Showing papers on "Robust control published in 1983"

Synthesis of robust controllers and filters

Abstract: This paper outlines a general framework for analysis and synthesis of linear control systems and reports on a new solution to a very general L?/H? optimal control problem.

Application of vector performance optimization to a robust control loop design for a fighter aircraft

Abstract: For a McDonnell-Douglas F-4C aircraft a robust, fixed gain controller is designed, which provides satisfying handling qualities of the longitudinal motion or the aircraft over the complete flight range without gain scheduling. Robustness is achieved in the sense of covering largo paramoter variations and providing good gain and phase margins, Only low control rates and low feedback gains are involved, The results are obtained by application of a performance vector optimization design method which accounts for a great many different design objectives simultaneously in a highly systematic fashion. Two different designs are presented placing emphasis on pitch rate control (pointing) and normal acceleration control (manoeuvring) respectively.

Robustness optimization of linear feedback systems

Abstract: The robustness of a linear, finite-dimensional, time-invariant, single-input single-output feedback system with respect to plant variations is analyzed and expressed in terms of the sensitivity function of the feedback system and its complement. The analysis leads to defining optimally robust control systems as control systems for which the supremum over all frequencies of a weighted combination of the sensitivity function and its complement is minimal. Besides accomodating robustness considerations, the approach allows handling specifications on the closed-loop bandwidth and controller pole excess. A complete solution of the problem is given. Specialization of the general formulation to the minimization of the supremum of the sensitivity function or its complement alone affords determining the achievable performance of a single-input single-output plant. This performance depends on the plant pole-zero configuration and is characterized by the so-called regulability number of the plant. The ideas are illustrated with an example involving a double pendulum system in four different equilibrium positions.

Robust stability of systems with integral control

Abstract: A necessary and sufficient condition is derived which must be satisfied by the plant steady state gain matrix of a linear time invariant system in order for an integral controller to exist for which the closed loop system is unconditionally stable. Based on this theorem the robustness of integral control systems is analyzed, i.e. the family of plants is defined which are stable when controlled with the same integral controller. Conditions for actuator/sensor failure tolerance of systems with integral control are also given. Finally, parallels are drawn between the results of this paper and the bifurcation theory of nonlinear systems.

Robust Control of Flexible Spacecraft

Abstract: A well-designed feedback control system exhibits the properties of external disturbance attenuation and performance robustness with respect to plant uncertainty. The plant uncertainties of flexible spacecraft include unmodeled dynamics and parameter uncertainties. Singular value robustness measures are used to compare performance and stability robustness properties of different control design techniques in the presence of residual modal interaction (control and observation spillover) for a design example which is representative of a practical flexible spacecraft system. The control designs evaluated include linear quadratic geometry (LQG) control, integral feedback, bias removal control, innovations feedthrough, and frequency-shaped LQG.

A generalization of the Routh-Hurwitz stability criteria and an application to a problem in robust controller design

Abstract: The classical results of Routh and Hurwitz on the stability of polynomials are generalized from the open left half plane to certain other subregions G of the complex plane. By our method, arbitrary conic sections can be handled. The results are interpreted as criteria for G -stability of linear systems. A numerical algorithm to compute the criteria is given. An application to a problem in robust controller design is outlined.

Robust non linear control of robotic manipulators

Abstract: This article addresses the problem of controlling robotic manipulators. A preliminary theoretical study is conducted so as to determine a large set of stable and robust controls for non-linear systems whose equations encompass the dynamic equations of any rigid manipulator. Sufficient conditions for obtaining a good tracking of a linear time-invariant model of reference are derived. The local stability of several well known control methods is rigourously established while it is shown that global stability requires the use of non-linear gains in the control expression. An interesting property is that the determination of such gains does not necessarily require an important knowledge of the system; which justifies the use of very simple control schemes in practice. However, a control better conditioned with respect to measurement noises is obtained when a good model of the system is used in the control derivation. Between these two alternatives lies the idea of using adjustable control gains that become large when needed and stay small otherwise. In light of this study, several control schemes proposed in the literature on the subject (including adaptive control schemes) are discussed and conclusions are drawn with a view to future studies.

Fractional representation theory: Robustness results with applications to finite dimensional control of a class of linear distributed systems

Abstract: This paper reviews and extends fractional representation theory. In particular, new and powerful robustness results are presented. This new theory is utilized to develop a preliminary design methodology for finite dimensional control of a class of linear evolution equations on a Banach space. We design for stability in an input-output sense but pay particular attention to internal stability as well.

Robustness studies in adaptive control

Abstract: This paper examines robustness issues in Model Reference Adaptive Control systems in the presence of unmodeled dynamics and output disturbances. We present an approximate technique, trend analysis, by which we can study the evolution of the parameter error trajectory under periodic excitation. This analysis provides new insights upon the size and spectral content of the excitation sufficient to guarantee local stability.

Robust controller for boundary control systems

Abstract: Some basic results of robust controller theory are generalized to distributed parameter systems with unbounded control and perturbation operators. The theory presented is then applied to construct a flow adaptive robust controller for heat exchangers.

Robust Multivariable Control System Design using Optimal Reduced Order Plant Models

Abstract: A procedure for the design of preccapensators for linear multivariable continuous-time systems based on reduced-order plant models is described. The reducedorder model is obtained via an optimal Hankel-norn approximation method, whose approximation error can be accurately predicted. The closed-loop stability of the full-order plant and compensator can then be deduced from this approximation error and a robust stability result.

Robust Adaptive Control: Conditions for Local Stability

Abstract: The question is examined of when an adaptive control system is robust to modeled dynamics and unknown bonded disturbances. Conditions are presented that insure the existence of such robustness properties, but only locally; i.e., restrictions are placed on the behavior of signals in the ideal, perfectly tuned adaptive system. Local L ? -stability is investigated when the tuned signals are assumed to be small, slowly varying, and/or persistently exciting.

Dynamic Simulation of Stability Enhancement Tools and Comparison of Control Strategies

Abstract: The paper presents a study of different stability enhancement techniques with emphasis on the damping effectiveness of proposed static phase shifters. A linearized state-space model is derived to simulate the phase shifting action in AC system dynamics. The paper also presents a robust controller design procedure that transforms static phase shifters into a powerful stability enhancement tool similar in action to switched load, series compensation, and HVDC transmission damping capabilities.

On the design of robustly performing adaptive controllers for partially modelled systems

Abstract: The problem of designing robustly performant adaptive controllers with explicit incorporation of a representation for the model-process mismatch (MPM) is addressed in this paper. Global stability conditions are derived for a discrete-time pole-zero placement (PZP) adaptive controller, assuming a set membership statement for the process transfer function with uncertainty characterized by conic bounded operators. The overall system is decomposed into interconnected operators whose I/O properties are studied using the functional analysis approach pioneered by Zames [17]. Using the sector stability theorem [2] and the sectoricity properties of systems with cone-bounded uncertainties [3], frequency-domain measures quantifying the robustness/ performance tradeoff are derived. The effect of smoothing and antialiasing filters and the properties of various parameter adaptation algorithms (PAA) regarding this tradeoff are studied.

Entwurfsverfahren für Robuste Regelungen

Abstract: The problem of robust control is introduced and formulated as a multi-model problem. A controller structure is assumed and its free parameters are designed by three methods: Frequency domain, pole region assignment and performance vector optimization. A brief survey of other robustness approaches for frequency domain stability margins and robust asymptotic tracking concludes the paper.

Conditions for local stability and robustness of adaptive control systems

Abstract: This paper reports some preliminary results concerning robustness properties of adaptive control systems to unmodeled dynamics and bounded disturbances. The analysis is conducted from the viewpoint of input/output stability theory. Generic representations are proposed for both continuous-time and discrete-time adaptive systems and conditions for stability and robustness are developed for each case. These conditions require varying degrees of a priori knowledge about the plant, e.g., global conditions involving minimal knowledge and local conditions involving more restrictive assumptions.

Robust stabilizability for a class of transfer functions

Abstract: This paper is concerned with the robust stabilizability for single-input single-output systems. The robust stabilizability means that all the transfer functions in the given class, characterized by the nominal plant model and the uncertainty band function, can be stabilized simultaneously by a fixed controller. A necessary and sufficient condition for robust stabilizability is derived based on a classical result in the interpolation theory of bounded real functions. It is shown that the magnitude of the uncertainty band function should be restricted within a certain range in order that the class is robustly stabilizable. An extension of the result to the servo problem is also discussed.

Robust control of a class of nonlinear servomechanism problem

Abstract: A set of sufficient conditions for a robust control of a nonlinear process consisting of memoryless time-varying nonlinearities is obtained by extending the results of the linear servomechanism problem. The robust controller consists of an error-driven servocompensator, containing the modes of all the endogenous (system states) and exogenous (reference and disturbance) signals present in the system, and a stabiliser.

Design of controllers to solve the robust servomechanism problem for a class of nonlinear systems

Abstract: This paper considers the following problem: given a nonlinear single-input, single-output system y = (c1 c2 c3...cn)x + f? where ai=ai(?), i=1,2,...,n, ci=ci(?), i=1,2,...,n, b=b(?), where ?g'x, it is desired to find a controller which solves the robust servomechanism problem for (I) so that robust asymptotic tracking occurs for all constant disturbances ? and all constant set-points, and such that the resultant closed loop system is globally asymptotically stable. Sufficient conditions are obtained to solve this problem, and an algorithm for obtaining a suitable controller is given. The controller obtained is a type of "gain-scheduling" controller. An extension of the result is then made to multivariable systems, and an application is made to an n-link rigid robotic manipulator problem.

A Self-Tuning Feedback Controller

Abstract: The self-tuning feedback controller (SFC) described in this paper is mathematically and structurally equivalent to a conventional, discrete, PID, feedback controller. However, it also includes a simple estimation or adaptive algorithm that tunes the controller constants such that a quadratic performance index with a control weighting term is minimized. Global stability is mathematically proven in the presence of bounded, external unmeasured inputs. Application of the SFC to a pilot-plant evaporator demonstrates the practicality of this algorithm.

A robust pitch pointing control law

Abstract: Eigenstructure assignment and command generator tracking are applied to the design of a pitch pointing control law for the AFTI F-16 aircraft. The eigenvalues are chosen to obtain desired damping and rise time and the eigenvectors are chosen to decouple the pitch attitude and flight path angle. Then the design is modified to improve the multivariable phase and gain margins. Finally, a proportional and integral and delay model of a pilot is utilized to illustrate the interaction between the pilot and the aircraft. This output feedback and feedforward gain design differs from previous designs in that only proportional control is required.

A frequency selective adaptive controller

Abstract: It has been established that currently available adaptive control algorithms may become unstable in the presence of high frequency unmodeled dynamics and additive sinuosidal disturbances [1]-[3]. It is argued here that these problems can be overcome by using a controller which is adaptive for some frequency range but fixed for another frequency range which includes high frequencies. One candidate for such a frequency selective adaptive controller is presented and tested by simulation.

Analysis of Multivariable Servo Systems Considering Sensor Dynamics

Abstract: Servo problems taking into consideration the sensor dynamics are considered in the transfer matrix setting. As a preparation, we propose a new definition of internal stability, and derive a few properties of this stability. Secondly, necessary and sufficient conditions for a stable system with sensor to have tracking, robust tracking, regulation, and robust regulation capability are obtained. In order to verify the validity of usual servo system synthesis methods which utilize internal models and to have insight into servo synthesis, the relation between internal models and sensor dynamics are considered in detail.

Robustness effects of sampling in model referencesand minimum variance control

Abstract: This paper investigates several issues relating to the effect of sampling in model reference and minimum variance control. It is shown that, in the case of stochastic systems, the continuous time response resulting from digital control is cyclostationary. A method is presented for computing the time-varying covariance between sampling instants. The results are used to examine the performance of several digital control algorithms including the minimum variance control strategy. It is shown that these algorithms can have poor continuous time responses especially for lightly damped systems. The fact that one step ahead controllers applied to lightly damped systems are overly responsive between sampling instants is well known but these issues have been largely overlooked in much of the recent literature on stochastic and adaptive control. We suggest that it may be preferable to use alternative design procedures which give suboptimal performance at the sampling instants but which actually result in superior continuous time results. The theoretical results in the paper are substantiated by both computer simulation studies and a practical application.

Design of robust asymptotic tracking and disturbance rejection

Abstract: In this paper, we propose a design of robust control to achieve asymptotic tracking and disturbance rejection by solving a single set of linear algebraic equations. The plant-entered and input-entered disturbances are considered. The plant is not restricted to be strictly proper, it can be proper.

The relationship between the Zames representation and LQG compensators

Abstract: Recently Zames [1] has introduced the so-called model reference transformation which can be used to conveniently parametrize the class of linear time-invariant multivariable compensators that lead to stable feedback control systems. A very popular design methodology for designing stable and robust multivariable control systems is that based on the Linear-Quadratic-Gaussian (LQG) design methodology with Loop Transfer Recovery (LTR). Thus, it is natural to inquire upon the relationship between the Zames representation and the LQG/LTR compensators. This paper summarizes this relationship.