Time-varying Multivariable Systems Research Articles

Optimal Power Tracking of DFIG-Based Wind Turbine Using MOGWO-Based Fractional-Order Sliding Mode Controller

AbstractThe doubly fed induction generator (DFIG)-based wind turbine as a nonlinear, compound, and multivariable time-varying system encompasses several uncertainties especially unfamiliar disturbances and unmodeled dynamics. The design of a high-performance and reliable controller for this system is regarded as a complex task. In this paper, an effective and roust fractional-order sliding mode controller (FOSMC) has been designed to accurately regulate the active and reactive power of DFIG. FOSMC has overcome the system uncertainties and abated the chattering amplitude. Since tuning the FOSMC is a challenging assignment, the application of a multi-objective optimization algorithm can efficiently and precisely solve the design problem. In this regard, non-dominated sorting multi-objective gray wolf optimizer (MOGWO) is taken into account to optimally adjust the FOSMC. In a word, the simulation results have definitively validated robustness of MOGWO-based FOSMC in order to accurately track DFIG's active and reactive power.

Research on the Identification of Tubular-Furnace Based on CARIMA Model

Atmospheric and vacuum furnace is a complex control object, in particular, combustion system and multi-branch feeding the outlet temperature control system is interconnected multiple-input and multiple-output coupling multivariable time-varying systems. Using multivariable decoupling control methods will have better control effect, but in fact, because of the nonlinear time-varying systems, and other factors, it is difficult to obtain more accurate mathematical model of the system. Based on CARIMA model, a distributed lags model is constructed in this paper. In the numerical simulation, the proposed model has a excellent recognition result, can achieve an arbitrary precision according to actual requirements.

Adaptive Model Predictive Control of Multivariable Time-varying Systems

In this work, we develop a novel adaptive model predictive control (AMPC) formulation for multivariable time-varying systems. A two-tier modeling scheme is proposed in which the deterministic and s...

INFINITE-HORIZON OPTIMAL CONTROL BASED ON CONTINUOUS-TIME CONTINUOUS-STATE HOPFIELD NEURAL NETWORKS

An optimal control method based on continuous-time continuous-state Hopfield neural network (CTCSHNN) is proposed for time-varying multivariable systems. The equivalence is built theoretically between receding-horizon linear quadratic (LQ) performance index and energy function of CTCSHNN, and the CTCSHNN is constructed to solve the above LQ optimization control problems. Moreover, the rolling optimization strategy is adopted to form closed-loop control structure that includes CTCSHNN so, the dynamic infinite-horizon optimization control is realized for multivariable time-varying systems. As an example, a second order time-varying system is simulated. Simulation results show the effectiveness and feasibility of the proposed method.

Time-varying pascal systems

This paper deals with structures and properties of time-varying multivariable Pascal systems. Semigroup properties of the time-varying Pascal systems are presented and corresponding solutions are established. The attractive feature of this technique is that it reduces the original differential system to a system of linear algebraic equations from which the solutions in any time-interval can be obtained very easy. The presented approach generalizes standard results of the Lyapunov-Floquet theory on time-periodic systems. The novelty of the present method is that it reduces any time-varying system to a corresponding time-varying Pascal system which can be solved by the established algorithm.

Robust tracking of linear MIMO time-varying systems

The asymptotic properties of the linear multivariable time-varying tracking systems, constructed from the fixed-degree matrix polynomials, under the unmodeled dynamics and external disturbances are investigated in this paper. The robust controllers are designed based on the frozen-time approach. First, the robust stabilization is assured. The asymptotic robust stability conditions on both the mismodeling errors, which only depend on the frozen-time computations, and the variation rates of the perturbed plants are found and quantitatively characterized. And, more essentially, the robust tracking performance is achieved. It is shown that if the time-varying plants and the time-varying nominal models are asymptotically slowly varying, then the exact tracking requirement, which has zero steady reference command signals tracking errors, is achieved in the time-varying feedback systems under the situations of the unmodeled dynamics, external disturbances and time-varying effects of the systems. The corresponding permissible ranges of mismodeling errors and the robustness enhancement are provided and discussed.

Adaptive algorithms for the simultaneous stabilization and decoupling of time-varying multivariable systems

The not previously considered problem of decoupling time varying multivariable systems is investigated and two dual-purpose algorithms, which decouple and regulate the system, are derived. One algorithm also gives pole assignment and the other minimum variance control. The algorithms are shown to stabilize and decouple the closed loop system.

Design of minimal-order state observers for time-varying multivariable systems

Abstract The design of minimal-order state observers is considered for linear time-varying multivariable continuous systems. Employing the observable block companion canonical transformation technique, a simple and straightforward design procedure is given for constructing the minimal-order state observers. This design technique also allows all eigenvalues of the observer to be arbitrarily assigned. Compared with existing observer design techniques for time-varying systems, the method developed has the advantage of being applicable to a more general class of systems and reducing the design complexity in the sense that various observer matrices can be determined as constant matrices. An example is also presented to illustrate the design technique.

Transformations for a class of nonlinear time-varying multivariable systems and their applications

Transformations for a class of nonlinear time-varying multivariable systems and their applications

Adaptive model-following control based on variable structure systems

This paper considers a class of multivariable linear time-varying systems which have a fast and wide range of unknown parameter variations, but whose boundaries are known. For such systems, an adaptive model-following control based on variable structure theory, is presented. An optimal observer, based on the sliding mode in variable structure systems, is then introduced. It has been shown that the proposed control structure guarantees both the system asymptotic stability and the error transient shaping capability. The application of the developed control scheme is demonstrated using a typical example.

Transforming time-varying multivariable systems into block companion canonical forms

The problem of transforming a class of linear time-varying continuous time systems into controllable and observable block companion canonical forms is considered. In terms of system block controllability (observability) matrix, this paper generalizes the results of Shieh et al. [3] and provides systematic and straightforward algorithms for obtaining block companion canonical forms. An example is provided to illustrate this transformation technique.

Design of single-functional observers for linear time-varying multivariable systems

A method is presented for the design of an observer capable of reconstructing a single linear functional of the states of a linear time-varying system. The method is based on a canonical transformation of uniformly observable time-varying multi-variable system. It is shown that this canonical form, along with certain pre-specified structures of observer coefficient matrices, leads to a systematic and straightforward procedure for designing a functional observer of minimal order.

Robust real-time algorithms for identification of linear multivariable time-varying systems

The paper presents a discussion on the problem of the robust real-time identification of linear multivariable time-varying dynamic systems working in a noisy environment. Two methodologically different approaches to the design of such algorithms are presented. The first is based on the one-step estimation, optimal in the sense of the minimal conditional mean-square error, combined with convenient approximations of the underlying error covariance matrix. The second is based on the general formulation of robustified stochastic approximation algorithms, characterized by a suitable non-linear transformation of normalized residuals. Particular algorithms are derived on the basis of step-by-step optimization with respect to the weighting matrix of the algorithm. Monte Carlo simulation results illustrate the discussion, and show the efficiency of the proposed robust algorithms in the presence of large disturbance realizations, the so-called outliers.

On The Lur'e Problem and Stability of Nonlinear Controllers

The Lur'e problem in linear multivariable time-varying systems is discussed. It is shown how to obtain and use a differential Riccati equation in order to establish admissible domains of absolute stability for nonlinear controllers.

Design of reduced-order state estimators for linear time-varying multivariable systems

The design of reduced-order state estimators for linear time-varying multivariable systems is considered. Employing the concepts of matrix operators and the method of canonical transformations, this paper shows that there exists a reduced-order state estimator for linear time-varying systems that are 'lexicography-fixedly observable'. In addition, the eigenvalues of the estimator can be arbitrarily assigned. A simple algorithm is proposed for the design of the state estimator.

Realization Algorithm for Time-varying Systems

This paper considers the problem of modelling discrete-time multivariable time-varying systems applying the results of stochastic realization theory for real data. A method is given for determining Eεε T /of the error process ε(t) of Kalman filter/by the output covariance function in an explicite way. This gives the possibility for computing an optimal exponential forgetting factor for the output covariance function when trEεε T = min. A noniterative solution of some Riccati equations of stochastic realization theory is presented for the adaptive case. Properties of the adaptive mean are discussed and tested.

Recursive solutions to deadbeat observers for time-varying multivariable systems

This paper describes a new construction of the deadbeat observer for the state estimation of linear time-varying multivariable systems. The proposed design methods are computationally attractive because of their simplicity and recursive nature, and are recommendable even for time-invariant multivariable systems.

Arbitrary eigenvalue assignments for linear time-varying multivariable control systems

The problem of eigenvalue assignments for a class of linear time-varying multi-variable systems is considered. Using matrix operators and canonical transformations, it is shown that a time-varying system that is ‘lexicography-fixedly controllable’ can be made via state feedback to be equivalent to a time-invariant system whose eigenvalues are arbitrarily assignable. A simple algorithm for the design of the state feedback is provided.

Transformations of a class of time-varying multivariable control systems to block companion forms

The problem of transforming a class of time-varying multivariable control system to the controllable and observable block companion forms is considered in this paper. The non-singular transformation matrices for obtaining the block companion forms are found in terms of the controllability and observability matrices and the conditions for the existence of such transformations is stated.

Comments on ‘Canonical transformation for a class of time-varying multivariable systems’

Comments on ‘Canonical transformation for a class of time-varying multivariable systems’