Showing papers on "Robust control published in 1990"

Adaptive sliding mode control of autonomous underwater vehicles in the dive plane

Abstract: The problem of controlling an autonomous underwater vehicle (AUV) in a diving maneuver is addressed. Having a simple controller which performs satisfactorily in the presence of dynamical uncertainties calls for a design using the sliding mode approach, based on a dominant linear model and bounds on the nonlinear perturbations of the dynamics. Nonadaptive and adaptive techniques are considered, leading to the design of robust controllers that can adjust to changing dynamics and operating conditions. The problem of using the observed state in the control design is addressed, leading to a sliding mode control system based on input-output signals in terms of drive-phase command and depth measurement. Numerical simulations using a full set of nonlinear equations of motion show the effectiveness of the proposed techniques. >

Robust Control for Automatic Steering

Abstract: Robust control problems in automatic steering are due to the wide range of velocity, mass and road conditions under which such vehicles operate. In earlier design studies and road tests for a bus it has been shown that it is possible to design a fixed gain controller such that the automatic steering operates satisfactorily over the entire range of parameters. In the present paper it is shown that the performance of such a robust automatic steering system can be considerably improved by the addition of a gyro measuring the yaw rate and feeding it back into the controller.

Force feedback control of robot manipulator by the acceleration tracing orientation method

Abstract: The authors propose a novel approach to force and compliance control of multi-degree-of-freedom (DOF) robot manipulators. The acceleration tracing orientation method (ATOM) is applied to both controllers. The control law is described in the Cartesian space; however, the final command is the acceleration in the joint space. The interactive terms in each joint disturb and deteriorate the joint motion. The disturbance observer cancels out the total sum of these terms and enables each joint to trace the acceleration command. As a result, a robust control is possible in the force task. The testing of the proposed system in a three-DOF robot manipulator is discussed. >

Robust control for the tracking of robot motion

Abstract: In this paper we examine the stability of a proportional derivative (PD) controller for the trajectory-following problem of a robot manipulator. We use Lyapunov's second method to derive a uniform boundness result for the PD controller. We show that if the PD controller gains are chosen greater than a specific bound and if the initial tracking error is zero, the velocity and position tracking errors are uniformly bounded. We then develop two additional controllers that use auxiliary control inputs along with the PD controller. Both of these controllers are shown to yield a uniform ultimate boundness property for the tracking error.

Robust stability and performance via fixed-order dynamic compensation with guaranteed cost bounds

Abstract: A feedback control-design problem involving structured plant parameter uncertainties is considered. Two robust control-design issues are addressed. The Robust Stability Problem involves deterministic bounded structured parameter variations, while the Robust Performance Problem includes, in addition, a quadratic performance criterion averaged over stochastic disturbances and maximized over the admissible parameter variations. The optimal projection approach to fixed-order, dynamic compensation is merged with the guaranteed cost control approach to robust stability and performance to obtain a theory of full- and reduced-order robust control design. The principle result is a sufficient condition for characterizing dynamic controllers of fixed dimension which are guaranteed to provide both robust stability and performance. The sufficient conditions involve a system of modified Riccati and Lyapunov equations coupled by an oblique projection and the uncertainty bounds. The full-order result involves a system of two modified Riccati equations and two modified Lyapunov equations coupled by the uncertainty bounds. The coupling illustrates the breakdown of the separation principle for LQG control with structured plant parameter variations.

Robust stabilization with positive real uncertainty: beyond the small gain theorem

Abstract: The properties of positive real transfer functions are used to guarantee robust stability in the presence of positive real (but otherwise unknown) plant uncertainty. These results are then used for controller synthesis to address the problem of robust stabilization in the presence of positive real uncertainty. One of the principal motivations for these results is to utilize phase information in guaranteeing robust stability. In this sense these results go beyond the usual limitations of the small gain theorem and quadratic Lyapunov functions, which may be conservative when phase information is available. The results of this study are based upon a Riccati equation formulation of the positive real lemma and thus resemble certain Riccati-based approaches to bounded real (H/sub infinity /) control. >

Adaptive control of a single-link flexible manipulator

Abstract: A method for controlling single-link lightweight flexible manipulators is proposed. The objective is to control the tip position of the flexible manipulator in the presence of joint friction and changes in payload. Both linear and nonlinear frictions are overcome by using a very robust control scheme for flexible manipulators. The control scheme is based on two nested feedback loops: an inner loop, to control the position of the motor, and an outer loop, to control the tip position. Compensation for changes in load is achieved by decoupling the dynamics of the system and then applying a very simple adaptive control for the tip position. This results in a simple control law that needs minimal computing effort and, thus, can be used for real-time control of the flexible arms. >

Model reference robust adaptive control without a priori knowledge of the high frequency gain

Abstract: A novel model-reference robust adaptive controller that does not require a priori knowledge of the high-frequency-gain sign is proposed. The scheme is applicable to minimum-phase plants of arbitrary relative degree and ensures that in the absence of unmodeled dynamics the tracking error converges to zero and all the signals remain bounded. The control law uses a particular projected parameter vector instead of the current estimates to avoid division by zero. >

Robust car steering by yaw rate control

Abstract: It is shown that feedback control can improve the robustness of the driver-car system with respect to uncertain operating conditions. Robustness is achieved by controlling the yaw rate instead of the steering angle. Integrating unit feedback of the yaw rate error makes the yaw mode unobservable from the front axle lateral acceleration and thereby take uncertainty out of the steering transfer function. Rear-wheel steering allows pole placement for the yaw mode. A main result of this study is a robust compensator/actuator design for all cars and all operating conditions. A further result applies to cars with additional rear-wheel steering. This second input can be used to place yaw-mode eigenvalues in desired locations. By the decoupling property, shifting of these eigenvalues has no influence on the transfer function from the steering wheel to the lateral acceleration of the front axle. >

Robustness of P-type learning control with a forgetting factor for robotic motions

Abstract: A class of simple learning control algorithms with a forgetting factor and a long-term memory and without use of the derivative of velocity signals is proposed for motion control of robot manipulators. The robustness of search learning laws with respect to initialization errors, fluctuations of the dynamics, and measurement noises is studied extensively. As a result the uniform boundedness of motion trajectories is proved based on the passivity analysis of robot dynamics. It is also proved that motion trajectories converge to a neighborhood of the desired one and eventually remain in it provided the content of the long-term memory is refreshed adequately after a sufficient number of trials. >

Robust Control for the Tracking of Robot Motion

Abstract: In this paper, we examine the stability of a Proportional Derivative (PD) controller for the trajectory following problem of a robot manipulator. We use Lyapunov's second method to derive a uniform boundness result for the PD controller. We show that if the PD controller gains are chosen greater than a specific bound and if the Initial tracking error is zero, the velocity and position tracking errors are uniformly bounded. We then develop two additional controllers that use auxiliary control inputs along with the PD controller. Both of these controllers are shown to yield a uniform ultimate boundness property for the tracking error.

Identification in H ∞ : a robustly convergent, nonlinear algorithm

Abstract: In this paper a system identification technique is developed which is compatible with current robust controller design methodologies. This technique is applicable to a broad class of stable, distributed, linear, shift-invariant systems. The information necessary for the application of this technique consists of a priori estimates on the relative stability and "steady state" gain of the unknown system together with a finite number of possibly corrupt frequency response estimates. Given this information an algorithm is specified which yields both an identified model and explicit H∞ norm error bounds. Several interesting properties of this algorithm are also discussed. Among them, the fact the algorithm is a nonlinear function of the frequency response data, and that it is robustly convergent with respect to the a priori information on relative stability and gain are singled out as characteristics which distinguish this algorithm from others currently under development by the authors.

Robustness and performance tradeoffs in control design for flexible structures

Abstract: The design of control laws for the Caltech flexible structure experiment using a nominal design model with varying levels of uncertainty is considered. A brief overview of the structured singular value ( mu ) H/sub infinity / control design, and mu -synthesis design techniques is presented. Tradeoffs associated with uncertainty modeling of flexible structures are discussed. A series of controllers are synthesized based on different uncertainty descriptions. It is shown that an improper selection of nominal and uncertainty models may lead to unstable or poor-performing controllers on the actual system. In contrast, if descriptions of uncertainty are overly conservative, performance of the closed-loop system may be severely limited. Experimental results on control laws synthesized for different uncertainty levels on the Caltech structure are presented. >

Robust near time-optimal control

Abstract: A robust control algorithm for a realization of nearly time-optimal control of double integrator plants is presented. The technique involves the combination of traditional bang-bang time-optimal control with the methods of sliding-mode control. The result is a nonlinear feedback scheme for maintaining a desired functional relationship among dynamic variables, in this case imitating the idealized dynamics of time-optimal control. The approach is nearly time optimal rather than exactly time optimal, since the bang-bang control components are restricted to values below full actuator saturation, thus reserving some actuator effort for compensation of disturbances and model imperfections. The algorithm blends smoothly into a linear controller near a stable goal location. >

Intelligent failure-tolerant control

Abstract: An overview of failure-tolerant control is presented, beginning with robust control, progressing through parallel and analytical redundancy, and ending with rule-based systems and artificial neural networks. By design or implementation, failure-tolerant control systems are 'intelligent' systems. All failure-tolerant systems require some degree of robustness to protect against catastrophic failure; failure tolerance often can be improved by adaptivity in decision making and control, as well as by redundancy in measurement and actuation. Reliability, maintainability, and survivability can be enhanced by failure tolerance, although each objective poses different goals for control system design. Artificial intelligence concepts are helpful for integrating and codifying failure-tolerant control systems, not as alternatives but as adjuncts to conventional design methods. >

Extreme Point Results for Robust Stabilization of Interval Plants with First Order Compensators

Abstract: It has recently been shown that a first order compensator robustly stabilizes an interval plant family if and only if it stabilizes all of the extreme plants. That is, if the plant is described by m-th order numerator and monic n-th order denominator with coefficients lying in prescribed intervals, it is necessary and sufficient to stabilize the set of 2m+n+l extreme plants. These extreme plants are obtained by considering all possible combinations for the extreme values of the numerator and denominator coefficients. In this paper, we prove a stronger result. Namely, it is necessary and sufficient to stabilize only sixteen of the extreme plants. These sixteen plants are generated using the Kharitonov polynomials associated with the numerator and denominator. Furthermore, when additional apriori information about the compensator is specified (sign of the gain and signs and relative magnitudes of the pole and zero), then in some cases, it is necessary and sufficient to stabilize eight critical plants while in other cases, it is necessary and sufficient to stabilize twelve critical plants.

Towards a Methodology for Robust Parameter Identification

Abstract: The paper considers the problem of estimating, from experimental data, real parameters for a model with uncertainty in the form of both additive noise and norm bounded perturbations. Such models frequently arise in robust control theory, and a framework is introduced for the consideration of experimental data in robust control analysis problems. If the analysis tools applied include robust stability tests for real parameter variations (real ?), then the framework can be used to address the problem of "robust" parameter identification. While the techniques discussed here can quickly become computationally overwhelming when applied to physical systems and real data, the approach introduces a new way of looking at the identification problem and may be helpful in arriving at a more tractable methodology.

Robust Control of Nonlinear Systems: Compensating for Uncertainty

Abstract: We propose a new approach to robust control of nonlinear systems. The approach is indirect in the sense that we will translate a robust control problem into an optimal control problem and apply optimal control methods to solve the robust control problem. We show that the method can be applied to nonlinear systems that satisfy the matching condition.

Robust control of linear systems and nonlinear control

Abstract: Invited Papers.- Nonlinear H-infinity control theory: A literature survey.- Primitives for robot control.- Optimal frequency design vs. an area of several complex variables.- Feedback stabilization of nonlinear systems.- Multivariable Feedback.- A monotonicity result for the periodic Riccati equation.- Results on generalized Riccati equations arising in stochastic control.- LQ-Problem: The discrete-time time-varying case.- The output-stabilizable subspace and linear optimal control.- The decomposition of (A,B) invariant subspaces and its application.- The set of feedback matrices that assign the poles of a system.- Model matching for linear Hamiltonian systems.- Connective stabilization of large-scale systems: A stable factorization approach.- Riccati equations, algebras, and invariant systems.- Maximal order reduction of proper transfer function matrices.- The matching condition and feedback controllability of uncertain linear systems.- Convergence properties of indefinite linear quadratic problems with receding horizon.- Robust Control.- Generalized stability of linear singularly perturbed systems including calculation of maximal parameter range.- Convex combinations of Hurwitz functions and its applications to robustness analysis.- Designing strictly positive real transfer function families: A necessary and sufficient condition for low degree and structured families.- Quadratic stabilizability of linear systems with structural independent time varying uncertainties.- A finite zero exclusion principle.- Design of controller with asymptotic disturbance attenuation.- H-infinity Control.- Gas turbine control using mixed sensitivity H-infinity optimisation.- Nonlinear H-infinity Theory.- A J-spectral factorization approach to H-infinity control.- Vector interpolation, H-infinity control and model reduction.- Sensitivity minimization and robust stabilization by stable controller.- Conjugation and H-infinity control.- Necessary and sufficient conditions for the existence of H-infinity con trollers: An interpolation approach.- On H-infinity contro4 LQG control and minimum entropy.- Optimal H-infinity SISO-controllers with structural constraints.- Super optimal H-infinity design.- H-infinity control with state feedback.- Adaptive Control.- Convergence analysis of self-tuning controllers by Bayesian embedding.- On bounded adaptive control with reduced prior knowledge.- Indirect techniques for adaptive input output linearization of nonlinear systems.- Stochastic Control and Filtering.- Interpolation approach to the H-infinity filter problem.- Stochastic disturbance decoupling.- Discrete-time filtering for linear systems in correlated noise with non-Gaussian initial conditions: Formulas and asymptotics.- Nonlinear Control.- Boundary feedback stabilization of distributed parameter systems.- Optimal nonlinear feedback system design for a general tracking problem.- Stability theory for differential/algebraic systems with application to power systems.- Feedback equivalence of planar systems and stabilizability.- Topological dynamics of discrete-time systems.- Another approach to the local disturbance decoupling problem with stability for nonlinear systems.- Stabilization of nonlinear systems and coprime factorization.- Observability and Identification of Nonlinear Systems.- Identification of linear systems via Prony's method.- On observability of chaotic systems: an example.- Interpolating uniquely with only a finite class of polynomials.- Sinc approximation method for coefficient identification in parabolic systems.- Observability and Harish-Chandra Modules.- Robotics.- Modelling and nonlinear control of an overhead crane.- On adaptive linearizing control of omnidirectional mobile robots.- Robot control via nonlinear observer.- Modelling and simulation of flexible beams using cubic splines and zero-order holds.- Towards a differential topological classification of robot manipulators.- An adaptive PD control algorithm for robots.- Robustness of Infinite-Dimensional Systems.- Comparison of robustness measures for a flexible structure.- Robust stabilization for infinite-dimensional linear systems using normalized co-prime factorizations.- Standard problem for distributed systems.- Robust stabilization of delay systems.- Topological aspects of transfer matrices with entries in the quotient field of H-infinity.- On the Nyquist criterion and robust stabilization for infinite-dimensional systems.- Real stability radii for infinite dimensional systems.- Robust stability condition for infinite-dimensional systems with internal exponential stability.

Reacting to scheduling exceptions in FMS environments

Abstract: Uncertainties in the production environment and modelling limitations inevitably result in operational deviations from schedules generated using predictive models. A production control mechanism monitors the environment for exceptions, and takes corrective actions, with the objective of adhering closely to planned objectives. This paper proposes a knowledge based (KB) methodology to perform such control in FMS environments. Use of KB techniques is motivated by the observation that control knowledge has a high heuristic content. A PROLOG implementation of this methodology, that generates automatic response to machine failures, dynamic introduction of new jobs, and dynamic increase in job priority, is presented. Experimental results appear to show that simple and generic design strategies for the KB can provide the basis for effective and robust control behavior. Handled by the Department of Computer and Information Sciences.

Survey of the Robust Control of Robots

Abstract: In this survey, we discuss current approaches to the robust control of the motion of robots and summarize the available literature on the subject. The three major designs discussed are the "Linear-Multivariable" Approach, the "Passivity" approach and the "Variable-Structure" approach. The survey is limited to rigid robots and nonadaptive controllers.

Robustness margin calculation with dynamic and real parametric uncertainty

Abstract: The problem of robust stability in feedback control systems with real uncertain parameters and unmodeled dynamics is considered. A robust margin r/sub m/ is defined, and an algorithm to calculate r/sub m/ and the closely related multivariable stability margin k/sub m/ is developed. How robust performance for real parametric uncertainty can be handled in this framework is also shown. The result essentially provides a method to check whether or not the infinity norm of a closed-loop transfer matrix is less than a specified level over a bounded set of real parametric variations. >

I-O map inversion, zero dynamics and flight control

Abstract: The trajectory control of aircraft in rapid, nonlinear maneuvers is discussed. Based on nonlinear invertibility theory, a control law is derived to independently control roll, pitch, and sideslip angles using rudder, elevator, and aileron. Integral feedback is introduced in order to obtain robustness in the control system to parameter uncertainty. The stability of the zero dynamics is examined. Simulation results are presented to show that in a closed-loop system, precise simultaneous lateral and longitudinal maneuvers can be performed despite the presence of uncertainty in the stability derivatives. >

Robustness Improvement of Actively Controlled Structures through Structural Modifications

Abstract: The parameter variations introduced by the analysis model, uncertain material properties, or optimization may adversely influence the stability and performance characteristics of a closed-loop controlled structure. The improvement of robustness of actively controlled structures through structural modifications is considered in this work. The stability and performance robustness indices are defined as measures of robustness of actively controlled structures. The integrated structural/control design problem is considered as a multiobjective optimization problem, in which three objectives—structural weight, stability robustness index, and performance robustness index—are considered for minimization. The utility function, lexicographic, and goal programming methods are applied to solve the multiobjective nonlinear programming problem. Two examples, a two-bar truss and two-bay truss, are considered to demonstrate the procedure. HERE has been a dramatic increase in the past decade in the use of active control systems to improve structural performance.1'2 The major challenge in the field of active control of structures is in the design of control systems for very large space structures. These structures are by nature distributed parameter systems with multiple inputs (controls) and a continuum of outputs (displacements). The finite-ele- ment method is commonly used for the description of these structures. This is a source of parameter errors and truncated (or reduced order) models in the system. In addition, the structural properties of large space structures cannot be tested before they are put into orbit and, hence, sizeable uncertain- ties exist in modal parameters. A great deal of research is currently in progress on develop- ing methods for the simultaneous (integrated) design of the structure and the control system. The weight of the structure was minimized, with constraints on the distribution of the eigenvalues and/or damping ratio of the closed-loop system by Khot et al.3 Miller and Shim4 considered the simultaneous minimization, in structural and control variables, of the sum of structural weight and the infinite horizon linear regulator quadratic control cost. The structure/control system optimiza- tion problem was formulated by Khot et al.,5 with constraints on the closed-loop eigenvalue distribution and the minimum Frobenious norm of the control gains. It can be seen that in all the above works the consideration of robustness of the control system has been ignored. The parameter variations introduced by the analysis model, uncertain material properties, or optimization may adversely influence the stability and performance characteristics of the control system. The robustness is an extremely important feature of a feedback control design. A robust control design is one that satisfactorily meets the system specifications, even in the presence of parameter uncertainties and other modeling errors. Since the system specifications could be in terms of