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Showing papers in "International Journal of Robust and Nonlinear Control in 1992"


Journal ArticleDOI
TL;DR: In this paper, an interpolation theory approach and a Riccati equation approach are proposed to solve the estimation problem, with each method having its own advantages, the first approach seems more numerically attractive whilst the second one provides a simple structure for the estimator with its solution given in terms of two algebraic REs and a parameterization of a class of suitable H, estimators.
Abstract: SUMMARY This paper deals with the problem of H, estimation for linear systems with a certain type of time-varying norm-bounded parameter uncertainty in both the state and output matrices. We address the problem of designing an asymptotically stable estimator that guarantees a prescribed level of H, noise attenuation for all admissible parameter uncertainties. Both an interpolation theory approach and a Riccati equation approach are proposed to solve the estimation problem, with each method having its own advantages. The first approach seems more numerically attractive whilst the second one provides a simple structure for the estimator with its solution given in terms of two algebraic Riccati equations and a parameterization of a class of suitable H, estimators. The Riccati equation approach also pinpoints the ‘worst-case’ uncertainty.

235 citations


Journal ArticleDOI
TL;DR: It is demonstrated that as a result of using sliding control, better use of the network's approximation ability can be achieved, and the asymptotic tracking error can be made dependent only on inherent network approximation errors and the frequency range of unmodelled dynamical modes.
Abstract: A neural-network-based direct control architecture is presented that achieves output tracking for a class of continuous-time nonlinear plants, for which the nonlinearities are unknown. The controller employs neural networks to perform approximate input/output plant linearization. The network parameters are adapted according to a stability principle. The architecture is based on a modification of a method previously proposed by the authors, where the modification comprises adding a sliding control term to the controller. This modification serves two purposes: first, as suggested by Sanner and Slotine,1 sliding control compensates for plant uncertainties outside the state region where the networks are used, thus providing global stability; second, the sliding control compensates for inherent network approximation errors, hence improving tracking performance. A complete stability and tracking error convergence proof is given and the setting of the controller parameters is discussed. It is demonstrated that as a result of using sliding control, better use of the network's approximation ability can be achieved, and the asymptotic tracking error can be made dependent only on inherent network approximation errors and the frequency range of unmodelled dynamical modes. Two simulations are provided to demonstrate the features of the control method.

158 citations


Journal ArticleDOI
TL;DR: In this paper, the problem of state-feedback laws for systems modelled by nonlinear differential equations which are affine in the inputs has been studied, where the purpose of the design is to obtain a (locally) internally stable closed-loop system in which the effect of exogenous inputs on a prescribed error (or, more in general, on a penalty variable) is attenuated.
Abstract: This paper deals with the design of (memoryless) state-feedback laws for systems modelled by nonlinear differential equations which are affine in the inputs. The purpose of the design is to obtain a (locally) internally stable closed-loop system in which the effect of exogenous inputs on a prescribed error (or, more in general, on a penalty variable) is attenuated. Two standard setups are considered: in the first one, the ratio between the energy associated with the penalty variable and that associated with the exogenous input is required to be bounded by a constant 0 < γ this setup includes (to some extent) the standard H∞control problem of linear system theory. In the second one, the penalty variable is required to converge to 0 as t ∞; this setup generalizes the so-called servomechanism problem of linear system theory.

123 citations



Journal ArticleDOI
TL;DR: In this paper, the authors show how to design compensators which would allow for a direct solution to these problems through cancellation of the offending 0e zeros, which is demonstrated for the inner-outer factorization (IOF) problem mentioned above.
Abstract: Many control problems fall into the category of what we call singular control problems, i.e., problems for which known solutions fail owing to the fact that the relevant transfer functions have zeros on the extended imaginary axis, 0e. An example of this is the inner–outer factorization (IOF) problem for such transfer functions. In this paper, we show how to design compensators which would allow for a direct solution to these problems through cancellation of the offending 0e zeros. This is demonstrated for the IOF problem mentioned above. Our interest lies primarily with infinite zeros but we develop formulae for finite 0e compensators as well. The paper also presents some discussions on the infinite zero structure of linear time-invariant systems.

43 citations


Journal ArticleDOI
TL;DR: In this article, it is shown that each control station must satisfy a certain robustness property and that the design of the whole decentralized controller can be replaced by the problem of designing the control stations separately from each other as robust centralized controllers.
Abstract: The controller of a crystal growth furnace with 15 heating zones must have a decentralized structure. It is shown that each control station must necessarily satisfy a certain robustness property and that the design of the whole decentralized controller can be replaced by the problem of designing the control stations separately from each other as robust centralized controllers. As a basis for this, it is shown that the model can be considerably reduced. Although the zones are strongly coupled it will be seen here that, owing to structural properties of the plant, the furnace can be described by a model which has regard to only three zones. Experimental results with furnace illustrate the modelling and design methods used.

28 citations


Journal ArticleDOI
TL;DR: In this article, structured singular value optimization techniques are used to design robust power system stabilizers (PSS) for a single-machine and a two-machine system with varying operating conditions.
Abstract: H∞ and structured singular value optimization techniques are used to design robust power system stabilizers (PSS) for a single-machine and a two-machine system with varying operating conditions. Realistic uncertainty models to represent the possible operating conditions as perturbations from a nominal operating condition are developed. System experience is used to select weighting functions to provide adequate damping and shape the controller frequency response. Computer simulations show that the PSS designed using the proposed technique provides improved damping compared to a conventional PSS.

22 citations


Journal ArticleDOI
TL;DR: In this article, the problem of generalizing elements of linear coprime factorization theory to a nonlinear context was considered, and it was shown that a suitably wide class of nonlinear systems can cover many practical situations, yet not cope with so broad a class as to disallow useful generalizations to the linear results.
Abstract: In this paper, we consider the problem of generalizing elements of linear coprime factorization theory to a nonlinear context. The idea is to work with a suitably wide class of nonlinear systems to cover many practical situations, yet not cope with so broad a class as to disallow useful generalizations to the linear results. In particular, we work with nonlinear systems characterized in terms of (possibly time-varying) state-dependent matrices A(x), B(x), C(x), D(x) and an initial state x0. (This class clearly does contain the class of finite-dimensional linear (time-varying) systems.) We achieve first right coprime factorizations for idealized situations. To achieve stable left factorizations we specialize to the case where the matrices are output-dependent. Alternatively, we work with systems, perhaps augmented by a direct feedthrough term, where the input is reconstructible from the output. For nonlinear feedback control systems, with plant and controller having stable left factorizations, then under appropriate regularity-conditions earlier results have allowed the generation of the class of stabilizing controllers for a system in terms of an arbitrary stable system (parameter). Plant uncertainties, including unknown initial conditions are modelled by means of a Yula–Kucera-type parametrization approach developed for nonlinear systems. Certain robust stabilization results are also shown, and simulations demonstrate the regulation of nonlinear plants using the techniques developed. All the results are presented in such a way that specialization for the case of linear systems is immediate.

16 citations


Journal ArticleDOI
TL;DR: In this article, the authors obtained the solution to the discrete-time, linear-quadratic, finite-horizon disturbance rejection problem, with hard bounds on the disturbance and with a known or an unknown non-zero initial state.
Abstract: In this paper, we obtain the solution to the discrete-time, linear-quadratic, finite-horizon disturbance rejection problem, with hard bounds on the disturbance and with a known or an unknown non-zero initial state. It is shown that there exist two regions in the space of initial conditions: one where a pure-strategy saddle point exists, and the other where no pure-strategy saddle point exists. In the latter region, the structure of the minimax controller is fixed throughout, and a saddle point exists in the class of mixed policies. The paper also develops a general algorithm for the construction of such saddle points under different information structures, and illustrates this algorithm on a numerical example.

15 citations


Journal ArticleDOI
TL;DR: In this article, a constructive method for absorbing an irrational outer factor of a plant into the Q-parameter in the H∞ optimal weighted sensitivity problem for single-input/single-output distributed parameter systems, when the plant has finitely many irrational zeros on the imaginary axis was presented.
Abstract: We present a constructive method for ‘absorbing’ an irrational outer factor of a plant into the ‘Q-parameter’ in the H∞ optimal weighted sensitivity problem for single-input/single-output distributed parameter systems, when the plant has finitely many irrational zeros on the imaginary axis. This problem could not be solved using previous results. We also extend our new results to the mixed sensitivity problem.

11 citations


Journal ArticleDOI
TL;DR: In this paper, the authors used H∞ optimization theory for the controller design of a two-axis magnetic suspension, flexible-beam system, which is a simplified model for a flexible magnetic bearing system.
Abstract: This paper deals with how to use H∞ optimization theory for the controller design of a two-axis magnetic suspension, flexible-beam system, which is a simplified model for a flexible magnetic bearing system. Both simulation and experimental results show that the designed system not only has good performance in robustness to the plant's parametric uncertainty and the unmodelled dynamics in the beam's vibration modes, mode shapes, etc., but also has good performance in response characteristics.

Journal ArticleDOI
TL;DR: In this article, the stability margins of singular perturbation systems are analyzed under unmodelled high-frequency dynamics control, composite control, and the original full-order linear quadratic (LQ) control.
Abstract: The gain and phase margins of singular perturbation systems are analysed under unmodelled high-frequency dynamics control, composite control, and the original full-order linear quadratic (LQ) control. The analysis is on the basis that there is a good relation between the minimum singular value of return difference transfer matrix and the stability margins. We begin with the examination of stability margins of subsystems and then show that state-feedback control design of subsystems could preserve gain and phase margins for the original full-order singularly perturbed system if the singular perturbation parameter epsiv; is sufficiently small. The effectiveness of e on stability margins is formulated and determined. It is found that the effectiveness can be evaluated by a simple method. Two examples are exploited to illustrate the analytic results.

Journal ArticleDOI
TL;DR: In this paper, the authors developed necessary conditions for a minimax problem involving control and exogenous inputs, which can be regarded as a finite horizon version of the H∞ optimal control problem.
Abstract: In this paper we develop necessary conditions for a minimax problem involving control and exogenous inputs. The problem can be regarded as a finite horizon version of the H∞ optimal control problem. We consider problems involving generalized cost functional and non-zero initial conditions. A criterion for the evaluation of the performance index is given in these cases. Our computational experience shows that the finite horizon performance is useful in computing the infimal H∞ norm in the infinite horizon case, as the final time becomes large. Also, expressions are derived for the variation in performance in terms of system parameter variations. These linear expressions are useful in the evaluation of the robustness of the proposed control strategy.

Journal ArticleDOI
TL;DR: The Neal-Smith pilot model for a compensatory tracking task is used to develop a technique which allows the designer to synthesize compensation in the outer loop, which includes a free compensator Fp(S).
Abstract: Nonlinear quantitative feedback theory (QFT) is used to design a flight control system for the nonlinear model of the YF-16 aircraft (A/C) with C* as the controlled output. The resulting closed loop stability augmentation system (SAS), Pe(S), becomes part of the outer loop containing the pilot. The Neal-Smith pilot model for a compensatory tracking task is used to develop a technique which allows the designer to synthesize compensation in the outer loop, which includes a free compensator Fp(S). The latter is chosen to minimize pilot workload, increase system bandwidth, and improve handling qualities ratings as per the Neal–Smith criteria, for the tracking task. The available pilot compensation abilities are then available for further increasing of system bandwidth to improve overall capabilities. This approach can be used at the early stages of flight control design, thus saving time and money over the current practice. Simulations in the time and frequency domains demonstrate that the desired performance is attained.

Journal ArticleDOI
TL;DR: In this paper, a technique for designing fixed order dynamic compensators in controller canonical form which are robust to both structured and unstructured uncertainty is presented, where a quadratic performance index is minimized subject to a constraint on the H∞ norm of the closed loop transfer function from disturbances to controlled outputs.
Abstract: This paper presents a technique for designing fixed order dynamic compensators in controller canonical form which are robust to both structured and unstructured uncertainty. The formulation uses an approach which combines an H2 and H∞ optimization process. Specifically, a quadratic performance index is minimized subject to a constraint on the H∞ norm of the closed loop transfer function from disturbances to controlled outputs. This provides robustness to unstructured uncertainty. To provide robustness to structured uncertainty, an upper bound is computed for the worst case parameter variations, and it is then included in the derivation of the optimality conditions. A robust controller for a jetfoil boat is used to demonstrate this design technique. For the specific case of no structured uncertainty, the results of this approach using the canonical form compensator are analytically related to the previously published results for a fixed-order dynamic compensator. It is demonstrated that the use of the canonical form greatly simplifies the system of necessary conditions.

Journal ArticleDOI
TL;DR: In this article, the influence functional is used as a measure of robustness for the choice of the error-shaping function in the correlation or instrumental variables approach to system parameter identification.
Abstract: The influence functional, developed by Martin and Yohai, is an asymptotic robustness measure of a parameter estimate's sensitivity to the infinitesimal occurrence of correlated outlier contamination of a measurement sequence. Here, the usefulness of the influence functional as a tool for characterizing estimator robustness in system parameter identification is explored. In particular, this utility is illustrated by examining the influence functional as a measure of robustness for the choice of the error-shaping function in the correlation or instrumental variables approach to system parameter identification.