On the filtered Smith predictor for MIMO processes with multiple time delays

This paper discusses about a unified implementation structure of the filtered Smith predictor (FSP) for MIMO processes with multiple time delays. Two kinds of dead-time free models are analyzed in order to extend the original properties of the SISO Smith predictor to MIMO processes with multiple time delays. It is demonstrated that FSP strategy can be applied to control open-loop unstable processes with multiple time delays by considering a model without any input, output or internal coupling delays. Moreover, for open-loop stable processes, it is shown that the FSP scheme can be used to speed-up disturbance rejection of processes with multiple time delays by using a nominal model without delay. Different simulation examples are used to illustrate the proposed strategy properties and advantages over other MIMO time-delay compensators. The results may be considered to control either square or non-square processes.     

Robust ℋ2/ℋ∞/reference model dynamic output-feedback control synthesis

This article presents a new strategy to design robust model matching dynamic output-feedback controllers that guarantee tracking response specifications, disturbance rejection and noise attenuation. The proposed synthesis methodology, based on a multi-objective optimisation problem, can be applied to uncertain continuous or discrete-time linear time-invariant systems with polytopic uncertainty, leading to both full-order and reduced-order robust-performance dynamic controllers. The objective functions represent the ?_∞-norm of the difference between the closed-loop transfer function matrix, from the reference signals and the plant outputs and the reference model matrix, the ?_∞-norm of the closed-loop transfer function matrix from the disturbances and the plant outputs and the ?₂-norm of the closed-loop transfer function matrix from the measurement noises and the control inputs. An integral control action is also introduced in order to achieve zero steady-state error. In the case of MIMO systems, the proposed strategy can be applied to decouple the closed-loop control system choosing an appropriated reference model matrix. Two examples are presented to illustrate both SISO and MIMO systems control synthesis.     

Multivariable adaptive control of instabilities arising in jet engines

We consider a class of MIMO LTI models with uncertain resonant modes and time delays, which are common in control of instabilities arising in jet engines. With uncertain delays preventing the use of model reference adaptive control, we develop an adaptive MIMO pole placement scheme for the system. We use indirect adaptation, estimating a small number of physical parameters from a nonlinearly parametrized plant. To address the highly noisy environment in jet engines we introduce the deadzone in the adaptation law and present simulations that successfully stabilize the system in the presence of noise and severe actuator saturation.     

多变量非线性时滞系统的内模控制

本文将单入单出非线性内模控制的设计方法推广到了含多步时滞的多入多出的非线性系统控制器设计中，对于不含纯滞后的过程，所设计的控制器能够实现所期望的常规性能。其中通过非线性滤波器的加入，能够获得当过程和模型存在失配时的鲁棒性，并使控制器结构得以实现。     

一类MIMO非线性时滞系统的鲁棒自适应控制

针对一类具有非线性输入的MIMO时变时滞系统,基于变结构控制原理,提出了一种稳定自适应控制器设计的新方案.该方案通过使用Lyapunov-Krasovskii(L-K)泛函抵消了因未知时变时滞带来的系统不确定性;进一步,利用Young's不等式和参数自适应估计取消了非线性死区输入模犁和不确定项假设中各种参数均为已知的要求.通过理论分析,证明了闭环控制系统半全局一致终结有界,跟踪误差收敛到零的一个邻域内.     

A harmonic balance approach to robust neural control of MIMO nonlinear processes applied to a distillation column

Robust stability and performance are the two most basic features of feedback control process. The harmonic balance analysis based on the describing function technique enables to analyze the stability of limit cycles arising from a closed loop control process operating over nonlinear plants. In this work a robust stability analysis based on the harmonic balance is presented and applied to a neural network controller in series with a dynamic multivariable nonlinear plant under generic Lur’e configuration. The neural controller is replaced by its sinusoidal input describing function while a linearized model is derived to represent the nonlinear plant dynamics. The uncertainty induced by the high harmonics effect for the neural controller, together with the neglected nonlinear dynamics due to plant linearization are incorporated in the robustness analysis as structured norm bounded uncertainties. Stability and robustness conditions for the neural closed loop control system are discussed using the harmonic balance equation together with the structured singular values of the uncertainty. The application to a multivariable binary distillation column under feedback neurocontrol illustrates the usefulness of the robustness approach here developed to predict the absence of limit cycles, which of course is subject to the usual restrictions of the describing function method.     

Robust stability bounds for multi-delay networked control systems

In this paper, the robust stability of a perturbed linear continuous-time system is examined when controlled using a sampled-data networked control system (NCS) framework. Three new robust stability bounds on the time-invariant perturbations to the original continuous-time plant matrix are presented guaranteeing stability for the corresponding discrete closed-loop augmented delay-free system (ADFS) with multiple time-varying sensor and actuator delays. The bounds are differentiated from previous work by accounting for the sampled-data nature of the NCS and for separate communication delays for each sensor and actuator, not a single delay. Therefore, this paper expands the knowledge base in multiple inputs multiple outputs (MIMO) sampled-data time delay systems. Bounds are presented for unstructured, semi-structured, and structured perturbations.     

Modeling the structure of vortex zones between periodic superficially located energizers of the flow of a rectangular cross section

The mathematical simulation is presented of the structure of vortex zones between periodical superficially located turbulators energizing the flow of a rectangular cross section based on multiblock computational technologies. The calculations are based on the solution of the Reynolds equations factorized by the finite-volume method and closed by Menter’s model of the shear stress transfer and the energy equation on different-scale intersecting structured grids. This method had previously been successfully applied and experimentally verified in [1–4]. An exhaustive analysis of the corresponding flow lines is presented.     

Robust identification and fault diagnosis based on uncertain multiple input–multiple output linear parameter varying parity equations and zonotopes

We present a robust fault diagnosis method for uncertain multiple input–multiple output (MIMO) linear parameter varying (LPV) parity equations. The fault detection methodology is based on checking whether measurements are inside the prediction bounds provided by the uncertain MIMO LPV parity equations. The proposed approach takes into account existing couplings between the different measured outputs. Modelling and prediction uncertainty bounds are computed using zonotopes. Also proposed is an identification algorithm that estimates model parameters and their uncertainty such that all measured data free of faults will be inside the predicted bounds. The fault isolation and estimation algorithm is based on the use of residual fault sensitivity. Finally, two case studies (one based on a water distribution network and the other on a four-tank system) illustrate the effectiveness of the proposed approach.     

具有不确定性时滞及仿射结构不确定性过程的简易自适应控制

讨论了具有不确定性时滞及仿射结构不确定系统的简易自适应控制问题.给出了对系统再建模方法,所提出的方法可更精确评价不确定性时滞.通过对受控对象附加鲁棒并行补偿器补偿,设计了简易自适应控制器.     

频域结构不确定性模型有效性分析——正切结构Nevanlinna-Pick 插值法

利用正切结构Ｎｅｖａｎｌｉｎｎａ－Ｐｉｃｋ插值理论,研究了扰动集有结构的具有线性分式传递函数的模型有效性分析问题。模型有效性与参数辨识相结合晃本领域目前的研究热点问题,故这里讨论的模型集的不确定性不仅仍扰动集的不稳定,还有不易观测的部分名义模型的不确定。我们将这类模型集的有效性分析问题转化为双线性矩阵不等式（ＢＭＩ）求解问题,构造了双迭代算法进行求解,并给出了算法的理论分析,提到了在有限步迭代后可     

Development of Box–Jenkins type time series models by combining conventional and orthonormal basis filter approaches

A unified scheme for developing Box–Jenkins (BJ) type models from input–output plant data by combining orthonormal basis filter (OBF) model and conventional time series models, and the procedure for the corresponding multi-step-ahead prediction are presented. The models have a deterministic part that has an OBF structure and an explicit stochastic part which has either an AR or an ARMA structure. The proposed models combine all the advantages of an OBF model over conventional linear models together with an explicit noise model. The parameters of the OBF–AR model are easily estimated by linear least square method. The OBF–ARMA model structure leads to a pseudo-linear regression where the parameters can be easily estimated using either a two-step linear least square method or an extended least square method. Models for MIMO systems are easily developed using multiple MISO models. The advantages of the proposed models over BJ models are: parameters can be easily and accurately determined without involving nonlinear optimization; a prior knowledge of time delays is not required; and the identification and prediction schemes can be easily extended to MIMO systems. The proposed methods are illustrated with two SISO simulation case studies and one MIMO, real plant pilot-scale distillation column.     

RCMAC Hybrid Control for MIMO Uncertain Nonlinear Systems Using Sliding-Mode Technology

A hybrid control system, integrating principal and compensation controllers, is developed for multiple-input-multiple-output (MIMO) uncertain nonlinear systems. This hybrid control system is based on sliding-mode technique and uses a recurrent cerebellar model articulation controller (RCMAC) as an uncertainty observer. The principal controller containing an RCMAC uncertainty observer is the main controller, and the compensation controller is a compensator for the approximation error of the system uncertainty. In addition, in order to relax the requirement of approximation error bound, an estimation law is derived to estimate the error bound. The Taylor linearization technique is employed to increase the learning ability of RCMAC and the adaptive laws of the control system are derived based on Lyapunov stability theorem and Barbalat's lemma so that the asymptotical stability of the system can be guaranteed. Finally, the proposed design method is applied to control a biped robot. Simulation results demonstrate the effectiveness of the proposed control scheme for the MIMO uncertain nonlinear system     

Non‐diagonal MIMO QFT controller design reformulation

This paper presents a reformulation of the full‐matrix quantitative feedback theory (QFT) robust control methodology for multiple‐input–multiple‐output (MIMO) plants with uncertainty. The new methodology includes a generalization of previous non‐diagonal MIMO QFT techniques; avoiding former hypotheses of diagonal dominance; simplifying the calculations for the off‐diagonal elements, and then the method itself; reformulating the classical matrix definition of MIMO specifications by designing a new set of loop‐by‐loop QFT bounds on the Nichols Chart, which establish necessary and sufficient conditions; giving explicit expressions to share the load among the loops of the MIMO system to achieve the matrix specifications; and all for stability, reference tracking, disturbance rejection at plant input and output, and noise attenuation problems. The new methodology is applied to the design of a MIMO controller for a spacecraft flying in formation in a low Earth orbit. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust stability analysis for uncertain delay systems with output feedback controller

A systematic approach is given in this paper for analyzing the robust stability of uncertain time-delay systems controlled by output feedback. By checking the eigenvalues of a Hamiltonian matrix, the stability of nominal systems can be examined first. Then, for the nominally stable uncertain systems with multiple time delays, a new method using structured singular value technique is proposed for finding a set of uncertain parameters within which the systems remain stable. Moreover, an illustrative example is given to show the usefulness of the proposed approach.     

Structured Set Membership identification of nonlinear systems with application to vehicles with controlled suspension

This paper considers an iterative algorithm for the identification of structured nonlinear systems. The systems considered consist of the interconnection of a MIMO linear systems and a MIMO nonlinear system. The considered interconnection structure can represent as particular cases Hammerstein, Wiener or Lur’e systems. A key feature of the proposed method is that the nonlinear subsystem may be dynamic and is not assumed to have a given parametric form. In this way the complexity/accuracy problems posed by the proper choice of the suitable parametrization of the nonlinear subsystem are circumvented. Moreover, the simulation error of the overall model is shown to be a nonincreasing function of the number of algorithm iteration. The effectiveness of the algorithm is tested on the problem of identifying a model for vertical dynamics of vehicles with controlled suspensions from both simulated and experimental data.     

Performance and Robustness of Flow Controllers Designed Using Non‐causal Uncertainty Blocks

According to some recent results, use of non‐causal uncertainty blocks may be advantageous in the robust controller design of systems with multiple uncertain time‐delays. In this work, performance and robustness improvements obtained by utilizing such an approach are presented. The flow controller design problem for networks with multiple uncertain time‐delays is considered as a case study. It is shown that higher performance levels and larger stability margins are, in general, obtained by using non‐causal uncertainty blocks. A number of simulations, which illustrate the time‐domain performance improvement, are also presented.     

Frequency-domain criteria of robust stability for slowlytime-varying systems

The problem of stability of feedback systems with structured slowly time-varying uncertain gains is considered. For the case when the pair “uncertain gain/derivative” belongs to a given convex set, a sufficient frequency-domain condition of stability is obtained. This condition is an MIMO generalization of the SISO results derived in the 60s in the context of the positivity theory     

Observer‐based Adaptive fuzzy control of time‐delay uncertain nonlinear systems

An observer‐based adaptive fuzzy model following controller is proposed for a class of MIMO nonlinear uncertain systems to cope with time‐delay, uncertainty in plant structure and disturbances. Based on universal approximation theorem the unknown nonlinear functions are approximated by fuzzy systems, where the premise and the consequent parts of the fuzzy rules are tuned with adaptive schemes. To have more robustness, and at the same time to alleviate chattering, an adaptive discontinuous structure is suggested. Moreover, the availability of the states measurement is not required and an adaptive observer is used to estimate the states. Asymptoic stability of the overall system is ensured using suitable a Lyapunov‐Krasovskii functional candidate. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A risk adjusted approach to robust simultaneous fault detection and isolation

This paper addresses the problem of detecting and isolating faults in noisy MIMO uncertain-systems, subject to structured dynamic uncertainty. Its main result shows that this problem can be efficiently solved using a combination of sampling and LMI optimization tools. These results are illustrated with two examples and benchmarked against existing methods.