A robust adaptive pole‐placement controller without strictly positive real condition

This paper considers the adaptive pole‐placement control problem for system (1) with unmodelled dynamics η_n dominated by a small constant ε multiplied by a quantity independent of ε but tending to infinity as the past input, output, and noise grow. Using bounded external excitation and randomly varying truncation techniques, we give a design method of adaptive pole‐placement controller. It is shown that the closed‐loop system is globally stable, the estimation error for the parameter contained in the modelled part is of order ε, and the closed‐loop system under the adaptive pole‐placement control law is suboptimal in the sense of $$\mathop{\lim\sup}\limits_{{n\to\infty }}{1\over n}\mathop{\sum}\limits_{i=0}^n{\left({A^{*}(z)y_{n}‐L(z)C(z)w_{n}‐B(z)R(z)y_{n}^{*}}\right)^{2}{\leq}O({\varepsilon}^{2})+\gamma^{2}\mathop{\sum}\limits_{j=1}^q{b_{j}^{2}}}$$\nopagenumbers\end while the SPR condition used usually in other papers is replaced by a stability condition. Copyright © 2001 John Wiley & Sons, Ltd.     

Logistic Regression Analysis of Customer Satisfaction Data

Variation exists in all processes. Significant work has been done to identify and remove sources of variation in manufacturing processes resulting in large returns for companies. However, business process optimization is an area that has a large potential return for a company. Business processes can be difficult to optimize due to the nature of the output variables associated with them. Business processes tend to have output variables that are binary, nominal or ordinal. Examples of these types of output include whether a particular event occurred, a customer's color preference for a new product and survey questions that assess the extent of the survey respondent's agreement with a particular statement. Output variables that are binary, nominal or ordinal cannot be modeled using ordinary least‐squares regression. Logistic regression is a method used to model data where the output is binary, nominal or ordinal. This article provides a review of logistic regression and demonstrates its use in modeling data from a business process involving customer feedback. Copyright © 2006 John Wiley & Sons, Ltd.     

An adaptive tracking problem for a family of retarded time-delay plants

Most of the existing switching control techniques are developed specifically for finite-dimensional linear time-invariant (LTI) systems. In many practical applications, however, it is essential to take time delay into consideration in the modelling as the control system can be highly sensitive to delay. In this paper, a multi-model switching control algorithm is proposed for retarded time-delay systems. It is assumed that the plant is represented by a family of known multi-input multi-output, observable, LTI models with multiple delays in the states, and that corresponding to each model in the known family, there exists a high-performance finite-dimensional LTI controller. In addition, it is supposed that a bound on the magnitude of the external inputs and disturbances is available. It is then shown that the proposed switching controller can stabilize the uncertain system, and that under some mild conditions, output tracking can be achieved in the given problem setting. Copyright © 2007 John Wiley & Sons, Ltd.     

Adaptive control of siso plants with unmodelled dynamics

In this paper we pursue a twofold aim. First we want to simplify the complexity of the classical Monopoli's scheme, the so-called ‘Augmented error signal control scheme’. Then we also wish to cope with the realistic situation in which the presence of unmodelled dynamics has to be taken into account. This latter problem has been faced in the literature by suitably modifying the adaptation mechanism in order to avoid undesired phenomena as well as to obtain an attractive stability region for the state trajectories starting from any point in a predefined initial condition set. In our case the necessity of introducing any sort of modification in the adaptation mechanism is completely avoided, but we still obtain asymptotic stability of the output error signal.     

Possibilities and extension of XRD material response analysis in failure research for the advanced evaluation of the damage level of Hertzian loaded components

Due to clearly distinguishable damage symptoms, it is differentiated between the surface and sub‐surface failure mode of rolling bearings. Material states red out by X‐ray diffraction (XRD) residual stress measurements point to a variety of loading conditions especially at raceway surfaces that are associated with several competing failure mechanisms. The corresponding lifetime reduction can range from the lower fatigue strength region to material ratcheting in extreme cases. Relevant position of the microstructural changes and nature of the failure mechanisms are characterized. The time alteration of the XRD material parameters measured at or near the surface and at the depth of the maximum equivalent stress correlates, in a different manner, with the statistical parameter of the 10 % bearing life. Both failure modes are illustrated by concrete examples. Contaminated lubricant and boundary lubrication, which represent practically important surface‐induced failures, are discussed in more detail. Gray staining, i.e. shallow pitting, often occurs without distinct indication of global material aging by means of XRD characteristics. Here, scanning electron microscopy observations and electron microprobe analyses point to corrosion fatigue as acting surface failure mechanism. The interaction between material and lubricant under complex loading regimes particularly of mixed friction and corrosion opens further failure research areas in the field of tribology.     

Robustness of VS-MRAC with respect to unmodelled dynamics and external disturbances

A variable structure model reference adaptive controller (VS-MRAC) using only input and output measurements was recently proposed and shown to be globally asymptotically stable with superior transient behaviour and disturbance rejection properties. In this paper a singular perturbation approach is used in order to establish the robustness of the controller in the presence of unmodelled dynamics (parasitics) and disturbances. We develop a new Lyapunov-based technique to analyse the overall system and show that for sufficiently small parasitics the system remains stable and the output error is small in some sense.     

Transient operation of a catalytic liquid-liquid plug flow reactor for kinetics measurements

A centrifugal partition chromatograph (CPC) was used as a liquid-liquid catalytic reactor for the isomerisation of hexen-3-ol into ethylpropylketone with a water soluble rhodium catalyst. Global mass transfer coefficients were measured and shown to depend on both the nature of the solute and the flow rate. Liquid-liquid partition isotherms were also determined with the CPC using elution chromatography. Finally, a reactor model was derived to account for the experimental results obtained both under stationary and transient (pulse) conditions. A parameter sensitivity evaluation is also presented.     

Two-level optimal output feedback stabilizer design

The paper addresses the design of two-level power system stabilizers using an optimal reduced order model whose state variables are torque angles and speeds. The reduced order model retains their physical meaning and is used to design a two-level linear feedback controller that takes into account the realities and constraints of electrical power systems. The two-level control strategy is used, and a global control signal is generated from the output variables to minimize the effect of interactions. The effectiveness of this controller is evaluated and a multimachine system is given as an example to illustrate the advantages of the proposed method. Responses of the system with a two-level scheme and an optimal reduced order scheme are included for comparative analysis.     

Lyapunov‐stable discrete‐time model reference adaptive control

Discrete‐time model reference adaptive control (MRAC) is considered with both least squares and projection algorithm parameter identification. For both cases complete Lyapunov proofs are given for stability and convergence. The results extend the approach of Johansson (Int. J. Control 1989; 50 (3):859–869) to include Lyapunov stability for MRAC when the normalized projection algorithm is used for parameter identification. Copyright © 2005 John Wiley & Sons, Ltd.