Showing papers on "Robust control published in 1985"

The Robust Control of Robot Manipulators

Abstract: A new scheme is presented for the accurate tracking control of robot manipulators. Based on the more general suction control methodology, the scheme addresses the following problem: Given the extent of parametric uncertainty (such as imprecisions or inertias, geometry, loads) and the frequency range of unmodeled dynamics (such as unmodeled structural modes, neglected time delays), design a nonlinear feedback controller to achieve optimal tracking performance, in a suitable sense. The methodology is compared with standard algorithms such as the computed torque method and is shown to combine in practice improved performance with simpler and more tractable controller designs.

Robust control of linear time-invariant plants using periodic compensation

Abstract: This paper considers the use and design of linear periodic time-varying controllers for the feedback control of linear time-invariant discrete-time plants. We will show that for a large class of robustness problems, periodic compensators are superior to time-invariant ones. We will give explicit design techniques which can be easily implemented. In the context of periodic controllers, we also consider the strong and simultaneous stabilization problems. Finally, we show that for the problem of weighted sensitivity minimization for linear time-invariant plants, time-varying controllers offer no advantage over the time-invariant ones.

Structured uncertainty in control system design

Abstract: This paper reviews control system analysis and synthesis techniques for robust performance with structured uncertainty in the form of multiple unstructured perturbations and parameter variations. The structured singular value, µ, plays a central role. The case where parameter variations are known to be real is considered.

Robust linear compensator design for nonlinear robotic control

Abstract: The motion control of robotic manipulators is investigated using a recently developed approach to linear multivariable control known as the stable factorization approach. Given a nominal model of the manipulator dynamics, the control scheme consists of an approximate feedback linearizing control followed by a linear compensator design based on the stable factorization approach. Using a multiloop version of the small gain theorem, robust trajectory tracking is shown under the assumption that the deviation of the model from the true system satisfies certain norm inequalities. In turn, these norm inequalities lead to quantifiable bounds on the tracking error.

Robust stability of systems with integral control

Abstract: A number of necessary and sufficient conditions are derived, which must be satisfied by the plant d.c. gain matrix of a linear time invariant system in order for an integral controller to exist for which the closed loop system is stable. Based on these results, 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 adaptive control: Conditions for global stability

Abstract: An input-output approach is presented for analyzing the global stability and robustness properties of adaptive controllers to unmodeled dynamics. The concept of a tuned system is introduced, i.e., the control system that could be obtained if the plant were known. Comparing the adaptive system to the tuned system results in the development of a generic adaptive error system. Passivity theory is used to derive conditions which guarantee global stability of the error system associated with the adaptive controller, and ensure boundedness of the adaptive gains. Specific bounds are presented for certain significant signals in the control systems. Limitations of these global results are discussed, particularly the requirement that a certain operator be strictly positive real (SPR)-a condition that is unlikely to hold due to unmodeled dynamics.

Roboust nonlinear control of robot manipulators

Abstract: In this paper we investigate the motion control of robotic manipulators using the recently developed stable factorization approach to tracking and disturbance rejection. Given a nominal model of the manipulator dynamics, the control scheme consists of an approximate feedback linearizing control followed by a linear compensator design based on the stable factorization approach to achieve optimal tracking and disturbance rejection. Using a multiloop version of the small gain theorem [17], the applicability of the linear design techniques and the stability of the closed loop system are rigorously demonstrated.

Persistence of Excitation in Linear Systems

Abstract: This paper develops output reachability characterizations of linear finite dimensional systems, so as to translate excitation properties of system inputs to excitation properties of system outputs, states, or associated regression vectors. Such properties are of fundamental concern for convergence of algorithms involving on-line identification, adaptive state estimation, prediction and control. The case of adaptive control is of particular interest since it is desirable that persistence of excitation of associated regression vectors be maintained in the presence of time-varying feedback controllers. Persistence of excitation guarantees convergence without a priori stability assumptions and ensures robustness properties. The theory of the paper suggests modifications to standard adaptive schemes to ensure the required persistence of excitation.

The optimal projection/maximum entropy approach to designing low-order, robust controllers for flexible structures

Abstract: The Optimal Projection/Maximum Entropy approach to designing low-order controllers for high-order systems with parameter uncertainties is reviewed. The philosophy of representing uncertain parameters by means of Stratonovich multiplicative white noise is motivated by means of the Maximum Entropy Principle of Jaynes and statistical analysis of modal systems. The main result, the optimal projection equations for fixed-order dynamic compensation in the presence of state-, control- and measurement-dependent noise, represents a fundamental generalization of classical LQG theory.

Hypothesis integration in image understanding systems

Abstract: The goal of this research is to develop a robust control strategy for constructing image understanding systems (IUS). This paper proposes a general framework based on the integration of related hypotheses. Hypotheses are regarded as predictions of the occurrences of objects in the image. Related hypotheses are clustered together. A composite hypothesis is computed for each cluster. The goal of the IUS is to verify the hypotheses. We constructed an image understanding system, SIGMA, based on this framework and demonstrated its performance on an aerial image of a suburban housing development.

Adaptive control of a batch reactor

Abstract: A globally stable adaptive predictive control system (APCS) is evaluated by application to a simulated PVC batch reactor. The reactor is run under APCS control with the objective of either temperature setpoint tracking or constant reaction rate. The batch nature of this system makes it possible to learn about the physical problem from successive runs. This knowledge is incorporated into the control strategy to improve the performance of the reactor. The problem of excessive manipulation of the control variable has been recognized and resolved by using control weighting. Performance of the adaptive technique is compared with previous results using self-tuning and PID control of the same reactor. APCS provides good, robust control despite the nonlinear dynamics of the system.

Nonlinear Compensator Synthesis via Sinusoidal-Input Describing Functions

Abstract: We describe a new nonlinear compensator synthesis approach and illustrate it with an application to a position servo design problem from robotics. The synthesis technique is based on a set of amplitude-dependent sinusoidal-input describing function (SIDF) models of the nonlinear plant. An intermediate step is the design of a linear compensator set based on these models; final synthesis of the nonlinear control system is accomplished by SIDE inversion to determine the required compensator nonlinearities. The major extension in comparison with earlier research is that the compensator so obtained is fully nonlinear; i.e., there is a nonlinear operator associated with each term (proportional, integral, derivative) in the compensator. This approach is capable of treating nonlinear plants of a very general type, with no restrictions as to system order, number of nonlinearities, configuration, or nonlinearity type, and can be extended readily to include other compensator types, e.g., lead/lag. The end result is a closed-loop nonlinear control system that is relatively insensitive to reference input amplitude.

Robust trajectory control of underwater vehicles

Abstract: The Deep Submergence Laboratory at the Woods Hole Oceanographic Institution is currently developing supervisory control system methodologies for underwater vehicles and manipulators. These technologies are currently being applied to Several tethered systems under development at the laboratory, however much of the work is directly applicable to untethered systems as well. Specific areas under investigation include man-machine interface design, control theoretic aspects of vehicle and manipulator control, and navigation sensors. The design of the closed-loop control system is a primary issue for any underwater vehicle that is not controlled manually. Precise trajectory control of all vehicles movements is particularly difficult due to the nonlinear, uncertain nature of the dynamics of underwater systems. A new control system design methodology called sliding control has been shown to deal with these difficult problems very effectively. In this paper, methodology and results from simulation and actual tests in the water are reviewed.

Robust simplified adaptive control for a class of multivariable continuous-time systems

Abstract: This paper presents a simple and robust adaptive control algorithm for a class of multivariable continuous-time linear systems. Boundedness of all values involved in the adaptation process is guaranteed in the presence of parasitic disturbances and dynamics provided that the controlled plant is stabilizable via unknown static output feedback. The usual need of prior knowledge about the order of the plant and about the pole-excess is also eliminated. Although these techniques can be generalized and their applicability can be extended to systems that need dynamic feedback in order to achieve stability, the present algorithm has his own importance, due to its extreme simplicity of implementation that may facilitate application of adaptive control in realistic complex control systems with unknown parameters.

Robust torque control of an elastic robotic arm based on invertibility and feedback stabilization

Abstract: We present an approach to the control of elastic robotic systems for space applications using inversion, servocompensation, and feedback stabilization. For simplicity, a robot arm (PUMA-type) with three rotational joints is considered. The third link is assumed to be elastic. Using an inversion algorithm, a non-linear decoupling control law, ud, is derived such that in the closed loop system, independent control of joint angles by the three joint torquers is accomplished. For the stabilization of elastic oscillations, a linear feedback torquer control law, us, is obtained applying linear quadratic optimization to the linearized arm model augmented with a servocompensator about the terminal state. Simulation results show that, in spite of uncertainties in the payload and vehicle angular velocity, good joint angle control and damping of elastic oscillations are obtained with the torquer control law u=ud+us.

Robust tracking in nonlinear systems and its applications to robotics

Abstract: A nonlinear feedback multivariable controller is used to implement multivariable tracking in a nonlinear system. The tracking error is measured by a general function of system state and the input command. The controller is robust in the sense that the tracking error is ultimately bounded in the presence of modelling errors. Free parameters, which affect the form of the controller, allow flexibility in determining such factors as: the size of the ultimate bound, the rate of error delay, excursion of the control, conditions on the class of modelling errors, the level of system gain. Restrictive assumptions on the structure of the model and the modelling errors are required but they are treated in a transformation framework which allows the generalization of similar conditions which appear in the prior literature. These assumptions hold for robotic manipulators. This application is investigated at some length and it appears that the resulting control scheme may have advantages over others which have been proposed in the robotics literature.

Nonlinear feedback control of PUMA 560 robot arm by computer

Abstract: It is shown that nonlinear feedback with diffeomorphic state transformation is applicable to dynamic control of PUMA 560 robot arm. This new dynamic control method externally (or exactly) linearizes the whole system and provides simultaneous output decoupling. To render the control robust, the nonlinear feedback is augmented with optimal error correcting controller which operates on the error in the task space. A key feature of this dynamic control method is that the nonlinear gains in the controller do not need readjustment from task to task. In that sense this controller is "intelligent" since it directly responds to changing task commands. A complete dynamic model in state equation form and with the necessary geometric and inertial parameters is also presented for PUMA 560 restricted to motions at the first three joints. This model is necessary to specify the nonlinear feedback and diffeomorphic transformation.

Predictive Controller Design for SISO Systems

Abstract: This paper presents a fundamental analysis of the stability of single-input/single-output closed-loop systems with predictive controllers. The analysis can incorporate modeling errors and be used to calculate allowable modeling errors for a given system and controller. Design parameter selection guidelines for predictive controllers in SISO systems have been developed by considering performance, robustness, and ease of tuning. The performance and robustness of the resulting controllers are demonstrated on four numerical examples and compared to controllers designed using other parameter choices.

Robust Detection, Isolation, and Accommodation for Sensor Failures

Abstract: Recent advances in multivariable robust control system design are extended to sensor failure, detection, isolation, and accommodation (FDIA) and estimator design. A new concept called threshold selector is introduced. It represents a significant and innovative tool for the analysis and synthesis of FDIA algorithms. Analytical results are obtained for the SISO case to compute optimal thresholds and size of minimum detectable failures, and a computer-aided technique is developed for the multivarlable case. The techniques have been applied to sensor FDIA for an aircraft turbine engine control system.

The Constrained Lyapunov Problem and its Application to Robust Output Feedback Stabilization

Abstract: Given a dynamical system whose description includes time-varying uncertain parameters, it is often desirable to design an output feedback controller leading to uniform stability of a given equilibrium point. When designing such a controller, one may consider static (i.e., memoryless) or dynamic compensation. In this paper, we show that solvability of various output feedback design problems is equivalent to existence of a solution to a certain Constrained Lyapunov Problem (CLP). The CLP can be stated in purely algebraic terms. Once the CLP is described, we provide necessary and sufficient conditions for its solution to exist. Subsequently, we consider application of the CLP to a number of robust stabilization problems involving static output feedback and observer-based feedback.

A New Approach to Robot Control

Abstract: State-of-the-art robots do not perform up to their physical speed or load capabilities. Currently, performance is limited by the form of control implemented, which gives rise to speed and load dependent errors and overshoots. In this paper, a new control algorithm is proposed which entails smooth real time reference paths and an adaptive feedforward path-tracking algorithm. The result is high accuracy independent of speed and load. With the trade-off between speed and accuracy eliminated, the full operational capabilities of the axis motors can be exploited. The utility of these principles is shown in a video tape demonstration of a new controller for a Unimation PUMA robot.

Robust control apparatus responsive against disturbance

Abstract: A process control apparatus comprises a main controller having a first integrator for integrating a difference signal between a set point and an output of a process and a PD (proportional-derivative) arithmetic operating unit for executing the PD arithmetic operation for the output of the process. The main controller obtains a control signal on the basis of an I-PD (integral-poroportional-derivative) control method and supplying this control signal to the process. A robust controller, connected to the output of the process, comprises a high-order differentiator for high-order differentiating the output of the process, a second integrator for integrating the difference signal between the set point and the output of the process, a subtractor for subtracting an output of the second integrator from an output of the high-order differentiator, and an amplifier for amplifying an output of the subtractor and feeding back this amplified output to the control signal.

Robust adaptive controller with zero residual tracking errors

Abstract: The adaptive control of a plant whose dominant part has transfer function with relative degree n*=1 has been considered in the presence of parasitics and disturbances. A new adaptive law is proposed which guarantees the existence of a large region of attraction from which all signals converge to a small residual set provided the adaptive gains and the magnitude and frequencies of the reference input signal, are small compared to the "speed" of parasitics. In contrast to the adaptive law used in [1,2] the new adaptive law guarantees smaller residual tracking errors, which reduce to zero when the parasitics become infinitely fast and the disturbances disappear, provided that a certain design parameter is properly chosen.

Adaptive control of decentralized systems: Known subsystems, unknown interconnections

Abstract: One of the common assumptions in control of large interconnected systems is that models of subsystems are to a large extent known to a designer, and an essential modeling uncertainty resides in the interconnections. Current decentralized adaptive control schemes take no advantage of this fact. In this paper an algorithm is presented in which adaptation of local feedback gains is in the a direction which compensates for the unknown interconnections, while exploiting the knowledge about the sub-systems. As a result, we broaden considerably the class of interconnected systems for which decentralized adaptation is feasible.