Showing papers in "International Journal of Robust and Nonlinear Control in 1997"
TL;DR: In this paper, a linear feedback control with state-dependent gains is proposed, where the gains become implicitly defined in terms of a nonlinear scalar equation, and the control function coincides in an ellipsoidal neighbourhood of the origin with a linear quadratic regulator problem.
Abstract: This work presents a technique for obtaining a bounded continuous feedback control function which stabilizes a linear system in a certain region. If the open-loop system has no eigenvalues with positive real part, the region of attraction of the resulting closed-loop system is all ℝn, i.e., the feedback control is a global stabilizer; otherwise, the region contains an invariant (‘cylindric-like’) set where the controller does not saturate. The proposed control is a linear-like feedback control with state-dependent gains. The gains become implicitly defined in terms of a nonlinear scalar equation. The control function coincides in an ellipsoidal neighbourhood of the origin with a linear feedback law which is a solution of a linear quadratic regulator problem. This design allows eigenvalue placement in a specified region. © 1997 by John Wiley & Sons, Ltd.
113 citations
109 citations
TL;DR: In this paper, an adaptive scheme to achieve output tracking for a class of minimum-phase dynamically input-output linearizable nonlinear systems with parametric uncertainties is considered, based upon a combination of the adaptive backstepping design method and a sliding mode control (SMC) scheme to design dynamical adaptive sliding mode controllers.
Abstract: An alternative adaptive scheme to achieve output tracking for a class of minimum-phase dynamically input–output linearizable nonlinear systems with parametric uncertainties is considered. The proposed approach is based upon a combination of the adaptive backstepping design method and a sliding mode control (SMC) scheme to design dynamical adaptive sliding mode controllers and provide robust output tracking even in the presence of unknown disturbances. The validity of the proposed approach, regarding tracking objectives and robustness with respect to bounded stochastic perturbation inputs, is tested through digital computer simulations. © 1997 by John Wiley & Sons, Ltd.
67 citations
TL;DR: Methods for the design of sliding mode controllers based on state feedback, static output feedback and dynamic output feedback, respectively, are proposed and sufficient conditions for the asymptotic stability and robustness of the closed–loop systems are given.
Abstract: This paper addresses the problem of robust stabilization of a class of uncertain systems subject to internal (i.e., in the state) point delays, external (i.e., in the input) point delays and nonlinear disturbances by using sliding mode control. Methods for the design of sliding mode controllers based on state feedback, static output feedback and dynamic output feedback, respectively, are proposed. Sufficient conditions for the asymptotic stability and robustnesss of the closed–loop systems are given under a wide class of admissible nonlinear disturbances. © 1997 by John Wiley & Sons, Ltd.
66 citations
45 citations
45 citations
TL;DR: In this article, a fixed-architecture controller analysis and synthesis framework was developed to address the problem of multivariable linear time-invariant systems subject to plant input and plant output time-varying nonlinearities.
Abstract: In this paper we develop a fixed-architecture controller analysis and synthesis framework that addresses the problem of multivariable linear time-invariant systems subject to plant input and plant output time-varying nonlinearities while accounting for robust stability and robust performance over the allowable class of nonlinearities. The proposed framework is based on the classical Lure problem and the related Aizerman conjecture concerning the stability of a feedback loop involving a sector-bounded nonlinearity. Specifically, we extend the classical notions of absolute stability theory to guarantee closed-loop stability of multivariable systems in the presence of input nonlinearities. In order to capture closed-loop system performance we also consider the minimization of a quadratic performance criterion over the allowable class of input nonlinearities. Our approach is directly applicable to systems with saturating actuators and provides full and reduced-order dynamic compensators with a guaranteed domain of attraction. The principal result is a set of constructive sufficient conditions for absolute stabilization characterized via a coupled system of algebraic Riccati and Lyapunov equations. The effectiveness of design approach is illustrated by several numerical examples. © 1997 John Wiley & Sons, Ltd.
44 citations
TL;DR: In this article, the authors developed an automatic station-keeping flight control system to regulate the position of an aircraft receiving fuel relative to the tanker aircraft during air-to-air refueling.
Abstract: Quantitative feedback theory is developed for the design of an automatic station-keeping flight control system to regulate the position of an aircraft receiving fuel relative to the tanker aircraft during air-to-air refueling. A robust flight control system is designed for automating the station-keeping task. A simple outer loop feedback control system is developed that achieves stable position regulation in the presence of wind gusts and fuel transfer related disturbances. The modelling and analysis clearly show the usefulness of QFT in the design of flight control systems for aircraft with large structured parametric uncertainty. Linear and nonlinear simulations are performed to validate the design. © 1997 by John Wiley & Sons, Ltd. This paper was produced under the auspices of the US government and it is therefore not subject to copyright in the US.
43 citations
41 citations
TL;DR: In this article, the authors developed a new low-and-high gain design procedure which is based on an explicit eigenstructure assignment algorithm, which avoids the solution of the numerically stiff parameterized ARE.
Abstract: The low-and-high gain design technique, which was initiated for a chain of integrators and completed for general linear asymptotically null controllable with bounded controls systems, was conceived for semiglobal control problems beyond stabilization and was related to the performance issues such as semi-global stabilization with enhanced utilization of the available control capacity and semi-global disturbance rejection. Although the low-and-high gain design technique as initiated for a chain of integrators is based on an explicit eigenstructure assignment algorithm, its full development is based on the solution of an algebraic Riccati equation (ARE) which is parameterized in an arbitrarily small scalar, called low gain parameter. In this paper, we develop a new complete low-and-high gain design procedure which is based on an explicit eigenstructure assignment algorithm. The new design approach avoids the solution of the numerically stiff parameterized ARE.
39 citations
TL;DR: In this article, a semi-global framework was proposed for the problem of controlling a linear discrete-time system subject to input saturation in order to have its output track (or reject) a family of reference (or disturbance) signals produced by some external generator.
Abstract: The purpose of this paper is to examine the problem of controlling a linear discrete-time system subject to input saturation in order to have its output track (or reject) a family of reference (or disturbance) signals produced by some external generator. It is shown that a semi-global framework, rather than a global framework, for this problem is a natural one. Within this framework, a set of solvability conditions are given and feedback laws which solve the problem are constructed. The theory developed in this paper parallels the one we developed earlier for the continuous-time system.
TL;DR: In this paper, an electro-hydrostatic actuator is considered for the control of an aircraft's flight control system and the quantitative feedback theory robust control method is used to design a controller for this actuator.
Abstract: The control of a novel aerospace actuator is considered, viz., an electro-hydrostatic actuator. It offers a high degree of maintainability and combat survivability of the aircraft's flight control system because all the actuator's elements are collocated. The quantitative feedback theory robust control method is used to design a controller for this novel actuator. Parameter variation, sensor noise and flight condition variability are explicitly considered in the design process. The resulting design is not only robust with respect to actuator parameter variations and flight condition and insensitive to sensor noise, but, in addition, the controlled actuator's phase lag is significantly reduced, thus improving the performance of the overall flight control system. © 1997 by John Wiley & Sons, Ltd. This paper was prepared under the auspices of the U.S. Government and it is therefore not subject to copyright in the U.S.
TL;DR: In this article, a guaranteed subset of the domain of attraction for a feedback system whose forward path contains a dynamic linear time-invariant system and whose feedback path contains multiple sector-bounded nonlinearities is constructed via open Lyapunov surfaces.
Abstract: SUMMARY In this paper we provide guaranteed stability regions for multivariable Lure« -type systems. Specifically, using the Lure« —Postnikov Lyapunov function a guaranteed subset of the domain of attraction for a feedback system whose forward path contains a dynamic linear time-invariant system and whose feedback path contains multiple sector-bounded time-invariant memoryless nonlinearities is constructed via open Lyapunov surfaces. It is shown that the use of open Lyapunov surfaces yields a considerable improvement over closed Lyapunov surfaces in estimating the domain of attraction of the zero solution of the nonlinear system. An immediate application of this result is the computation of transient stability regions for multimachine power systems and computation of stability regions of anti-windup controllers for systems subject to input saturation. ( 1997 by John Wiley & Sons, Ltd.
TL;DR: In this article, a robust multivariable output tracking controller using sliding mode concepts is proposed for high temperature furnaces, where only measured outputs are available and uses a sliding mode observer to reconstruct estimates of the internal system states for use in a full information sliding mode control law.
Abstract: The paper describes a theoretical framework for the design of a robust multivariable output tracking controller using sliding mode concepts. The approach assumes that only measured outputs are available and uses a sliding mode observer to reconstruct estimates of the internal system states for use in a full information sliding mode control law. This scheme is applied to a control problem associated with high temperature furnaces. The paper describes the synthesis of the proposed control scheme from design through to implementation on an industrial test facility. © 1997 by John Wiley & Sons, Ltd.
TL;DR: In this article, the Nyquist robust stability margin kN is proposed as a new tool for analysing the robustness of uncertain systems using Nyquist arguments involving eigenvalues instead of singular values, and yields exact necessary and sufficient conditions for robust stability.
Abstract: The Nyquist robust stability margin kN is proposed as a new tool for analysing the robustness of uncertain systems. The analysis is done using Nyquist arguments involving eigenvalues instead of singular values, and yields exact necessary and sufficient conditions for robust stability. The concept of a critical line on the Nyquist plane is defined and used to calculate a critical perturbation radius which in turn is used to produce kN. The new approach gives alternatives to computing exact stability margins in some cases of highly directional uncertainty templates where other models are not applicable. © 1997 by John Wiley & Sons, Ltd.
TL;DR: In this article, a sliding-mode control approach is proposed to stabilize a class of nonlinear singularly perturbed systems using sliding mode control techniques, which consists of decomposing the original system into two reduced order systems, for which stabilizing slidingmode controllers are applied and combined in a two-time scale slidingmode control for the full order system.
Abstract: The paper deals with the robust asymptotic stabilization of a class of nonlinear singularly perturbed systems using sliding-mode control techniques. The approach consists of decomposing the original system into two reduced order systems, for which stabilizing sliding-mode controllers are applied and combined in a two-time scale sliding-mode control for the full order system. A stability analysis allows us to provide sufficient conditions for the asymptotic stability of the full order closed-loop system. An example illustrates the design procedure and performance of the proposed control scheme. © 1997 by John Wiley & Sons, Ltd.
TL;DR: In this paper, an algorithm is developed that reduces the dimension of the realizations while improving numerical accuracy, reducing computational expense, and reducing run-time memory requirements for large scale uncertain systems, which have large numbers of inputs, outputs, states and uncertain parameters.
Abstract: SUMMARY The prevailing framework for robust stability and performance analysis requires that the uncertain system be written as a linear fractional transformation of the uncertain parameters. This problem is algebraically equivalent to the problem of deriving the state space realization for a multidimensional transfer function matrix, for which a systematic algorithm was recently provided by Cheng and DeMoor. 1 In this work an algorithm is developed that reduces the dimension of the realizations while improving numerical accuracy, reducing computational expense, and reducing run-time memory requirements. Such improvements are required for the realization of large scale uncertain systems, which have large numbers of inputs, outputs, states, and=or uncertain parameters.
TL;DR: In this paper, a manual flight control system for the lateral-directional dynamics of a modern fighter aircraft incorporating thrust vectoring is presented, where the need for gain scheduling a dynamic controller is eliminated by using an inner loop dynamic inversion/outer loop structured singular value (μ)-synthesis control structure which separately addresses operating envelope variations and robustness concerns.
Abstract: A manual flight control system for the lateral-directional dynamics of a modern fighter aircraft incorporating thrust vectoring is presented. Design goals are posed in terms of maintaining acceptable flying qualities during high angle of attack (α) manoeuvring while also achieving robustness to model parameter variations and unmodelled dynamics over the entire flight envelope. The need for gain scheduling a dynamic controller is eliminated by using an inner loop dynamic inversion/outer loop structured singular value (μ)-synthesis control structure which separately addresses operating envelope variations and robustness concerns, respectively. Performance objectives are based on commanding sideslip angle and stability axis roll rate. Realistic representations of both structured (real parametric) and unstructured uncertainty are included in the design/anlysis process. A flight condition dependent control selector maps generalized controls to physical control deflections, considering actuator redundancy, effectiveness and saturation issues. An angle of attack dependent command prefilter shapes commands to produce desired responses. Structured singular value analysis, low-order equivalent system (LOES) fits, and linear step responses demonstrate satisfaction of design goals. Simulation shows excellent control at both low and high angles of attack. © 1997 John Wiley & Sons. Ltd.
TL;DR: In this article, the authors considered a MIMO asymptotically stable linear plant and defined the quadratic stability margin and multivariable gain margin, and derived a lower bound on this margin with the aid of parameter dependent Lyapunov functions.
Abstract: In this paper we consider a MIMO asymptotically stable linear plant. For such a system the classical concepts of quadratic stability margin and multivariable gain margin can be defined. These margins have the following interpretation: consider the closed-loop system composed of the plant and several real parameters, one inserted in each channel of the loop; then any time-varying (time-invariant) parameters whose amplitudes are smaller than the quadratic stability (multivariable gain) margin result in a stable closed-loop system. For time-varying parameters whose magnitudes are between these two stability measures, stability may depend on the rate of variation of the parameters. Therefore it makes sense to consider the stability margin given by the maximal allowable rate of variation of the parameters which guarantees stability of the closed loop system. As shown in this paper, a lower bound on this margin can be obtained with the aid of parameter dependent Lyapunov functions. © 1997 by John Wiley & Sons, Ltd.
TL;DR: In this article, a robust flight control system is designed for the aircraft's longitudinal and lateral directional channels and validated with simulations containing nonlinear saturation elements using the frequency domain based quantitative feedback theory (QFT) robust control system design method.
Abstract: This paper addresses flight control system synthesis and the accommodation of controlled plant variation in an aircraft design envelope by using the frequency domain based quantitative feedback theory (QFT) robust control system design method. Plant variations considered include varying flight conditions in the flight envelope and damage to aerodynamic control surfaces. A robust flight control system is designed for the aircraft's longitudinal and lateral directional channels and validated with simulations containing nonlinear saturation elements. © 1997 by John Wiley & Sons, Ltd. This paper was produced under the auspices of the US Government and it is therefore not subject to copyright in the US.
TL;DR: A higher order generalization of the traditional first order sliding mode reachability condition is proposed which enables the designer to transfer non-minimum phase characteristics from the state responses to the artificial output (i.e., sliding function) responses if the zero dynamics has no finite escape time.
Abstract: Output tracking for a class of nonlinear SISO systems is considered whereby the output tracking error and its derivatives to some order are driven to a neighbourhood of the origin whilst the states and input remain bounded. A higher order generalization of the traditional first order sliding mode reachability condition is proposed. This enables the designer to transfer non-minimum phase characteristics from the state responses to the artificial output (i.e., sliding function) responses if the zero dynamics has no finite escape time. It is shown that this non-minimum phase artificial output behaviour may be curbed by defining a second control policy which becomes effective within a neighbourhood of the sliding surface. Possible problems with singularity are also addressed. The ball and beam system is used to illustrate the design method. © 1997 by John Wiley & Sons, Ltd.
TL;DR: In this paper, a probability-one homotopy continuation algorithm for mixed structured singular value controller synthesis using general xed-structure multipliers has been proposed, which can be initialized using an arbitrary (admissible) multiplier and a stabilizing compensator.
Abstract: SUMMARY Continuation algorithms that avoid multiplier{controller iteration have been developed earlier for xedarchitecture, mixed structured singular value controller synthesis. These algorithms have only been formulated for the special case of Popov multipliers and rely on an ad hoc initialization scheme. In addition, the algorithms have not used the prediction capabilities obtained by computing the Jacobian matrix of the continuation (or homotopy) map, and have assumed that the homotopy zero curve is monotonic. This paper develops probability-one homotopy algorithms based on the use of general xed-structure multipliers. These algorithms can be initialized using an arbitrary (admissible) multiplier and a stabilizing compensator. In addition, as with all probability-one algorithms, the homotopy zero curve is not assumed to be monotonic and prediction is accomplished by using the homotopy Jacobian matrix. This approach also appears to have some advantages over the bilinear matrix inequality (BMI) approaches resulting from extensions of the LMI framework for robustness analysis.
TL;DR: In this article, an extension of the concept of componentwise asymptotic (exponential) stability of linear systems in the non-symmetrical case is presented, and necessary and sufficient conditions for componentwise exponential stability in the symmetrical case are given.
Abstract: In this paper, we present an extension of the concept of componentwise asymptotic (exponential) stability of linear systems in the non-symmetrical case. The main motivation for these results is the need for a more detailed evaluation of the dynamical behaviour of linear systems in electrical engineering and biology. Necessary and sufficient conditions for componentwise asymptotic (exponential) stability in the non-symmetrical case are given. The symmetrical case is obtained as a particular case. © 1997 by John Wiley & Sons, Ltd.
TL;DR: In this article, the authors considered the problem of optimal guaranteed cost control of an uncertain system via output feedback, and gave a necessary and sufficient condition for the existence of a guaranteed cost controller guaranteeing a specified level of performance.
Abstract: This paper considers the problem of optimal guaranteed cost control of an uncertain system via output feedback. The uncertain system under consideration contains a single uncertainty block subject to an integral quadratic constraint. The cost function considered is a quadratic cost function defined over an infinite time interval. The main result of the paper gives a necessary and sufficient condition for the existence of a guaranteed cost controller guaranteeing a specified level of performance. This condition is given in terms of the existence of suitable solutions to an algebraic Riccati equation and a Riccati differential equation. The resulting guaranteed cost controller is in general time-varying. >
TL;DR: In this paper, a robust feedback controller that maintains the idle speed within a 150 rpm tolerance about 600 rpm despite a 20 Nm step torque disturbance delivered by the power steering pump is presented.
Abstract: Presented in this paper is the robust idle speed control of a Ford 4⋅6 L V-8 fuel injected engine. The goal of this investigation is to design a robust feedback controller that maintains the idle speed within a 150 rpm tolerance about 600 rpm despite a 20 Nm step torque disturbance delivered by the power steering pump. The controlled input is the by-pass air valve which is subjected to an output saturation constraint. Issues complicating the controller design include the nonlinear nature of the engine dynamics, the induction-to-power delay of the manifold filling dynamics, and the saturation constraint of the by-pass air valve. An experimental verification of the proposed controller is included. © 1997 by John Wiley & Sons, Ltd.
TL;DR: In this article, a solution to the singular H = control problem via state feedback for a class of nonlinear systems is presented, where the problem of almost disturbance decoupling with stability plays a fundamental role in the solution.
Abstract: SUMMARY This paper presents a solution to the singular H = control problem via state feedback for a class of nonlinear systems. It is shown that the problem of almost disturbance decoupling with stability plays a fundamental role in the solution of the considered problem. We also point out when the singular problem can be reduced to a regular one or solved via standard H = technique. We must stress that the solution of the singular problem is obtained without making any approximation of it by means of regular problems. ( 1997 by John Wiley & Sons, Ltd.