Class Of Multi-input Multi-output Systems Research Articles

Plant-Input-Mapping Discretization Method for a Feedback System in the State-Space Form

AbstractThe paper proposes the digital redesign technique called plant-input-mapping (PIM) method for a feedback system described in the state-space form. The PIM method, which was originally presented in the transfer function form, focuses on the plant input signal via the plant input transfer function (PITF) and discretizes it so as to satisfy the control zero principle in the resulting discrete-time closed-loop system, which leads to guaranteeing the closed-loop stability for any nonpathological sampling interval. In accordance with this approach, the proposed PIM method focuses on the control zeros included in the plant input signal. The paper proves that the matched-pole-zero discrete-time model of the plant input state-equation (PISE) satisfies the control zero principle with the step-invariant model of the plant. Then, when the matched-pole-zero model is set as the target of model matching, the parameters of the state-space PIM controller employing the observer-based dynamic state-feedback can systematically be determined from the underlying continuous-time closed-loop system with guaranteed stability. This discretization process can immediately be applied to a state-feedback system and a class of multi-input multi-output systems without any modification, which cannot be discretized by the conventional PIM methods. The discretization performance of the proposed PIM method is evaluated through illustrative examples with comparable digital redesign methods, which reveal that the proposed method performs a good reproduction of the characteristics of the underlying closed-loop system.

Synchronization problem for a class of multi-input multi-output systems with terminal sliding mode control based on finite-time disturbance observer: Application to Chameleon chaotic system

This paper studies the synchronization problem of two nonlinear multi-input multi-output (MIMO) systems in finite-time period. For this purpose, a terminal sliding mode controller (TSMC) with a finite-time disturbance observer (FTDO) is employed. Using an FTDO, in a finite time interval, the disturbance parameters precisely can be identified which produce a better transient performance compared to the Lyapunov parameter estimation (LPE) method. Unlike previous literature, the imposed restrictions over external disturbances have been relaxed, i.e., the upper bounds of disturbances and the restrictive condition over the disturbances’ first derivatives have been removed. According to the proposed FTDO, a continuous control input is developed that eliminates chattering in synchronization of nonlinear MIMO master-slave system; as a result, a chattering-free TSMC is attained which makes the synchronization errors converge to the origin in finite-time period. By means of the Lyapunov function (CLF), the stability of the introduced TSMC and the FTDO are proved. Finally, in the simulation section, the efficiency and the accuracy of the proposed approach are revealed by applying the proposed method on a Chameleon master-slave chaotic flow.

Minimum-Learning-Parameters-Based Adaptive Neural Fault Tolerant Control With Its Application to Continuous Stirred Tank Reactor

In this paper, a decentralized neural network (NN) output feedback fault tolerant control (FTC) problem is addressed for a class of multi-input multi-output systems with actuator fault. In order to avoid the noncausal problem, the original system is transformed into an input-output expression in accordance with the diffeomorphism theory. Then, in order to establish a quick response to the fault, the fault tolerant controller with minimum learning parameters has been designed such that the semiglobal uniform ultimate boundedness of all the variables in the resulting closed-loop systems can be guaranteed. Finally, the output feedback FTC approach is applied to the interconnected CSTRs, and the comparisons with existing methods are provided to show the effectiveness of the proposed strategy.

On extended state based Kalman filter design for a class of nonlinear time-varying uncertain systems

This paper considers the filtering problem for a class of multi-input multi-output systems with nonlinear time-varying uncertain dynamics, random process andmeasurement noise. An extended state based Kalman filter, with the idea of timely estimating the unknown dynamics, is proposed for better robustness and higher estimation precision. The stability of the proposed filter is rigorously proved for nonlinear time-varying uncertain system with weaker stability condition than the extended Kalman filter, i.e., the initial estimation error, the uncertain dynamics and the noises are only required to be bounded rather than small enough. Moreover, quantitative precision of the proposed filter is theoretically evaluated. The proposed algorithm is proved to be the asymptotic unbiased minimum variance filter for constant uncertainty. The simulation results of some benchmark examples demonstrate the feasibility and effectiveness of the method.

A Novel Extended State Observer for Output Tracking of MIMO Systems With Mismatched Uncertainty

In this paper, we develop a novel extended state observer (ESO), in terms of tracking error only, for output tracking of a class of multi-input multioutput systems with mismatched uncertainty. A novel ESO is constructed from the nonsmooth function “ $\text{fal}$ ” to estimate both uncertainty and state of the system. An ESO-based output feedback controller is then designed to compensate (cancel) the uncertainty and to achieve the output tracking. The convergence of the closed-loop system is proved. The effectiveness of the proposed method is demonstrated by numerical results of trajectory tracking for a practical autonomous underwater vehicle model. We show that in the presence of measurement noise, this novel ESO leads to better performance than the linear ESO. Moreover, this type of ESO has much smaller peaking value than the linear ESO under the same tuning gain.

Neural Approximation-Based Adaptive Control for a Class of Nonlinear Nonstrict Feedback Discrete-Time Systems.

In this paper, an adaptive control approach-based neural approximation is developed for a class of uncertain nonlinear discrete-time (DT) systems. The main characteristic of the considered systems is that they can be viewed as a class of multi-input multioutput systems in the nonstrict feedback structure. The similar control problem of this class of systems has been addressed in the past, but it focused on the continuous-time systems. Due to the complicacies of the system structure, it will become more difficult for the controller design and the stability analysis. To stabilize this class of systems, a new recursive procedure is developed, and the effect caused by the noncausal problem in the nonstrict feedback DT structure can be solved using a semirecurrent neural approximation. Based on the Lyapunov difference approach, it is proved that all the signals of the closed-loop system are semiglobal, ultimately uniformly bounded, and a good tracking performance can be guaranteed. The feasibility of the proposed controllers can be validated by setting a simulation example.

Nonlinear output regulation for invertible nonlinear MIMO systems

SummaryIn this paper, we address the problem of output regulation for a broad class of multi‐input multi‐output (MIMO) nonlinear systems. Specifically, we consider input–affine systems, which are invertible and input–output linearizable. This class includes, as a trivial special case, the class of MIMO systems which possess a well‐defined vector relative degree. It is shown that if a system in this class is strongly minimum phase, in a sense specified in the paper, the problem of output regulation can be solved via partial‐state feedback or via (dynamic) output feedback. The result substantially broadens the class of nonlinear MIMO systems for which the problem in question is known to be possible. Copyright © 2015 John Wiley & Sons, Ltd.

Parametric transfer matrices for sampled-data systems with linear periodic continuous process and input delay

For the class of multi-input multi-output systems being composed of a linear continuous periodic (LCP) process, pure delay, and a digital controller, the paper provides closed expressions for the parametric transfer matrix (PTM), even for the diffcult, but practically important case, when the external excitations act on continuous system parts. In the same way as ordinary transfer matrices in the linear time-invariant (LTI) case, the PTM for LCP systems is a fundamental concept for analysis and design of those systems. The properties of the constructed parametric transfer matrices as functions of the real parameter and the complex variable are investigated. These properties are similar to those from ordinary transfer matrices, so that the PTM after some modifications, can be applied with similar tools. Moreover, formulae are derived that are appropriate for the practical computation of the PTM. An example demonstrates, how the fromulae can be handled.

Coupled‐least‐squares identification for multivariable systems

This article studies identification problems of multiple linear regression models, which may be described a class of multi-input multi-output systems (i.e. multivariable systems). Based on the coupling identification concept, a novel coupled-least-squares (C-LS) parameter identification algorithm is introduced for the purpose of avoiding the matrix inversion in the multivariable recursive least-squares (RLS) algorithm for estimating the parameters of the multiple linear regression models. The analysis indicates that the C-LS algorithm does not involve the matrix inversion and requires less computationally efforts than the multivariable RLS algorithm, and that the parameter estimates given by the C-LS algorithm converge to their true values. Simulation results confirm the presented convergence theorems.

Adaptive output feedback control of a class of multi-input multi-output systems using neural networks

For a class of uncertain multi-input multi-output non-linear systems an adaptive output feedback control methodology is developed using linearly parameterized neural networks. The neural network operates over a tapped delay line of memory units, comprised of system input/output signals. The adaptive laws for neural network parameters are written in terms of a linear observer of the nominal system's error dynamics. Ultimate boundedness of the error signals is shown through Lyapunov's direct method. Simulations illustrate the theoretical results.

Semi-global observer for multi-output nonlinear systems

We present an explicit form of nonlinear observers for a class of multi-input multi-output systems. Observer construction for multi-output nonlinear systems is not a trivial extension of single output case, especially when the global error convergence is of interest. In this paper, we consider a class of systems in which the subsystem for each output has a triangular dependence on the states of that subsystem itself, and the overall system has a block triangular form for each subsystem. Hence, the contribution is to extend the results existing in the literature in that interconnections between the subsystems are allowed. The construction is based on the saturation of some estimates, which is originated by Khalil and Esfandiari for the use of semi-global output feedback control.

Nonlinear deterministic observer for state estimation: Application to a continuous free radical polymerization reactor

A nonlinear deterministic observer is developed for a class of multi-input multi-output systems. This observer is a Luenberger-like one that uses a constant gain which can be tuned by a high-gain technique to control the speed of convergence. The observer is used for estimating the state in a continuous free radical polymerization process. In open-loop simulations of this process the observer converges very well in much less than one residence time, provided the convergence parameter is well tuned. The observer shows good robustness with respect to measurement noise and to modelling errors. It must be pointed out that this observer works owing to the particular property of strong observability of the model, which in the general nonlinear case is not guaranteed.

Synthesis of transfer function matrices with invariant zeros

A class of multi-input multi-output systems is considered in which the zeros of the transfer function matrix remain invariant with respect to a form of state variable feedback.