Showing papers on "Robust control published in 1984"

Robust stabilizability for a class of transfer functions

Abstract: This paper is concerned with the robust stabilizability for single-input single-output plants. Robust stabilizability means that a fixed controller can stabilize simultaneously all the plants in a given class which is characterized by a frequency-dependent uncertainty band function around the transfer function of a nominal model. A necessary and sufficient condition for robust stabilizability is derived based on the well-known Nevanlinna-Pick theory in classical analysis. It is shown that the values of the uncertainty band function should be restricted within a certain range at the unstable poles of the nominal model, in order for the class to be robustly stabilizable. A procedure of synthesizing a robust stabilizer is given and the parametrization of all the robust stabilizers is also shown.

Robust Adaptive Control

Abstract: The paper addresses an open problem concerned with the boundedness of signals in an adaptive loop when external perturbations are present. A complete solution is provided for the case of a first order plant with an unknown parameter by analyzing a nonlinear differential equation in R2. It is shown that if the persistent excitation of the reference input is larger than the perturbation in some sense, the solutions will be globally bounded. The same methodology appears to be applicable to the general adaptive control problem.

Robust model reference adaptive controllers, Part I: Stability analysis

Abstract: We study the stability given by a modified model reference adaptive controller. Modifications are projections of the adapted parameters into a compact set, normalization of the signals entering the adaptation law by a weighted L2-norm of the I/O signals. The a priori knowledge about the plant is implicit: order of a stabilizing regulator, compact set containing its coefficients. Global boundedness of the signals is established using both the error to signal approach of [10] and the operator theoretic approach of [8]. A conicity condition is involved but its robustness with respect to the graph topology of [20] is proved.

The control of robot manipulators with bounded input: Part II: Robustness and disturbance rejection

Abstract: In this paper we continue the investigations begun in [13] and [14] on the control of robot manipulators. Using the theory of uncertain dynamical systems developed in [4], [5], [16], [17] we derive a robust nonlinear control strategy with guaranteed tracking properties which can be quantified given bounds on the extent of model uncertainty, sensor noise, input disturbances, etc. We also extend the class of pointwise optimal control strategies of [13] to the case of systems with uncertainty in order to treat the problem of input constraints within the context of uncertain systems.

A variable structure approach to robust control of VTOL aircraft

Abstract: This paper examines the application of variable structure control theory to the design of a flight control system for the AV-8A Harrier in a hover mode. The objective in variable structure design is to confine the state trajectories to a subspace of the total state space. The motion in this subspace is insensitive to system parameter variations and external disturbances that lie in the range space of the control. A switching type of control law results from the design procedure. The control system was designed to track a vector-valued velocity command. For comparison, a proportional controller was designed using optimal linear regulator theory. Both controllers were evaluated for their transient response performance using a linear model; then a nonlinear simulation study of a hovering approach to landing was conducted. The variable structure controller outperformed its linear counterpart in the presence of wind disturbances and plant parameter uncertainties afforded by the simulation.

Applied Digital Control: Theory, Design, and Implementation

Abstract: Introduction to the key features of digital control discrete-time signals idealized approximation frequency spectrum reconstruction Z transform techniques methods of analysis and design digital control algorithms hardware systems for implementation case histories state-variable techniques control of large-scale systems control system implementation and integration commercially available computer control systems and their industrial application adaptive, self-tuning and robust control.

Robust direct adaptive control

Abstract: This paper proposes a new model reference adaptive control algorithm which has good robustness properties in the presence of unmodeled plant dynamics. The new algorithm requires filtering of the plant input and output with low pass first order filters, prior to their use in the adaptive algorithms. In the case where the dominant transfer function of the plant has a relative degree n* = 1 a global convergence result has been proven in the presence of unmodeled dynamics. When n* > 1 the algorithm employs an adaptive law with normalized signals in order to improve robustness with respect to unmodeled dynamics. It is shown that two of the most crucial factors for robustness, the speed of adaptation and the magnitude of the estimated parameters relative to the speed of the parasitics can be adjusted using the normalized adaptive law.

Robustness of Luenberger Observers: Linear Systems Stabilized via Nonlinear Control

Abstract: Given a dynamical system whose state equations include time-varying uncertain parameters, it is often desirable to design a state feedback controller leading to uniform asymptotic stability of a given equilibrium point If, however, the controller operates on some estimate of the state, instead of the true state itself, it is of interest to know whether the desired stability will be preserved; eg, suppose that the measured output is processed by a Luenberger observer This paper concentrates on the scenario above and in addition, our analysis permits the controller to be nonlinear As a first step, inequalities are developed which have implications on the system's robustness; that is, when the uncertain parameters satisfy these inequalities, it becomes possible to separately design controller and observer This amounts to an extension of the classical separation theorem to the case when the controller is nonlinear It is also of interest to note that the approach given here enables us to guarantee stability for some nonzero range of admissible parameter variations This is achieved by introducing a certain "tuning parameter" into the Lyapunov function which is used to assure the stability of the cambined plant-observer-controller system

Invertibility and robust nonlinear control of robotic systems

Abstract: Based on the theory of invertibility and functional reproducibility in multivariable nonlinear systems, a unified framework for the trajectory control of robotic systems is presented. An inversion algorithm is used to derive a decoupling control law such that independent control of certain desired outputs is accomplished. For obtaining robustness in the control system under large variation of payloads, design of a servocompensator around the inner decoupled-loop using servomechanism theory is suggested. These results are applied for the trajectory control of a three degrees of freedom robot arm. For trajectory following two control laws, C? and CH, based on the choice of joint angles or coordinates of the end effector as the controlled outputs, respectively, are derived. It is seen that, whereas control C? has no singularity, certain singular surfaces arise where feedback elements of CH become infinity. Digital simulation results are presented to show the capability of the controls C? and CH.

Asymptotic Reproducibility in Nonlinear Systems and Attitude Control of Gyrostat

Abstract: A control law is presented for asymptotic function reproducibility in a class of nonlinear-systems such that the output of the system asympotically tends to a given function. The controller consists of a prefilter and a servocompensator. Based on this result, a nonlinear feedback control law for the attitude control of a satellite containing symmetric rotors, in a circular orbit, is derived. In the closed-loop system, given trajectories of pitch, yaw, and roll angles are asymptotically followed, and set point control of attitude is accomplished. Digital simulation results are presented to show the capability of the nonlinear controller.

Robust control of a robot manipulator with nonlinearity

Abstract: This paper deals with the control technique of a computer-controlled manipulator with high nonlinearity. To overcome the nonlinearity, a linearization of the system by nonlinear feedback has been employed. Because of the difficulty of the parameter identification under the variation of load, it is not easy to make correct nonlinear compensation for its linearization. In this paper, to solve this problem a robust servo controller based on a model is designed for the linearized manipulator, and a control system is constructed taking account of input nonlinearity. The method is applied to the three-joint manipulator endowed with a software servo using a minicomputer, and the effect of the proposed method is investigated.

Self-tuning control with a priori plant knowledge

Abstract: Most adaptive control methods assume the plant to be completely unknown except for a parameterized structure. Often, however, the plant will have some dynamic modes which are known and do not vary. This paper presents two methods for including a priori plant knowledge in the explicit self-tuning controller (STC). The first method constrains the plant estimates to be consistent with the known information. The second method filters the measurements in an attempt to remove the known dynamics and to estimate only the unknown dynamics. The stability and convergence of these methods is studied. The first method, while stable, is quite numerically complex. The second method is superior. It gives a controller of reduced computational burden and increased robustness to non-persistently exciting signals.

Robust Fault Detection: The Effect of Model Error

Abstract: This paper examines the issues involved in robust fault detection in the presence of system model error. The underlying theory presented is analogous to concepts in robust control design, e.g., [1]-[5], which require the introduction of a metric or norm measure of signals defined on an appropriate function space.

Robust Nyquist array methodology : a new theoretical framework for analysis and design of robust multivariable feedback systems

Abstract: A novel extension of the Nyquist array methods to accommodate for system uncertainties is presented. The concept of robust diagonal dominance is introduced ; necessary and sufficient conditions for robust stability are developed and the issue of robust performance is addressed. Two examples are given to demonstrate the power of the method for analysis and design of robust feedback control systems.

Robust compensation for a robotic manipulator

Abstract: In a suboptimally controlled manipulator arm, friction torque variations cause trajectory deviations and performance deterioration. On the other hand, the on-line computation of nonlinear terms of the suboptimal controller is time consuming or requires large memory space when table lookup techniques are used. In order to obtain robustness against variations in open-loop dynamics and decrease the effect of nonlinear terms due to couplings in suboptimal control systems with quadratic performance indexes, in addition to state proportional feedback, it is necessary to introduce feedback associated with the derivatives of the state variables. This additional feedback may be implemented as minor compensating loops built around the individual joints with analog devices. As an example, torque compensation and acceleration compensation for the M.I.T. Scheinman arm are considered. They yield a simple linear controller with improved robustness.

Design of ripple-free multivariable robust servomechanisms

Abstract: The design of multivariable control systems to provide zero steady-state error in the presence of non-decaying reference and disturbance signals and in spite of perturbations to system parameters is referred to as the robust servomechanism problem. The application of standard robust servomechanism theory to sampled data systems can guarantee asymptotic tracking at sampling instants only. Between sampling instants, the output will normally contain a component referred to as ripple. In this paper, the robust servomechanism theory is extended to sampled-data systems and a technique is proposed for ripple-free tracking of nondecaying inputs including sinusoids and polynomials. It is shown that a continuous internal model is necessary and sufficient, to provide ripple-free response. All the poles of the system can be assigned to the origin to yield a continuous ripple-free deadbeat response. The integrators of the hold devices are used as part of the continuous internal model for constant inputs. An example is provided to illustrate the design technique.

Exponential convergence and robustness margins in adaptive control

Abstract: The paper presents general results on the stability of ordinary nonlinear differential equations in the presence of bounded disturbances. These are used to study the robustness of a simple model reference adaptive control algorithm. It is shown that the system is guaranteed to remain stable in the presence of disturbances (arising from input disturbances, plant parameter variation, output disturbances, unmodelled dynamics...) provided that the unperturbed system is exponentially stable. Moreover, the bounds on the level of disturbances that can be tolerated increase with the rate of convergence. In the present application (and also for most adaptive systems), exponential convergence follows from persistent excitation of the exogeneous reference signal. The paper concludes with remarks on consequences of the results on practical applications.

Flight Control System Reconfiguration Design Using Quantitative Feedback Theory.

Abstract: : Quantitative theory is used to develop control laws for the AFTI/F-16 with a reconfigurable flight control system. Compensators are synthesized to control pitch rate and roll rate through individually controlled elevators and flaperons. Robust control of these variables is required over a larger portion of the flight envelope despite flight control surface failures. Linearized aerodynamic data are used to develop the aircraft model in state-variable format. The longitudinal and lateral-directional equations are coupled in the control matrix. Individual control of the elevators and flaperons is obtained by dividing the dimensionalized control derivatives for a control surface pair in half and assigning each surface of the pair one-half of the total derivative value. The system with individually controlled surfaces represents a four input-two output system which is transformed into an equivalent two input-two output system for each control surface configuration and flight condition. Quantitative feedback theory is then applied to the equivalent systems. Originator-supplied keywords included: Inherent Reconfiguration; Loop Transmission; Flight control Systems; Quantitative Feedback Theory; Control Systems; Computer Programs; Theses.

Nonlinear Trajectory Control of Autonomous Underwater Vehicles Using the Sliding Methodology

Abstract: A new variation on sliding control is shown to be very effective for the control of underwater vehicles. The method deals with nonlinearities directly, is highly robust to imprecise models, and is intuitively appealing. The method is demonstrated using a nonlinear vehicle simulation.

Robust controller synthesis for a large flexible space antenna

Abstract: This paper considers the problem of synthesizing a fine-pointing control system for a large flexible space antenna in the presence of modeling uncertainties. The plant to be controlled is a 122-meter diameter, space-based, "Hoop/Column" antenna. The mathematical model, based on a finite element analysis, consists of three rigid-body rotational modes, and the first 10 elastic modes. A preliminary robust compensator design for achieving the required pointing performance is obtained using linear-quadratic-Gaussian (LQG) and loop transfer recovery (LTR) methods for loop-shaping. The computations are performed using the LQG design package "ORACLS," and a recently developed singular value analysis package.

Robust Design of a Digital PID Predictor Controller

Abstract: A digital proportional integral-derivative (PID) predictor controller is analyzed, and its advantages relative to the normal PID controller are derived. A design procedure which results in a robust control system is developed. This procedure applies to both the PID predictor and the normal PID controllers. A regulator carbon dioxide control system which requires disturbance rejection is designed as an example.

Robust Control of Self-Adjoint Distributed-Parameter Structures

Abstract: This paper examines the active vibration control-of distributed-parameter structures in which a self-adjoint differential operator expresses the stiffness distribution. For large and complex structures, computational requirements and/or modeling limitations ensure that a reduced-order controller is used. However, although in practice only discrete actuators and discrete sensors are available, spatially distributed control forces and spatially distributed observations are desirable for implementing a reduced-order controller. Therefore a distinction arises among 1) designing distributed control forces for a reduced-order model, 2) implementing the control forces with a number of actuators, and 3) estimating the distributed state from a number of sensors. Herein the distinctions are realized by introducing three appropriate projection operations. The effects of the three projections on the actual closed-loop eigenvalues are investigated in detail. A criterion for the controller to be robust in the stability sense is discussed and illustrative examples are presented.

Robust adaptive control: Conditions for local stability

Abstract: The question is examined of when an adaptive control system is robust to unmodeled dynamics and unknown bounded disturbances. Conditions are presented that ensure 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 certain tuned signals are assumed to be persistently exciting.

Robust control of the characteristic values of systems with possible parameter variations

Abstract: An analytical method to control by multiparameter output feedback the characteristic values of a closed loop multi-input multi-output system inside (or outside) general aubregions of the complex plane, is presented. The method pertains to analogue as well as discrete systems. The design method is robust in the sense that the characteristic values are designed to cluster inside the desired subregion, even though any number of the specifying parameters are only known to within a given interval. The interval may possibly be disjoint and possibly infinite (completely unknown). Examples are provided which illustrate the broadness and effectiveness of the method.