Showing papers on "Robust control published in 1989"

Robot dynamics and control

Abstract: From the Publisher: This self-contained introduction to practical robot kinematics and dynamics includes a comprehensive treatment of robot control. Provides background material on terminology and linear transformations, followed by coverage of kinematics and inverse kinematics, dynamics, manipulator control, robust control, force control, use of feedback in nonlinear systems, and adaptive control. Each topic is supported by examples of specific applications. Derivations and proofs are included in many cases. Includes many worked examples, examples illustrating all aspects of the theory, and problems.

Parameter space methods for robust control design: a guided tour

Abstract: The results obtained in studies of robust stability and stabilizability of control systems with parametric (structured) uncertainties are reviewed. Both the algebraic methods based upon characteristic equations and the methods using Lyapunov functions and Riccati equations are discussed and compared. In the context of algebraic methods, most promising are the Kharitonov-type approach and the optimization procedure of embedding a geometric figure of some kind inside the stability regions of the parameter space, maximizing its size using minimax or some other mathematical programming technique. In the framework of Lyapunov's direct method, the dominant approach has been a quadratic function estimation of stability regions in the parameter space. In large-sale systems, the concept of vector Lyapunov functions has been used with the possibility of choosing quadratic forms, norm-like functions, and their combinations. >

A new technique for robust control of servo systems

Abstract: The robust controller has very simple structures and can be divided into two separate parts: a servo controller and an auxiliary controller. The two controllers are designed independently. The function of the auxiliary controller is to cancel out the plant uncertainties directly without the use of the high loop gain principle. Interpretation of robot controller as a signal-synthesis adaptive controller is given. Practical implementation issues of the auxiliary controller are discussed. Simulations of a design example with large parameter uncertainty, nonlinearity, and external disturbance are presented to demonstrate the effectiveness of the design technique. This technique is further tested with success in an experimental study of joint position control of a PUMA 560 robot arm. >

Adaptive control of flexible joint manipulators

Abstract: The authors present an adaptive control result for flexible-joint robot manipulators. Under the assumption of weak joint elasticity, a singular perturbation argument is used to show that recent adaptive control results for rigid robots can be used to control flexible-joint robots, provided a simple correction term is added to the control law to damp out the elastic oscillations at the joints. In this way, fundamental properties of rigid robot dynamics can be used to design robust adaptive control laws for flexible-joint robots. The implementation of the full controller requires only joint position and velocity information. Thus, robustness to parametric uncertainty is achieved without the need for acceleration and jerk measurements. >

Exact recursive polyhedral description of the feasible parameter set for bounded-error models

Abstract: A method is described which exactly characterizes the set of all the values of the parameter vector of a linear model that are consistent with bounded errors on the measurements. It provides a parameterized expression of this set, which can be used for robust control design or for optimizing any criterion over the set. This approach is based on a new variant of the double description method for determining the edges of a polyhedral cone. It can be used in real time and provides a suitable context for implementation on a computer. Whenever a new measurement modifies the set, the characterization is updated. The technique is illustrated with a simple example. >

Robustness in Identification and Control

Abstract: Robustness in identification.- Comments on model validation as set membership identification.- SM identification of model sets for robust control design from data.- Robust identification and the rejection of outliers.- Semi-parametric methods for system identification.- Modal robust state estimator with deterministic specification of uncertainty.- The role of experimental conditions in model validation for control.- Modeling and validation of nonlinear feedback systems.- Towards a harmonic blending of deterministic and stochastic frameworks in information processing.- Suboptimal conditional estimators for restricted complexity set membership identification.- Worst-case simulation of uncertain systems.- On performance limitations in estimation.- Design criteria for uncertain models with structured and unstructured uncertainties.- Robustness and performance in adaptive filtering.- Nonlinear identification based on unreliable priors and data, with application to robot localization.- Robust model predictive control: A survey.- Intrinsic performance limits of linear feedback control.- Puzzles in systems and control.- Robust regional pole placement: An affine approximation.- On achieving L p (?p) performance with global internal stability for linear plants with saturating actuators.- Control under structural constraints: An input-output approach.- Multi-objective MIMO optimal control design without zero interpolation.- Robustness synthesis in l 1: A globally optimal solution.- Optimal control of distributed arrays with spatial invariance.- Numerical search of stable or unstable element in matrix or polynomial families: A unified approach to robustness analysis and stabilization.- A convex approach to a class of minimum norm problems.- Quantified inequalities and robust control.- Dynamic programming for robust control: Old ideas and recent developments.- Robustness of receding horizon control for nonlinear discrete-time systems.- Nonlinear representations and passivity conditions in discrete time.- Robust ripple-free output regulation and tracking under structured or unstructured parameter uncertainties.- An experimental study of performance and fault-tolerance of a hybrid free-flight control scheme.

Robust Controller Design for a Nonlinear CSTR

Abstract: A design methodology is presented for the analysis and synthesis of robust linear controllers for a nonlinear continuous stirred tank reactor. Regions are defined in the phase plane in which the maintenance of robust stability and the achievement of robust performance levels are guaranteed. The results are based upon new extensions of the structured singular value theory to a class of nonlinear and time-varying systems.

Pole-placement designs of power system stabilizers

Abstract: This paper examines four pole placement techniques applied to the design of power system stabilizers. These methods are the full state feedback, an output feedback by the projective method [1], a design based on a full order observer, and a low order dynamic compensator also based on the projective method [2]. A single machine infinite bus power system is used to illustrate the different design approaches. The power system stabilizer is designed to provide damping to the local mode of this system. It is shown that in order to provide the same amount of damping improvement, the power system stabilizers designed using the different methods have similar gains and plases at the modal frequency, Figure 1. This result is explained by establishing a link between the frequency modal response method and the close-loop system electromechnical modes. The response of the dynamic controllers with modes close to the local mode is also investigated. It is shown that this situation causes a resonant condition which, in general, should be avoided. This paper also presents a simple robust damping controller design considering two different operating conditions of the power system: a weak connection case and a strong connection case. The robust controller is based on the reduction of two controllers using a Hankel-Norm model reduction algorithm [3].

Near-minimum time open-loop slewing of flexible vehicles

Abstract: Minimum time, open-loop, optimal controls are calculated for single-axis maneuvers of a flexible structure. By shaping the control profiles with two independent parameters, a wide variety of control histories can be pro- duced. Based on the dynamics of the model, with a normalized time scale, the resulting Pontryagin's necessary conditions yield a nonlinear fixed final time, fixed final state, two-point boundary value problem with the maneuver time as a control parameter. Upon generating numerical solutions to the problem, the final maneuver time and residual flexural energy are compared to the bang-bang solution as a measure of the success of a given maneuver. Examples presented illustrate near-minimum time maneuvers with control of flexible modes in addi- tion to the rigid body modes, as well as the qualitative and quantitative effect of the torque shaping parameters. EAR-MINIMUM time attitude control of flexible spacecraft with active vibration suppression is a topic of current research. Although minimum time/fuel maneuvers have been previously examined,1 such bang-bang controls cause spillover effects that may induce high residual flexural energy. The source of the energy spillover into the flexural modes is the instantaneous switching that results from the bang-bang controls, a potential problem for the control hard- ware (reaction wheels, control moment gyros, etc.) as well. Consequently, minimum-time optimal control problems are often of academic interest only for producing theoretical lower bounds for the maneuver time. We have also found that near bang-bang controls are usually very sensitive to model er- rors; therefore, control shaping is an important issue in ob- taining robust controls. Upon modifying the control profile with a smoothing func- tion and transforming the independent variable (time), a near- minimum-time problem is generated with the mathematical form of a fixed-time nonlinear optimal control problem. The resulting boundary-value problem yields to a number of established methods of numerical solution. The controls are attenuated in such a way that the magnitude of the control rises smoothly from zero to the bounded maximum at the in- itiation of the maneuver and typically has an identically shaped reduction to zero at the final time. In addition, any in- stantaneous switch during the maneuver is shaped using a smooth, continuous function. The sharpness of the control trajectory is determined by a set of arbitrary parameters such that we can produce profiles with low control rates as well as controls that approach, to any desired degree, the bang-bang minimum time solution. The independent variable is transformed such that a linear free-final-time optimal control problem is converted to a nonlinear fixed-time problem, where the maneuver time is contained explicitly as a parameter in the transformed system. This augmented fixed-time problem can then be solved numerically for the controls and the corresponding minimum time required to complete the maneuver.

Advanced motion control in robotics

Abstract: An analysis of robustness and a design principle for advanced motion control in robotics are presented. The performance of motion control in a single joint is evaluated according to its robustness. A robust control technique for robotic motion is developed. For quick recovery, the feedforward loop compensates the interactive torque, which the observer identifies with a certain time delay. If the time delay of the observer is negligibly small, an acceleration controller is realized. In the observer-based system, it is possible to show that this delay also determines the sensitivity function, which is the index of how the controller reduces the effect of not only the interactive torque but also the parameter variations. In a multi-degree-of-freedom motion system, the total mechanical system is described by the dynamical equations and the kinematic equations. If a drive system in each joint is an observer-based acceleration controller, only the kinematics need be taken into account in the motion control. Several examples in robotics of motion systems applied to position control and force control systems are discussed. >

Robot motion control based on joint torque sensing

Abstract: The author proposes a joint-torque feedback (JTF) control scheme with a conventional position compensator for robot motion control. The advantage of this control scheme is that real-time computation is not required for the dynamic compensation. Also, the control system is robust against unexpected external disturbances, such as the action of gravity on objects picked up and put down, and other interactions with the environment. The author discusses the modeling and analysis of the JTF control and proposes a joint-torque sensing technique using the elasticity of the harmonic drive. The JTF control system worked well and insulated the conventional PD control loop from dynamic interventions in experiments with a two-link robot arm. >

Robust Control of Robotic Manipulators

Abstract: This paper introduces a new control system design methodology that allows the use of linearly controlled manipulators in fast, more complex maneuvers. This is made possible by guaranteeing a prescribed degree of relative stability while constraining the system state variables and inputs. The closed-loop linear system is also assigned desirable eigenvectors. The robustness of the system is evaluated using a new measure of robustness. The design methodology is applied to a 2-D.O.F. robotic manipulator. Simulation results demonstrate that the final design must be a compromise between robustness, relative stability, and other considerations.

Robust control for linear systems with structured state space uncertainty

Abstract: A recent sufficient condition for the stability robustness of linear systems with time-varying norm bounded state space uncertainty is extended to include the structure of the uncertainty. Our new result requires that the nominal eigenvalues lie to the left of a vertical line in the complex plane which is determined by a norm involving the structure of the uncertainty and the nominal closed-loop eigenvector matrix. Therefore, this robustness result is especially well suited to the design of control systems using eigenstructure assignment. When the uncertainty is time-invariant, our norm is also an upper bound on the incremental eigenvalue perturbations. We also consider the use of Perron weightings to reduce conservatism and the extension of the results to discrete time systems.

Adaptive control of a single-link flexible manipulator in the presence of joint friction and load changes

Abstract: A method for controlling single-link, lightweight, flexible manipulators is proposed. The objective of this method is to control the tip position of the flexible manipulator in the presence of joint friction and changes in the payload. Both linear and nonlinear friction are overcome using a very robust control scheme that 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. Changes in the load are compensated by decoupling the dynamics of the system and then applying a very simple adaptive control for the tip position. This results in a quite simple control law that requires minimal computing effort and thus can be used for real-time control of flexible arms. >

Nonlinear adaptive motion control for a manipulator with flexible joints

Abstract: The authors present an adaptive control scheme for trajectory tracking of robot motion. A dynamic model of a manipulator with flexible joints that is particularly useful for derivation of the control law is adopted. Based on this model, a two-stage controller consisting of a feedback loop and a parameter adaption loop is established. It is shown that without precise knowledge of the parameters of the manipulator and its joint flexibilities the tracking error converges to zero asymptotically. This implies robustness of the control scheme to the variation of payload or parameters as long as their rate of change is moderate. The convergence can be sped up by increasing the suitable controller gains. >

Robust stabilization and disturbance rejection for systems with structured uncertainty

Abstract: A method based on the algebraic Riccati equation is presented for designing state- and output-feedback control laws for plants with structured uncertainty. The designs provide both robust stability and disturbance rejection with robust H/sub infinity /-norm bounds. The design method consists of incorporating information on the plant uncertainty into the algebraic Riccati equations used for nominal H/sub infinity / disturbance-rejection designs. >

Model Invalidation: A Connection between Robust Control and Identification

Abstract: This paper begins to address the gap between the models used in robust control theory and those obtained from identification experiments by considering the connection between uncertain models and data. The model invalidation problem considered here is: given experimental data and a model with both additive noise and norm-bounded perturbations, is it possible that the model could produce the input/output data?

Dynamic modelling and robust control of a wind energy conversion system

Abstract: The application of wind energy conversion systems for the production of electrical energy requires a cheap and reliable operation. Especially at high wind velocities fluctuations from the wind field result in large mechanical loads of the wind turbine. Also fluctuations in the grid voltage may yield large dynamic excitations. In order to realize a long lifetime and a reliable operation active control systems are necessary. The main goal of the study described in this thesis is to develop an approach for the design of a high performance control system for a wind turbine with variable speed. The wind turbine system under investigation has a three-bladed rotor which is connected to the generator by a transmission. The electrical conversion system consists of a synchronous generator with a rectifier, direct current transmission and an inverter. The manipulable inputs are the pitch angle of the turbine blades, the field voltage of the generator and the delay angle of the rectifier. Both the generator speed and the direct current are being measured. The control design problem at full load is to minimize fluctuations in speed and current while reducing the mechanical (fatigue) loads. The feedback system should realize this without excessive use of the input variables and must also be simple to implement. I In order to be able to design a high performance control system a high quality dynamic model is required. Much attention has been given to the. modelling of the electrical conversion system. The switching of the thyristors of the rectifier bridge results in periodic behaviour at a high frequency. In order to design a control system an averaged model has been derived through the application of Floquet theory for periodic systems. The properties of the aerodynamic transfer and of the drive train only have been approximately modelled. Deviations of these nominal models from the real system are accounted for using norm-bounded uncertainty models. Using the nominal model and the uncertainty models the control system design has been carried out. The control design problem can suitably be handled by the Linear Quadratic design method. However, instead of using the standard solution with observers, in this study the optimization theory has been applied with respect to a predefined structure of the feedback law. In this approach the order and structure of the controller can be selected as part of the problem formulation. The application to the wind turbine system shows that a high performance control system can be obtained using a relatively simple, low order multivariable feedback law. The use of frequency weighting effectively reduces the role of mechanical parasitic dynamics. Application of the multi-model principle in combination with LQ optimization theory provides a way to synthesize controllers which are robust for large (aerodynamic) changes in operating conditions. A quantitative robustness analysis shows how the design parameters of the feedback law can be adapted in order to enhance the robustness of the controller. The approach taken, involving extensive modelling combined with uncertainty models and with the use of optimization theory and robustness analysis, has been shown to result in a high performance control system. Its main characteristic is the integrated approach of the control problem, with combined control action via the mechanics and the electrical conversion system. It is recommended to apply this integrated approach also to other types of wind turbine systems.

Introduction to the parametric approach to robust stability

Abstract: Recent results relating to the parametric approach to robust stability are discussed. The general problem of robust stability is defined, and a brief review of Kharotinov-type, edge, and zero-exclusion results is given. Several open research directions are indicated, followed by some remarks on the potential of the approach. >

Adaptive control for partially known systems : theory and applications

Abstract: 1. Introduction. Adaptive control schemes. Adaptive control in partially known plants - Short survey. A priori plant knowledge - A classification. The expected benefits. The hybrid approach - An overview. PART I: THEORY. 2. Hybrid Estimation. Plant description and identifiability properties. The estimation scheme. Estimator properties. Selection of the design parameters. Conclusions and final remarks. 3. Hybrid Estimation in Presence of Bounded Disturbances. Introduction and background. A new estimation algorithm. User guidelines and some examples. Final remarks. 4. Hybrid Estimation for Systems with Variable Time-Delay. Plant model. Parameter estimation. Conclusions. 5. Hybrid Adaptive Control for Partially Known Systems. Fixed control strategy. Estimation scheme and adaptive control law. Modified persistently excited (M-PE) signal algebra. Closed-loop stability. Concluding remarks. 6. Conclusions and Further Research. Resume. The contributions. Further research. PART II: APPLICATIONS. 7. Adaptive Friction Compensation with Application to Robotics. Mathematical models. Friction beating - some strategies. Linear control design. Adaptive friction compensation. Experiments. Conclusions and further research. 8. Adaptive Control in Flexible Arms. Arm model. Payload mass and friction estimation. Control policies. Simulation results. Conclusions and recommendations for future research. 9. Adaptive Robust Control of Robots with Flexible Joints. Robot model. Control design. Robust considerations and stability issues. Parameter estimation. References. Appendices. Subject Index.

Digital robust control law synthesis using constrained optimization

Abstract: Development of digital robust control laws for active control of high performance flexible aircraft and large space structures is a research area of significant practical importance The flexible system is typically modeled by a large order state space system of equations in order to accurately represent the dynamics The active control law must satisy multiple conflicting design requirements and maintain certain stability margins, yet should be simple enough to be implementable on an onboard digital computer Described here is an application of a generic digital control law synthesis procedure for such a system, using optimal control theory and constrained optimization technique A linear quadratic Gaussian type cost function is minimized by updating the free parameters of the digital control law, while trying to satisfy a set of constraints on the design loads, responses and stability margins Analytical expressions for the gradients of the cost function and the constraints with respect to the control law design variables are used to facilitate rapid numerical convergence These gradients can be used for sensitivity study and may be integrated into a simultaneous structure and control optimization scheme

Robust high-performance control for robotic manipulators

Abstract: A robust control scheme to accomplish accurate trajectory tracking for an integrated system of manipulator-plus-actuators is proposed. The control scheme comprises a feedforward and a feedback controller. The feedforward controller contains any known part of the manipulator dynamics that can be used for online control. The feedback controller consists of adaptive position and velocity feedback gains and an auxiliary signal which is simply generated by a fixed-gain proportional/integral/derivative controller. The feedback controller is updated by very simple adaptation laws which contain both proportional and integral adaptation terms. By introduction of a simple sigma modification to the adaptation laws, robustness is guaranteed in the presence of unmodeled dynamics and disturbances. >

An optimal control approach to the decentralized robust servomechanism problem

Abstract: A linear-quadratic optimal control approach is presented for designing linear time-invariant decentralized controllers to solve the robust servomechanism problem. It is assumed that not only the plant and the measurements but also the controllers may be subject to certain disturbances. A physically meaningful quadratic cost functional is defined, making it possible to assign desired weights to the errors, to their derivatives, to the system effort, and to the controller efforts. It is shown that the resulting controlled system has many properties like asymptotic tracking, stability, and robustness. The solution does not require much control effort at high frequencies, and the system is guaranteed not to have high frequency oscillations. >

Application of robust adaptive control using combined direct and indirect methods

Abstract: A new approach, combining direct and indirect control methods, recently proposed by the authors is used to adaptively control plants with unknown parameters. The plant parameters are known to lie in a specified compact set in parameter space and the output of the plant has to follow a desired output in the presence of a piecewise-constant input disturbance. Simulation results indicate that the combined method performs better than either the direct or the indirect method.