptation law is introduced to stabilize the plate vibration in response to disturbances with unknown bounds, and the stability of the robust boundary control with disturbance adaptation is studied using Lyapunov. Simulation results verify the efficiency of the suggested control. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Modern power systems have experienced a significant increase in its complexity, and extremely large-scale system models have to be addressed in the study of stability analysis and control. Model reduction is a technique for developing an approximate system model with lower dimensions that shares similar properties to the original system. This work proposes a computationally efficient approach for linear system model reduction in large-scale power systems that is based on the balanced truncation method using an extended Krylov subspace technique. Key algorithm improvements, including sparsity handling of the linearized power system models and efficient computational techniques for solving dual Lyapunov equations, are discussed in detail. In addition, application of the proposed model reduction is extended to unstable systems, and a power system stabilizer (PSS) parameter optimization method based on reduced system models is used to validate the effectiveness of the proposed method. Case studies show that the resulting reduced models preserve the unique characteristics of the original high-dimensional models, including time and frequency domain responses as well as eigenvalues. Numerical results based on test systems with up to 12\thinspace685 buses demonstrate the computational efficiency and validity of the proposed approach. [ABSTRACT FROM PUBLISHER]

In the paper, a model predictive controller based on reduced order model is proposed to control belt conveyor system, which is an electro-mechanics complex system with long visco-elastic body. Firstly, in order to design low-degree controller, the balanced truncation method is used for belt conveyor model reduction. Secondly, MPC algorithm based on reduced order model for belt conveyor system is presented. Because of the error bound between the full-order model and reduced order model, two Kalman state estimators are applied in the control scheme to achieve better system performance. Finally, the simulation experiments are shown that balanced truncation method can significantly reduce the model order with high-accuracy and model predictive control based on reduced-model performs well in controlling the belt conveyor system. [ABSTRACT FROM AUTHOR]

This paper describes a novel zero moment point (ZMP) tracking control strategy using a disturbance observer (DOB) in the presence of ground slope change for balance control of an android robot. With regard to conventional ZMP controls, many researchers have studied ZMP tracking control strategies using an inverted pendulum model on flat level ground, and they have solved a slow response problem of nonminimum phase systems by using suitable feedforward motions called walking patterns. However, the conventional methods lead to ZMP offset errors in the presence of ground slope change; it is hence necessary to quickly eliminate the ZMP offset errors to realize robust balance control. In this paper, we rapidly eliminate the ZMP offset errors through a DOB using a model inversion for robust balance control in the presence of ground slope change. In particular, a dynamic model that uses the projected center of mass (CoM) position on the ground is additionally used as an output to solve a problem that generates an unstable pole during model inversion. Finally, the proposed control strategy is verified through MATLAB simulations and experiments using a real android leg. [ABSTRACT FROM AUTHOR]

A practical procedure based on implicit time integration methods applied to the differential Lyapunov equations arising in the square root balanced truncation method is presented. The application of high-order time integrators results in indefinite right-hand sides of the algebraic Lyapunov equations that have to be solved within every time step. Therefore, classical methods exploiting the inherent low-rank structure often observed for practical applications end up in complex data and arithmetic. Avoiding the additional effort in treating complex quantities, a symmetric indefinite factorization of both the right-hand side and the solution of the differential Lyapunov equations is applied. [ABSTRACT FROM AUTHOR]

Model reduction is a significant issue in dynamic system simulation and control, as a consequence of the unmanageable levels of storage and computational requirements for large-scale systems. In this paper, the concept of a balanced truncation approximation method is extended to large-scale systems with interval uncertainties to get the reduced-order model with uncertainties. In order to get the balanced system, the balancing transformation matrix is introduced by using the nominal system, and the reduced-order model with uncertainties is obtained by using balanced truncation. A major characteristic of this model reduction method is that the reduced-order model obtained in this way is also as uncertain as the original model. The closeness of the reduced-order model to the original model relies on the upper bounds of the ignored Hankel singular values. To compare the original model and the reduced-order model, a perturbation method is proposed to give the interval bounds of the responses of the original model and the reduced-order model. As applications of the proposed method, three numerical examples are given. [ABSTRACT FROM AUTHOR]

We introduce a notion of balanced truncation for generalized Lyapunov operators and show that it preserves asymptotic stability. The proof relies on the theory of positive mappings and a result by Hans Schneider. Applications of our result can be found in model order reduction of stochastic linear systems. [ABSTRACT FROM AUTHOR]

Limited frequency interval Gramians-based model reduction techniques for generalized non-singular systems are presented. These techniques generalize the results of existing limited frequency interval Gramians schemes for general non-singular systems. Numerical examples are also presented to illustrate the effectiveness of proposed techniques. [ABSTRACT FROM AUTHOR]

In this study, the authors study the power control for a two-tier network system which is comprised of a central macrocell and several femtocells. In practice, the communication environment is fairly complex and dynamic which leads to the imperfect channel state information (CSI). To enhance the robustness of the two-tier network system, the imperfect CSI in both signal links and interference links are considered and the uncertainties of the CSI are uniformly distributed in an ellipsoid uncertainty set. Then, a probability-constrained optimisation problem is formulated to deal with the uncertainties and protect the quality-of-service of all users. A novel method is provided to convert probability constraints into deterministic ones. Based on them, they propose an iterative algorithm and an admission control algorithm to enhance the network efficiency. They also investigate the case when the distributions of the uncertainties of the CSI are unknown. Finally, numerical results are given to illustrate the effectiveness of the authors' power control scheme. [ABSTRACT FROM AUTHOR]

This paper investigates active disturbance rejection control involving the fractional-order tracking differentiator, the fractional-order PID controller with compensation and the fractional-order extended state observer for nonlinear fractional-order systems. Firstly, the fractional-order optimal-time control scheme is studied to propose the fractional-order tracking differentiator by the Hamilton function and fractional-order optimal conditions. Secondly, the linear fractional-order extend state observer is offered to acquire the estimated value of the sum of nonlinear functions and disturbances existing in the investigated nonlinear fractional-order plant. For the disturbance existing in the feedback output, the effect of the disturbance is discussed to choose a reasonable parameter in fractional-order extended state observer. Thirdly, by this observed value, the nonlinear fractional-order plant is converted into a linear fractional-order plant by adding the compensation in the controller. With the aid of real root boundary, complex root boundary, and imaginary boot boundary, the approximate stabilizing boundary with respect to the integral and differential coefficients is determined for the given proportional coefficient, integral order and differential order. By choosing the suitable parameters, the fractional-order active disturbance rejection control scheme can deal with the unknown nonlinear functions and disturbances. Finally, the illustrative examples are given to verify the effectiveness of fractional-order active disturbance rejection control scheme. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We provide a theoretical framework that fits realistic challenges related to spacecraft formation with disturbances. We show that the input-to-state stability of such systems guarantees some robustness with respect to a class of signals with bounded average-energy, which encompasses the typical disturbances acting on spacecraft formations. Solutions are shown to converge to the desired formation, up to an offset, which is somewhat proportional to the considered moving average of disturbances. In the presence of fast peaking perturbations, the approach provides a tighter evaluation of the disturbances' influence, which allows for the use of more parsimonious control gains. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Stabilizing a flow around an unstable equilibrium is a typical problem in flow control. Model-based designed of modern controllers like LQR/LQG or H∞ compensators is often limited by the large-scale of the discretized flow models. Therefore, model reduction is usually needed before designing such a controller. Here we suggest an approach based on applying balanced truncation for unstable systems to the linearized flow equations usually used for compensator design. For this purpose, we modify the ADI iteration for Lyapunov equations to deal with the index-2 structure of the underlying descriptor system efficiently in an implicit way. The resulting algorithm is tested for model reduction and control design of a linearized Navier-Stokes system describing von Kármán vortex shedding. [ABSTRACT FROM AUTHOR]

This paper proposes a controller reduction of linear parameter dependent systems. A measure of the degradation is derived for the parameter dependent closed-loop performance caused by applying the reduced-order parameter dependent controller. This measure can be obtained by extending the degradation of the closed-loop performance of the balanced truncation of the corresponding time invariant systems. To verify the performance of the reduced-order controller, an application of the proposed controller reduction method to vertical acceleration of a missile is presented.