Showing papers on "Robust control published in 1988"

Robust control of dynamically interacting systems

Abstract: Dynamic interaction with the environment is fundamental to the process of manipulation. This paper describes an approach to the design of ‘interaction controllers’ and contrasts this with an approa...

Stability theory for linear time-invariant plants with periodic digital controllers

Abstract: This paper considers the control of a linear time-invariant plant by a digital controller composed of a sampler. a periodic discrete-time component, and a zero-order hold. The stability of such a configuration is analyzed in detail. It is shown how closed-loop zeros can be placed using such a scheme. As a consequence. it is proved that the gain margin can be arbitrarily assigned by suitable choice of sampling time and digital controller. The design procedure is constructive, using state-space methods.

Robust control of ill-conditioned plants: high-purity distillation

Abstract: Using a high-purity distillation column as an example, the physical reason for the poor conditioning and its implications on control system design and performance are explained. It is shown that an acceptable performance/robustness tradeoff cannot be obtained by simple loop-shaping techniques (using singular values) and that a good understanding of the model uncertainty is essential for robust control system design. Physically motivated uncertainty descriptions (actuator uncertainties) are translated into the H/sup infinity //structured singular value framework, which is demonstrated to be a powerful tool to analyze and understand the complex phenomena. >

Theory and design of robust direct and indirect adaptive-control schemes

Abstract: A general approach for designing and the theory for analysing robust direct and indirect adaptive-control schemes for continuous-time plants is presented. The design approach involves the development of a general robust adaptive law and the use of the certainty equivalence principle to combine it with robust model reference and pole placement control structures. The global stability properties and robustness of the developed adaptive control schemes are established by using a general theory which relates the properties of signals in the mean sense over intervals of time. The developed theory and design approach are used to analyse and compare the robustness properties and performance of a wide class of robust adaptive laws which employ a dead-zone, fixed-σ, e1, and a switching-σ modification as well as their variations.

Robust control with structure perturbations

Abstract: The problem of making a given stabilizing controller robust so that the closed-loop system remains stable for prescribed ranges of variations of a set of physical parameters in the plant. The problem is treated in the state-space and transfer-function domains. In the state-space domain a stability hypersphere is determined in the parameter space using Lyapunov theory. The radius of this hypersphere is iteratively increased by adjusting the controller parameters until the prescribed perturbation ranges are contained in the stability hypersphere. In the transfer-function domain a corresponding stability margin is defined and optimized on the basis of the recently introduced concept of the largest stability hypersphere in the space of coefficients of the closed-loop characteristic polynomial. The design algorithms are illustrated by examples. >

Model Reduction for Robust Control: A Schur Relative-Error Method

Abstract: A numerically robust Relative Error Method (REM) for state-space model order reduction is described. Our algorithm is based on Desai's Balanced Stochastic Truncation (BST) technique for which M. Green has obtained an L? relative-error bound. However, unlike previous methods, our Schur method completely circumvents the numerically delicate initial step of obtaining a minimal balanced stochastic realiztion (BSR) of the the power spectrum matrix G(s)GT(-s).

Model reduction for robust control: A schur relative error method

Abstract: A numerically robust relative error method for state-space model order reduction is described. Our algorithm is based on Desai's balanced stochastic truncation technique for which Green has obtained an L∞ relative error bound. However, unlike previous methods, our Schur method completely circumvents the numerically delicate initial step of obtaining a minimal balanced stochastic realization of the power spectrum matrix G(s)GT(−s).

Controller Design for Uncertain Systems via Lyapunov Functions

Abstract: We present a controller design methodology for uncertain systems which is based on the constructive use of Lyapunov functions The uncertainties, which are deterministic, are characterized by certain structural conditions and known bounds As a consequence of the Lyapunov approach, the methodology is not restricted to linear systems The robustness of these controllers in the presence of singular perturbations is considered The situation in which the full state of the system is not available for measurement is also considered These controllers are illustrated by application to the tracking control of a Manutec r3 robot which has an uncertain payload

Robust stability of discrete systems

Abstract: The objective of this paper is to show how to choose a Liapunov function to obtain the best and sometimes exact estimates of the degree of exponential stability for linear time-invariant discrete systems. The choice is interesting because it is also shown that it provides the largest robustness bounds on non-linear time-varying perturbations which can be established by either norm-like or quadratic Liapunov functions. By applying the results obtained to large-scale systems, where the role of perturbations is played by the interconnections among the subsystems, the least conservative stability conditions are derived for the overall system which are available in the context of vector Liapunov functions and M-matrices.

Decentralized robust control system design for large-scale uncertain systems

Abstract: A deterministic design approach for decentralized robust controls of a class of large-scale uncertain dynamical systems is proposed. The uncertainty under consideration can be fast time-varying; no a priori statistical information is assumed or utilized. Only the possible bound of this uncertainty is known. Two important types of robust control algorithms are proposed. The local control utilizes the local state of each subsystem as the feedback information. The global control utilizes the local state as well as the states of the neighbouring subsystems as the feedback information. Both types of control algorithms are continuous functions of the state.

Robust hyperplane design in multivariable variable structure control systems

Abstract: The problem of designing a stable sliding mode giving robust performance of a variable structure control system is studied. A set of specified eigenvalues is assigned to the closed-loop feedback system during the sliding mode. The design philosophy seeks to build on the known robustness and invariance properties associated with the use of discontinuous (or continuous) non-linear controls, by assigning the eigenvectors associated with the sliding-mode eigenvalues in a manner that leads to a robust control scheme. A previously developed canonical form for the hyperplane design problem is again employed. The design technique centres on a recently published eigenvalue assignment algorithm, and is illustrated by the inclusion of an example.

Independent parameterization of two-degree-of-freedom compensators in general robust tracking systems

Abstract: Consideration is given to a general robust tracking problem in which the controlled object is a linear multivariable system having measured variables that are not necessary coincident with the output variables to be controlled. A necessary and sufficient condition for the two-degree-of-freedom compensator to achieve a robust tracking system with internal stability is given. An existence condition is derived for such a compensator, and the class of all such compensators is parameterized, so that two specifications with respect to responses for reference commands and feedback properties can be satisfied independently by the two free parameters. >

Control of a single-link flexible beam using a Hankel-norm-based reduced order model

Abstract: A single-link flexible beam is an infinite-dimensional system. A full-order model containing all the modes of the system within the bandwidth of the actuator and sensors is presented. Such a model would result in a high-order controller which may not be feasible to implement in practice. Hence, a low-order model for the system is obtained using Hankel norm minimization. A controller is designed for the beam on the basis of the reduced-order model thus obtained. Experimental results show that a controller designed for the reduced-order model guarantees effective vibration control of the flexible beam. >

H ∞ robust control synthesis for a large space structure

Abstract: In a design study involving the use of H∞ optimal control theory, an 11-state control law is generated for a 116-state model of a large flexible space structure. A combination of co-located rate feedback, modal truncation, and optimal Hankel-norm model techniques is found to lead to a vastly simplified four-state model for the structure which, by singular-value theory, is proved to be satisfactory for design of a controller whose bandwidth exceeds the natural frequencies of all of the modes of the original 116-state model. Specifications regarding disturbance attenuation, bandwidth, and stability robustness are quantitatively expressed as weighting functions in a mixed-sensitivity H∞ optimal control synthesis problem, the solution to which is computed by the authors' program LINF.

Two algorithms for frequency domain design of robust control systems

Abstract: Two algorithms are described that are useful in the computer-aided design implementation of the robust controller design scheme proposed by Horowitz (1963) and Horowitz and Sidi (1972).

Robust independent robot joint control: design and experimentation

Abstract: An approach is presented for the design of simple robust independent joint controllers which result in linear decoupled joint motions. In this approach each joint is treated as a simple inertial systems plus a disturbance torque representing all the unmodeled dynamics. By means of a very simple procedure, the disturbance is instantly estimated and rejected, thus allowing simple PD control to be used. The controllers are inherently robust. Experimental evaluations of the controller on a PUMA 560 are are performed, and the experimental results are presented. >

Robust stability for linear time-delay systems with linear parameter perturbations

Abstract: A new robust state feedback controller design in the time domain is developed for parametrically perturbed linear systems with time delay. The properties of the matrix measure and comparison theorem are employed to investigate the robust stability conditions of systems with linear structured or unstructured perturbations. A method is proposed to design the robust state feedback controller to satisfy the robustness requirement. Examples are given to illustrate the proposed method.

Application of modern control techniques to motor control

Abstract: An overview is presented of digital control problems arising in the use of microprocessors and the application of modern control theory, from both the theoretical and practical viewpoints. The discussion covers optimal control, robust control, feedback and feed-forward control, and active and passive adaptive control. Various application are described, drawing on the author's own experience. It is concluded that a robust optimal digital controller for motor control can be practically designed and implemented with currently available techniques and hardware. >

Nonlinear Robotic Control Including Drive Motor Interactions

Abstract: A unified approach to a robust robotic control design which retains all the nonlinearities inherent in the dynamics is developed for motor-robot configuration considered as an interacting system. This control system design, based on decomposition and Freund's nonlinear decoupling control theory with arbitrary pole placement, decouples the motor-robot configuration into robot, motor, and series compliance (interaction) subsystems. This approach is in contrast to the conventional treatment of the motor as a pure torque source and the neglect of dynamic interactions between the robot joint and the motor drive mechanism.

Fast Computation of the Multivariable Stability Margin for Real Interrelated Uncertain Parameters

Abstract: A new algorithm for computing the Miutivariable Stability Margin for checking the robust stability of feedback systems with real parametric uncertainty is proposed. This method eliminates the need for the frequency search involved in the algorithm of [1,2,3] by reducing it to checking a finite number of conditions. These conditions have a special structure, which allows a significant improvement on the speed of computations.

Some results on robust stability of discrete-time systems

Abstract: The theorem of Kharitonov on the Hurwitz property of interval families of polynomials cannot be extended, in genera, to obtain sufficient conditions for the stability of families of characteristic polynomials of discrete-time systems. Necessary and sufficient conditions for this stability problem are given. Such conditions naturally give rise to a computationally efficient stability test which requires the solution of a one-parameter optimization problem and which can be considered as a counterpart to the Kharitonov test for continuous-time systems. At the same time, the method used to derive the stability conditions provides a procedure for solving another stability robustness problem, i.e. the estimation of the largest domain of stability with a rectangular box shape around given nominal values of the polynomial coefficients. >

Robust Model Reference Adaptive Control for Multivariable Plants

Abstract: A complete procedure for generating and analyzing robust model reference adaptive control schemes for multivariable plants is developed, which includes: the characterization of the integral structure of the modeled part of the plant, and the associated parameterization of the controller structure; a general robust adaptive law for adjusting the controller parameters so that the closed-loop plant is globally stable despite the presence of unmodeled dynamics and bounded disturbances; and the use of dominantly rich signals for improving parameter convergence and the bounds for the tracking and parameter error.

Controller reduction using canonical interactions

Abstract: A conceptual approach to controller reduction is proposed that is based on closed-loop considerations. The method assesses the interactions between the plant and a high-order controller as described by canonical correlation coefficients. A free parameter in the algorithm of the reduced controller makes it possible to trade stability robustness versus performance. Several examples demonstrate the efficacy of the method. >

Robust stability and performance analysis for state space systems via quadratic Lyapunov bounds

Abstract: The authors consider quadratic Lyapunov bounds to obtain a simultaneous treatment of both robust stability and performance. The approach is based on the construction of modified Lyapunov equations which provide sufficient conditions for robust stability along with robust performance bounds. One of the principal features of this work is the unified treatment and extension of several quadratic Lyapunov bounds developed previously for feedback control design. >

Adaptive Robust Control via Transfer Function Uncertainty Estimation

Abstract: An adaptive control system is examined where the traditional parameter estimator is replaced by a parameter set estimator which provides a measure of uncertainty of the estimated parameters. It is shown how to construct a parameter set estimator with the property that the true system is always in the model set, and furthermore, how to design the estimation experiment so that the set of uncertainty is as small as possible given some a priori information.