Showing papers in "International Journal of Adaptive Control and Signal Processing in 2001"

Multiple model adaptive control with safe switching

Abstract: SUMMARY The purpose of this paper is to marry the two concepts of multiple model adaptive control and safe adaptive control. In its simplest form, multiple model adaptive control involves a supervisor switching among one of a "nite number of controllers as more is learnt about the plant, until one of the controllers is "nally selected and remains unchanged. Safe adaptive control is concerned with ensuring that when the controller is changed in an adaptive control algorithm, the frozen plant}controller combination is never (closed-loop) unstable. This is a non-trivial task since by de"nition of an adaptive control problem, the plant is not fully known. The proposed solution method involves a frequency-dependent performance measure and employs the Vinnicombe metric. The resulting safe switching guarantees depend on the extent to which a closed-loop transfer function can be accurately identi"ed. Copyright 2001 John Wiley & Sons, Ltd.

Adaptive control of Burgers' equation with unknown viscosity

Abstract: In this paper, we propose a fortified boundary control law and an adaptation law for Burgers' equation with unknown viscosity, where no a priori knowledge of a lower bound on viscosity is needed. This control law is decentralized, i.e., implementable without the need for central computer and wiring. Using the Lyapunov method, we prove that the closed-loop system, including the parameter estimator as a dynamic component, is globally H1 stable and well posed. Furthermore, we show that the state of the system is regulated to zero by developing an alternative to Barbalat's Lemma which cannot be used in the present situation. Copyright © 2001 John Wiley & Sons, Ltd.

Adaptive robust control of a class of dynamic delay systems with unknown uncertainty bounds

Abstract: In this paper, a robust adaptive controller is developed for a class of uncertain dynamic systems with time-varying delays and subject to uncertainties whose bounds are unknown but their functional properties are known. It is shown that if a constraint on the norm of the matrix associated with the delayed state is met, then the adaptive controller designed guarantees that all solutions of the class of systems considered converge to a ball with any prespecified exponential convergence rate towards it. Finally, an example is included to illustrate the results developed in this paper. Copyright © 2001 John Wiley & Sons, Ltd.

Reduced spatial order model reference adaptive control of spatially varying distributed parameter systems of parabolic and hyperbolic types

Abstract: This paper presents control laws for distributed parameter systems of parabolic and hyperbolic types with unknown spatially varying parameters. These laws, based on the model reference adaptive control approach, guarantee asymptotic tracking of the output of the reference model by the output of the plant for arbitrary time invariant, but spatially varying reference input. The novel capabilities of the algorithms proposed are providing reduced sensitivity to measurement noise due to the reduced order of the spatial differentiation of the output data and permitting on-line estimation of the spatially varying plant parameters, constructively enforceable through the reference input and/or boundary conditions. The parameter estimation is carried out by means of an auxiliary system with the time-varying parameters that simultaneously converge in L2 to plant parameters when appropriate input signals in the reference model are used. The orthogonal expansions of these time-varying parameters, which can be computed by passing the auxiliary system parameters through the integrator block, converge to the plant parameters pointwise if the latter are sufficiently smooth. The parameter convergence is obtained by combining the adaptation laws with sufficiently rich input signals, referred to as generators of persistent excitation, which guarantee the existence of a unique steady state for the parameter errors. Copyright © 2001 John Wiley & Sons, Ltd.

Semi-adaptive control of convexly parametrized systems with application to temperature regulation of chemical reactors

Abstract: In this paper, we are interested in the problem of adaptive control of non-linearly parametrized systems. We investigate the viability of defining a stabilizing parameter update law for the case when the plant model is convex on the uncertain parameters. We show that, when the only prior knowledge is convexity, there does not exist an adaptation law - derivable from the standard separable Lyapunov function technique of Parks - applicable for all the state space. Therefore, we propose a semi-adaptive state feedback controller where adaptation takes place only in the region of the state space where convexity can be used to reduce parameter uncertainty. In the remaining part of the state space we freeze the adaptation and switch to a robust controller. This scheme ensures semi-global stability for convexly parametrized non-linear systems with matched uncertainty. The proposed controller is then applied to the problem of temperature regulation of continuous stirred exothermic chemical reactors where reaction heat is convex in the uncertain parameters. Copyright (C) 2001 John Wiley & Sons, Ltd.

Parameter identifiability of differential delay equations

Abstract: Parameter identifiability is concerned with the question whether the parameters of a specific model can be identified from knowledge about certain solutions of the model, assuming perfect data. In this paper we shall consider conditions for identifiability of parameters and time delays in infinite dimensional dynamical systems, described by linear differential delay equations, assuming knowledge of particular solutions on bounded time intervals. We shall show how methods from operator theory can be exploited to give necessary and sufficient conditions which guarantee that the inverse problem has a unique solution. Copyright © 2001 John Wiley & Sons, Ltd.

On‐line robust parameter identification for parabolic systems

Abstract: In this paper a robust scheme for the adaptive parameter identification of parabolic distributed parameter systems is developed. Results from the finite-dimensional treatment of the parameter projection method and σ (sigma) modifications to the standard adaptation rules are extended to infinite-dimensional systems. For the class of systems under study, modifications to these standard parameter adaptation rules were deemed necessary in order to account for the additional mathematical subtleties that arise when dealing with infinite-dimensional systems. Copyright © 2001 John Wiley & Sons, Ltd.

Stochastic adaptive control using multiple models for improved performance in the presence of random disturbances

Abstract: The use of multiple models for adaptively controlling an unknown continuous-time linear system was proposed in Narendra and Balakrishnan (IEEE Transactions on Automatic Control 1994; 39(9):1861–1866). and discussed in detail in Narendra and Xiang (IEEE Transactions on Automatic Control 2000, 45(9):(1669–1686) Technical Reports 9801 and 9803, Centre for System Science, Yale University, 1998). Recently, the same concepts were extended to discrete-time systems, both for the noise free case as well as when a stochastic disturbance is present, and the convergence of the algorithms was established. In this paper we consider structurally different estimation models, and use the multiple models approach to select, on-line, the one that results in the best performance of the overall system for the given disturbance characteristics. The principal objective of the paper is to demonstrate that the convergence of these schemes can be treated in a unified manner. Simulations are included towards the end of the paper to indicate the improvement in performance that can be achieved using such schemes. Copyright © 2001 John Wiley & Sons, Ltd.

State observation and adaptive linearizing control for distributed parameter (bio)chemical reactors

Abstract: This paper is concerned with the design and real-life application of observers and control algorithms for distributed parameter (bio)chemical reactors. The designed observer does not require the knowledge of the process kinetics and belongs to the class of observers for systems with unknown inputs. The designed controller is an adaptive linearizing controller. The performances of both observer and controller are illustrated with real-life applications: a chemical process (synthesis of ETBE) and a biochemical process (denitrifying biofilter). Copyright (C) 2001 John Wiley & Sons, Ltd.

On the design of adaptive notch filters

Abstract: In instrumentation and other applications, the on-line estimation of the frequency and amplitude of a noise-corrupted sinewave is of great practical interest. Recently an adaptive notch filter (ANF) with global convergence properties has been developed, and is a candidate approach to our problem. This paper analyses the transient and noise properties of this ANF and equips the method with design equations. Using frequency ranges greater than (up to 2 decades) and signal/noise ratios less than (down to −16 dB) those commonly found in the ANF literature, it is verified by extensive simulations that the new frequency estimator has excellent tracking and noise-rejection properties, provided that the signal/noise ratio is not too small. A comparison is made of its behaviour with that of a phase-locked loop, a method commonly used in practice. Copyright © 2001 John Wiley & Sons, Ltd.

A unified adaptive oculomotor control model

Abstract: In order to understand mechanisms of oculomotor control systems, an oculomotor model based on eye's anatomical structure and physiological mechanism is developed. In this model, various types of eye movements are considered, and two learning systems, one based on adaptive characteristics of flocculus and the other on vestibular nuclei's are developed. The role of neural paths from ocular muscle stretch receptors into flocculus, which were thought to not contribute in eye movement, is discussed in detail from the viewpoint of system control engineering. The experimental results through simulation show good control performance of the proposed model. Copyright © 2001 John Wiley & Sons, Ltd.

On a class of switched, robustly stable, adaptive systems

Abstract: A class of switched algorithms for adaptive control of siso linear systems is described The systems considered are assumed to belong to one among a finite number of classes of admissible process models, and each class is robustly stabilizable by some linear time-invariant controller The control used is chosen in real time by a tuner or supervisor, according to observations of suitably defined ‘identification errors’ The method preserves the robustness properties of the linear control design in an adaptive context, thus extending earlier ideas in multiple-model adaptive control by presenting a more flexible and less conservative framework for considering such systems One motivating application is fault-tolerant control Copyright © 2001 John Wiley & Sons, Ltd

A brief look at the Tsypkin criterion: from analysis to design

Abstract: Tsypkin was among the first to recognize the importance of the Popov criterion and to extend it to discrete-time systems in the form now known as the Tsypkin criterion. This paper briefly reviews the evolution of the Tsypkin criterion from its original use in absolute stability analysis to its current application as a design tool. Copyright © 2001 John Wiley & Sons, Ltd.

Subspace based direct adaptive ℋ︁∞ control

Abstract: This paper presents extensions of the model free subspace based ℋ∞ control approach. In particular, a fast algorithm for computing a subspace predictor from experimental data is introduced. The paper also describes a fast algorithm for updating the subspace predictor when new experimental data are available. These algorithms can be applied in conjunction with model free subspace based ℋ∞ control in order to create a novel adaptive control law. A defining feature of this control law is that an estimate of achievable performance is maintained throughout the operation of the closed-loop system. These algorithms are used to demonstrate the closed-loop control of a flexible structure. Copyright © 2001 John Wiley & Sons, Ltd.

Adaptive internal model control: the discrete-time case

Abstract: This paper considers the design and analysis of a discrete-time H2 optimal robust adaptive controller based on the internal model control structure. The certainty equivalence principle of adaptive control is used to combine a discrete-time robust adaptive law with a discrete-time H2 internal model controller to obtain a discrete-time adaptive H2 internal model control scheme with provable guarantees of stability and robustness. The approach used parallels the earlier results obtained for the continuous-time case. Nevertheless, there are some differences which, together with the widespread use of digital computers for controls applications, justifies a separate exposition. Copyright © 2001 John Wiley & Sons, Ltd.

Optimal design for discrete-time linear systems via new performance index

Abstract: We introduce a class of linear discrete-time systems called ‘superstable’. For the SISO case this means that the absolute value of the constant term of the characteristic polynomial is greater than the sum of absolute values of all other coefficients, while superstable MIMO systems have a state matrix with l1 norm less than one. Such systems have many special features. First, non-asymptotic bounds for the output of such systems with bounded input can be easily obtained. In particular, for small enough initial conditions, we get the equalized performance property, recently introduced for the SISO case by Blanchini and Sznaier (36th CDC, San Diego, 1997, pp. 1540–1545). Second, the same bounds can be obtained for LTV systems, provided all the frozen LTI systems are super stable. This makes the notion well suited for adaptive control. These bounds can be used as the performance index for optimal controller design, as proposed by Blanchini and Sznaier for the SISO case. Then to obtain disturbance rejection in SISO or MIMO systems, we design a controller which guarantees super stability of the closed-loop system and minimizes the proposed performance index (γ-optimality). This problem happens to be quasiconvex with respect to the controller coefficients and can be solved via parametric linear programming. Compared with the well-known l1 optimization-based design technique, the approach allows low-order controllers to be designed (while l1 optimal controllers may have high order) and can take into account non-asymptotic time-domain behaviour of the system with non-zero initial conditions. For unbounded controller orders we prove the existence and finite dimensionality of γ-optimal designs. We also address the robustness issues for transfer functions with coprime factor uncertainty bounded in l1 norm. A robust performance problem can be formulated and similarly solved via linear programming. Numerous examples are provided to compare the proposed design with optimal l1 and H∞ controllers. Copyright © 2001 John Wiley & Sons, Ltd.

Neural network adaptive robust control with application to precision motion control of linear motors

Abstract: In this paper, neural networks (NNs) and adaptive robust control (ARC) design philosophy are integrated to design performance-oriented control laws for a class of single-input–single-output (SISO) nth-order non- linear systems. Both repeatable (or state dependent) unknown non-linearities and non-repeatable unknown non-linearities such as external disturbances are considered. In addition, unknown non-linearities can exist in the control input channel as well. All unknown but repeatable non-linear functions are approximated by outputs of multi-layer neural networks to achieve a better model compensation for an improved performance. All NN weights are tuned on-line with no prior training needed. In order to avoid the possible divergence of the on-line tuning of neural network, discontinuous projection method with fictitious bounds is used in the NN weight adjusting laws to make sure that all NN weights are tuned within a prescribed range. By doing so, even in the presence of approximation error and non-repeatable non-linearities such as disturbances, a controlled learning is achieved and the possible destabilizing effect of on-line tuning of NN weights is avoided. Certain robust control terms are constructed to attenuate various model uncertainties effectively for a guaranteed output tracking transient performance and a guaranteed final tracking accuracy in general. In addition, if the unknown repeatable model uncertainties are in the functional range of the neural networks and the ideal weights fall within the prescribed range, asymptotic output tracking is also achieved to retain the perfect learning capability of neural networks in the ideal situation. The proposed neural network adaptive control (NNARC) strategy is then applied to the precision motion control of a linear motor drive system to help to realize the high-performance potential of such a drive technology. NN is employed to compensate for the effects of the lumped unknown non-linearities due to the position dependent friction and electro-magnetic ripple forces. Comparative experiments verify the high-performance nature of the proposed NNARC. With an encoder resolution of 1 µm, for a low-speed back-and-forth movement, the position tracking error is kept within ±2 µm during the most execution time while the maximum tracking error during the entire run is kept within ±5.6 µm. Copyright © 2001 John Wiley & Sons, Ltd.

Unfalsified direct adaptive control of a two‐link robot arm

Abstract: An application of unfalsified control theory to the design of a switching adaptive controller for a non-linear robot manipulator is described. In the unfalsified control approach, candidate controllers are eliminated and discarded when their ability to meet performance goals is falsified by evolving experimental data. Switching occurs when the currently active control law is among those falsified. In this design study, the candidate controllers are non-linear, and have a non-linear ‘computed torque’ control structure with four switchable parameters corresponding to unknown masses, inertias and other dynamical coefficients of a class of ideal, but imperfect robot arm models. Simulations confirm that our unfalsified switching controller permits significantly more precise and rapid parameter adjustments than a conventional adaptation law having continuous parameter update rules, especially when the manipulator arm is subject to sudden random changes in mass or load properties. Copyright © 2001 John Wiley & Sons, Ltd.

Supervisory field‐oriented control of induction motors with uncertain rotor resistance

Abstract: SUMMARY It is well known that the performance of the (industry standard) "eld-oriented control (FOC) for induction motors is highly sensitive to uncertainties in the rotor resistance. In this paper we describe how to use supervisory control to obtain an adaptive implementation of FOC for current-fed machines. The unknown rotor resistance is assumed to belong to a discrete set, while the uncertain load torque ranges in a given compact set. Even though no restrictions are a priori imposed on the size of these sets, their de"nitions re#ect the prior knowledge of the designer, which is e!ectively incorporated in the supervisory control algorithm. The supervisor selects from these sets values for the parameters to be applied to the FOC, a choice that is made by continuously comparing suitably de"ned performance signals. We prove that the proposed supervisor achieves global stabilization of the system when the load torque is known to belong to a given "nite set of values. Apparently, this is the "rst globally convergent adaptive algorithm for current-fed machines which simply adds adaptation to the widely popular FOC and is not a radically new complicated controller, hence it is more likely to be adopted by practitioners. Some simulation results illustrate the properties of the algorithm. Copyright 2001 John Wiley & Sons, Ltd.

Recursive least-squares and accelerated convergence in stochastic approximation schemes

Abstract: The so-called accelerated convergence is an ingenuous idea to improve the asymptotic accuracy in stochastic approximation (gradient based) algorithms. The estimates obtained from the basic algorith ...

Designing predictors for MIMO switching supervisory control

Abstract: The paper studies the problem of inferring the behaviour of a linear feedback loop made up by an uncertain MIMO plant and a given candidate controller from data taken from the plant possibly driven by a different controller. In such a context, it is shown here that a convenient tool to work with is a quantity called normalized discrepancy. This is a measure of mismatch between the loop made up by the unknown plant in feedback with the candidate controller and the nominal ‘tuned-loop’ related to the same candidate controller. It is shown that discrepancy can in principle be obtained by resorting to the concept of a virtual reference, and conveniently computed in real time by suitably filtering an output prediction error. The latter result is of relevant practical value for on-line implementation and of paramount importance in switching supervisory control of uncertain plants, particularly in the case of a coarse distribution of candidate models. Copyright © 2001 John Wiley & Sons, Ltd.

A genetic search approach to unfalsified PI control design for a weigh belt feeder

Abstract: This paper proposes and experimentally demonstrates an approach to automated PI tuning for an industrial weigh belt feeder that is based on unfalsified control concepts. Unfalsified control is used here as a means of using either open- or closed-loop test data to identify a subset of controllers (from an initial set) that is not proved to violate the multiple objectives specified by the control engineer. A novel feature of the unfalsified approach is that it allows controllers to be eliminated from consideration by predicting their performance without actually inserting the controllers in the loop. In addition, this methodology does not require an explicit model. However, in practice, it does require some closed-loop experimentation to determine the cost functions used to perform the unfalsification. When the unfalsified PI autotuning approach is applied to the industrial weigh belt feeder, it is able to successfully identify a subset of PI control laws that meets the performance specs. A key feature of this paper is the use of a genetic search algorithm to reduce the computational requirements of unfalsified control, especially when the initial set of controllers is large. Copyright © 2001 John Wiley & Sons, Ltd.

Experimental modelling and intelligent control of a wood‐drying kiln

Abstract: Proper control of the wood-drying kiln is crucial in ensuring satisfactory quality of dried wood and in minimizing drying time. This paper presents the development, implementation, and evaluation of a control system for a lumber drying kiln process incorporating sensory feedback from in-wood moisture content sensors and intelligent control such that the moisture content of lumber will reach and stabilize at the desired set point without operator interference. The drying process is difficult to model and control due to complex dynamic nonlinearities, coupling effects among key variables, and process disturbances caused by the variation of lumber sizes, species, and environmental factors. Through system identification scheme using experimental data and recursive least-squares algorithm for parameter estimation, appropriate models are developed for simulation purpose and controller design. Two different control methodologies are employed and compared: a conventional proportional-integral-derivative (PID) controller and a direct fuzzy logic controller (FLC), and system performance is evaluated through simulations. The developed control system is then implemented in a downscaled industrial kiln located at the Innovation Centre of National Research Council (NRC) of Canada. This experimental set-up is equipped with a variety of sensors, including thermocouples for temperature feedback, an air velocity transmitter for measuring airflow speed in the plenum, relative humidity sensors for measuring the relative humidity inside the kiln, and in-wood moisture content sensors for measuring the moisture content of the wood pieces. For comparison, extensive experimental studies are carried out on-line using the two controllers, and the results are evaluated to tune the controller parameters to achieve good performance in the wood-drying kiln. The combination of conventional control with the intelligent control promises improved performance. The control system developed in this study may be applied in industrial wood-drying kilns, with a clear potential for improved quality and increased speed of drying. Copyright © 2001 John Wiley & Sons, Ltd.

Convergence of control performance by unfalsification of models - levels of confidence

Abstract: A general framework is introduced for iterative/adaptive controller design schemes by model unfalsification. An important feature of the schemes is their convergence near to the best possible controller given a set of model and controller structures. The problem of stability assured controller tuning is examined through unfalsified Riemannian bands of the Nyquist plot. Instability tolerant H(?) and l(1)-norm-based controller tuning schemes are introduced. Computational problems are discussed and a simulation is used to illustrate the new scheme.

Effects of the design parameters of multimodel adaptive control on the performance of a flexible transmission system

Abstract: SUMMARYDesign parameters selection in the multimodel adaptive control based on switching and tuning will beinvestigated. Some design parameters like number of " xed and adaptive models, forgetting factor andminimum time delay between switchings will be considered. A recently developed parameter adaptationalgorithm based on closed-loop output error will be compared with the classical least-squares predictionerror algorithm in the multimodel adaptive control. The e! ects of these parameters on the performance intracking and in regulation of a # exible transmission system will be studied via several simulation examples.Copyright ! 2001 John Wiley & Sons, Ltd. KEY WORDS: adaptive control; multimodel; switching; closed-loop identi " cation 1. INTRODUCTIONThe plants subjected to abrupt and large parameter variations are generally very di$ cult tocontrol. A classical adaptive controller or a " xed robust controller encounter the di$ culties tosolve this problem. An adaptive controller is not fast enough to follow the parameter variationsand unacceptable transients occur. Whereas a " xed robust controller normally leads to poorperformances because of large uncertainties.A solution based on switching between di! erent controllers for this type of plants has beenprobably proposed for the " rst time in Reference [1]. The main problem of switching is to decidewhen a controller should be switched to the plant. Some authors proposed a predeterminedswitching sequence [2 }4] but the multimodel approach seems m ore interesting. This approachbased on multiple models and switching will allow the transient responses to be improved in thepresence of large and fast parametric variations [5 }7]. In this approach, we suppose that a set ofmodels for di! erent operating points is a priori known. Then at every instant a controllercorresponding to the model yielding the minimum of a performance index is used to compute the

Force control of a reciprocating surface grinder using unfalsification and learning concept

Abstract: A plant model is an essential requirement in conventional methods for controller synthesis. However, it is possible to find a set of controllers that are not falsified by the performance specification or the measured data without any plant model or prejudicial assumptions. This concept is used to select and implement a force controller for a reciprocating surface grinder. Copyright © 2001 John Wiley & Sons, Ltd.

Stable neural control of uncertain multivariable systems

Abstract: Tracking control of a class of non-linear, uncertain, multi-input, multiple-output systems is addressed in this paper. The control system architecture uses neural networks for function approximation, certainty equivalent control inputs to cancel plant dynamics and smoothed sliding mode control to insure that the trajectories remain bounded. Lyapunov analysis is used to derive equations for the sliding mode control, neural network training, and to show uniform ultimate boundedness of the closed-loop system. Stability analysis results are shown for single-input single-output and two-input two-output systems. Results are then extended to the more general multiple-input multiple-output case where the number of inputs is equal to the number of outputs. Simple simulation examples are used to illustrate control system performance. Copyright © 2003 John Wiley & Sons, Ltd.

Non‐linear adaptive control of a heat exchanger

Abstract: In this contribution, two methods for adaptation of non-linear adaptive controllers are presented and compared, namely the data-driven and the knowledge-based adaptation. A dynamic Takagi–Sugeno fuzzy model is utilized to model the non-linear process behaviour. Based on this model, a non-linear predictive controller is designed to control the process. In the presence of time-variant process behaviour and changing unmodelled disturbances, high control performance can be achieved by performing an on-line adaptation of the fuzzy model. First, a local weighted recursive least-squares algorithm is used for adaptation. It exploits the local linearity of the Takagi–Sugeno fuzzy model. In the second approach, process knowledge that is obtained from theoretical insights is utilized to design a knowledge-based adaptation strategy. Both approaches are compared and their effectiveness and real-world applicability are demonstrated by application to temperature control of a heat exchanger. Copyright © 2001 John Wiley & Sons, Ltd.