Showing papers on "Robust control published in 1997"

Essentials of Robust Control

Abstract: 1. Introduction. 2. Linear Algebra. 3. Linear Systems. 4. H2 and Ha Spaces. 5. Internal Stability. 6. Performance Specifications and Limitations. 7. Balanced Model Reduction. 8. Uncertainty and Robustness. 9. Linear Fractional Transformation. 10. m and m- Synthesis. 11. Controller Parameterization. 12. Algebraic Riccati Equations. 13. H2 Optimal Control. 14. Ha Control. 15. Controller Reduction. 16. Ha Loop Shaping. 17. Gap Metric and ...u- Gap Metric. 18. Miscellaneous Topics. Bibliography. Index.

Robust, fragile, or optimal?

Abstract: We show by examples that optimum and robust controllers, designed by using the H/sub 2/, H/sub /spl infin//, l/sup 1/, and /spl mu/ formulations, can produce extremely fragile controllers, in the sense that vanishingly small perturbations of the coefficients of the designed controller destabilize the closed-loop control system. The examples show that this fragility usually manifests itself as extremely poor gain and phase margins of the closed-loop system. The calculations given here should raise a cautionary note and draw attention to the larger issue of controller sensitivity which may be important in other nonoptimal design techniques as well.

The unfalsified control concept and learning

Abstract: Without a plant model or other prejudicial assumptions, a theory is developed for identifying control laws which are consistent with performance objectives and past experimental data-possibly before the control laws are ever inserted in the feedback loop. The theory complements model-based methods such as H/sup /spl infin//-robust control theory by providing a precise characterization of how the set of suitable controllers shrinks when new experimental data is found to be inconsistent with prior assumptions or earlier data. When implemented in real time, the result is an adaptive switching controller. An example is included.

Delay-dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approach

Abstract: This paper considers the problems of robust stability analysis and robust control design for a class of uncertain linear systems with a constant time-delay. The uncertainty is assumed to be norm-bounded and appears in all the matrices of the state-space model. We develop methods for robust stability analysis and robust stabilization. The proposed methods are dependent on the size of the delay and are given in terms of linear matrix inequalities.

Robust, fragile or optimal?

Abstract: We show by examples that optimum and robust controllers, designed by using the H/sub 2/, H/sub /spl infin//, l/sup 1/ and /spl mu/ formulations, can produce extremely fragile controllers, in the sense that vanishingly small perturbations of the coefficients of the designed controller destabilize the closed loop control system. The examples show that this fragility also usually manifests itself as extremely poor gain and phase margins of the closed loop system.

Supervisory control of families of linear set-point controllers. 2. Robustness

Abstract: A simply structured high-level controller, called a "supervisor", has recently been proposed in part I of this article (ibid., vol.41, 1996) for the purpose of orchestrating the switching of a sequence of candidate set-point controllers into feedback with an imprecisely modeled SISO process so as to cause the output of the process to approach and track a constant reference input. The process is assumed to be modeled by an SISO linear system whose transfer function is in the union of a number of subclasses, each subclass being small enough so that one of the candidate controllers would solve the set-point tracking problem, if the process transfer function was to be one of the subclass members. This paper proves that without any further modification, the same supervisor described in Part I can also perform this function in the face of norm-bounded unmodeled dynamics, and moreover that none of the signals within the overall system can grow without bound in response to bounded disturbance and noise inputs, whether they are constant or not.

An overview of robot force control

Abstract: This paper reports on the existing robot force control algorithms and their composition based on the review of 75 papers on this subject. The objective is to provide a pragmatic exposition with speciality on their differences and different application conditions, and to give a guide of the existing robot force control algorithms. The previous work can be categorized into discussion, design and/or application of fundamental force control techniques, stability analysis of the various control algorithms, and the advanced methods. Advanced methods combine the fundamental force control techniques with advanced control algorithms such as adaptive, robust and learning control strategies.

A small-gain control method for nonlinear cascaded systems with dynamic uncertainties

Abstract: Some robust control problems for a class of nonlinear cascaded systems in the presence of state and input driven unmeasured dynamics are analyzed. A stepwise constructive control methodology is proposed on the basis of the nonlinear small-gain theorem. The flexibility of the approach in tackling dynamic uncertainties is illustrated by demonstrating that several results for special classes of cascaded systems, considered previously in the literature, may be viewed as special instances of the present results.

H ∞ -control for Markovian jumping linear systems with parametric uncertainty

Abstract: This paper studies the problem of H∞-control for linear systems with Markovian jumping parameters The jumping parameters considered here are two separable continuous-time, discrete-state Markov processes, one appearing in the system matrices and one appearing in the control variable Our attention is focused on the design of linear state feedback controllers such that both stochastic stability and a prescribed H∞-performance are achieved We also deal with the robust H∞-control problem for linear systems with both Markovian jumping parameters and parameter uncertainties The parameter uncertainties are assumed to be real, time-varying, norm-bounded, appearing in the state matrix Both the finite-horizon and infinite-horizon cases are analyzed We show that the control problems for linear Markovian jumping systems with and without parameter uncertainties can be solved in terms of the solutions to a set of coupled differential Riccati equations for the finite-horizon case or algebraic Riccati equations for the infinite-horizon case Particularly, robust H∞-controllers are also designed when the jumping rates have parameter uncertainties

Improving power system dynamics by series-connected FACTS devices

Abstract: This paper examines improvement of power system dynamics by use of unified power flow controllers, thyristor controlled phase shifting transformers and thyristor controlled series capacitors. Models suitable for incorporation in dynamic simulation programs for studying angle stability are analysed. A control strategy for the damping of electromechanical power oscillations using an energy function method is derived. The achieved control laws are shown to be effective both for the damping of large signal and small signal disturbances and are robust with respect to loading condition, fault location and network structure. Furthermore, the control inputs are easily attainable from locally measurable variables. The effectiveness of the controls are demonstrated for model power systems.

High-performance robust motion control of machine tools: an adaptive robust control approach and comparative experiments

Abstract: This paper studies the high-performance robust motion control of machine tools. The newly proposed adaptive robust control (ARC) is applied to make the resulting closed-loop system robust to model uncertainties, instead of the disturbance observer (DOB) design previously tested by many researchers. Compared to DOB, the proposed ARC has a better tracking performance and transient in the presence of discontinuous disturbances, such as Coulomb friction, and it is of a lower order. As a result, time-consuming and costly rigorous friction identification and compensation is alleviated, and overall tracking performance is improved. The ARC design can also handle large parameter variations and is flexible in introducing extra nonlinear robust control terms and parameter adaptations to further improve the transient response and tracking performance. An anti-integration windup mechanism is inherently built in the ARC and, thus, the problem of control saturation is alleviated. Extensive comparative experimental tests are performed, and the results show the improved performance of the proposed ARC.

High performance adaptive robust control of nonlinear systems: a general framework and new schemes

Abstract: A general framework is proposed for the design of a new class of high-performance robust controllers based on the recently proposed adaptive robust control (ARC). Robust filter structures are used to attenuate the effect of model uncertainties as much as possible while learning mechanisms such as parameter adaptation are used to reduce the model uncertainties. Under the proposed general framework, a simple new ARC controller is also constructed for a class of nonlinear systems transformable to a semi-strict feedback form. The new design utilizes the popular discontinuous projection method in solving the conflicts between the deterministic robust control design and the adaptive control design. The controller achieves a guaranteed transient performance and a prescribed final tracking accuracy in the presence of both parametric uncertainties and uncertain nonlinearities while achieving asymptotic stability in the presence of parametric uncertainties without using a discontinuous control law or infinite-gain feedback.

Sensorless current mode control-an observer-based technique for DC-DC converters

Abstract: Sensorless current mode (SCM) control is an observer method that provides the operating benefits of current mode control without current sensing. SCM has significant advantages over both conventional peak and average current-mode control techniques in noise susceptibility and dynamic range. The method supports both line and bulk load regulation, and reduces control complexity to a single loop. The static and dynamic performance of SCM are analyzed and verified experimentally for DC-DC converters. Performance in continuous and discontinuous modes compares favorably to conventional techniques when noise is not a factor, but is significantly better when noise and wide load ranges are a concern. The SCM method encompasses one-cycle control as a special case; the general SCM method is introduced here as a public domain control technique.

GeneAS: A Robust Optimal Design Technique for Mechanical Component Design

Abstract: A robust optimal design algorithm for solving nonlinear engineering design optimization problems is presented. The algorithm works according to the principles of genetic algorithms (GAs). Since most engineering problems involve mixed variables (zero-one, discrete, continuous), a combination of binary GAs and real-coded GAs is used to allow a natural way of handling these mixed variables. The combined approach is called GeneAS to abbreviate Genetic Adaptive Search. The robustness and flexibility of the algorithm come from its restricted search to the permissible values of the variables. This also makes the search efficient by requiring a reduced search effort in converging to the optimum solution. The efficiency and ease of application of the proposed method are demonstrated by solving four mechanical component design problems borrowed from the optimization literature. The proposed technique is compared with traditional optimization methods. In all cases, the solutions obtained using GeneAS are better than those obtained with the traditional methods. These results show how GeneAS can be effectively used in other mechanical component design problems.

Experimental evaluation of uncalibrated visual servoing for precision manipulation

Abstract: We present an experimental evaluation of adaptive and non-adaptive visual servoing in 3, 6 and 12 degrees of freedom (DOF), comparing it to traditional joint feedback control. While the purpose of experiments in most other work has been to show that the particular algorithm presented indeed also works in practice, we do not focus on the algorithm but rather on properties important to visual servoing in general. Our main results are: positioning of a 6 axis PUMA 762 arm is up to 5 times more precise under visual control than under joint control; positioning of a Utah/MIT dextrous hand is better under visual control than under joint control by a factor of 2; and a trust-region-based adaptive visual feedback controller is very robust. For m tracked visual features the algorithm can successfully estimate online the m/spl times/3 (m/spl ges/3) image Jacobian (J) without any prior information, while carrying out a 3 DOF manipulation task. For 6 and higher DOF manipulation, a rough initial estimate of J is beneficial. We also verified that redundant visual information is valuable. Errors due to imprecise tracking and goal specification were reduced as the number of visual features, m, was increased. Furthermore highly redundant systems allow us to detect outliers in the feature vector and deal with partial occlusion.

Robustness analysis of nonlinear feedback systems: an input-output approach

Abstract: This paper presents an approach to robustness analysis for nonlinear feedback systems. We pursue a notion of model uncertainty based on the closeness of input-output trajectories which is not tied to a particular uncertainty representation, such as additive, parametric, structured, etc. The basic viewpoint is to regard systems as operators on signal spaces. We present two versions of a global theory where stability is captured by induced norms or by gain functions. We also develop local approaches (over bounded signal sets) and give a treatment for systems with potential for finite-time escape. We compute the relevant stability margin for several examples and demonstrate robustness of stability for some specific perturbations, e.g., small-time delays. We also present examples of nonlinear control systems which have zero robustness margin and are destabilized by arbitrarily small gap perturbations. The paper considers the case where uncertainty is present in the controller as well as the plant and the generalization of the approach to the case where uncertainty occurs in several subsystems in an arbitrary interconnection.

A modular system for robust positioning using feedback from stereo vision

Abstract: This paper introduces a modular framework for robot motion control using stereo vision. The approach is based on a small number of generic motion control operations referred to as primitive skills. Each primitive skill uses visual feedback to enforce a specific task-space kinematic constraint between a robot end-effector and a set of target features. By observing both the end-effector and target features, primitive skills are able to position with an accuracy that is independent of errors in hand-eye calibration. Furthermore, primitive skills are easily combined to form more complex kinematic constraints as required by different applications. These control laws have been integrated into a system that performs tracking and control on a single processor at real-time rates. Experiments with this system have shown that it is extremely accurate, and that it is insensitive to camera calibration error. The system has been applied to a number of example problems, showing that modular, high precision, vision-based motion control is easily achieved with off-the-shelf hardware.

Robust control prevents car skidding

Abstract: The author discusses a system of robust unilateral decoupling of car steering dynamics. Its effect is that the driver has to concern himself much less with disturbance attenuation. The important quick reaction to disturbance torques is done by the automatic feedback system. The yaw dynamics no longer interfere with the path-following task of the driver. The safety advantages have been demonstrated in experiments with a test vehicle. By empirical improvements, we have modified the controller such that it preserves the robust decoupling advantages for the first 0.5 seconds after a disturbance and then returns the steering authority gradually back to the driver.

Variable structure control of shape memory alloy actuators

Abstract: A shape memory alloy (SMA) actuator consisting of a number of thin NiTi fibers woven in a counter rotating helical pattern around supporting disks is first described. This structure accomplishes a highly efficient transformation between force and displacement overcoming the main mechanical drawback of shape memory alloys, that being limited strain. Time domain open loop experiments were then conducted to determine the intrinsic properties of the actuator. From these experiments and from the knowledge of the underlying physics of SMAs, a multiterm model, including linear and nonlinear elements, was proposed. After further investigation and simulation, it was found that most of these complexities did not need to be considered in order to explain the reported results, and that the model could be reduced to that of a single integrator. A variable structure controller was then applied to a pair of antagonist actuators. The feedback switches between the two actuators according to the sign of the displacement error. A further improvement was added to compensate for known gross nonlinearities by modulating the current magnitude in a discrete manner as a function of the state space position. It was therefore possible to realize smooth and robust control with very little cost in complexity.

Adaptive neural network control of robot manipulators in task space

Abstract: In this paper, the adaptive neural network control of robot manipulators in the task space is considered. The controller is developed based on a neural network modeling technique which neither requires the evaluation of inverse dynamical model nor the time-consuming training process. It is shown that, if Gaussian radial basis function networks are used, uniformly stable adaptation is assured and asymptotically tracking is achieved. The controller thus obtained does not require the inverse of the Jacobian matrix. In addition, robust control can be easily incorporated to suppress the neural network modeling errors and the bounded disturbances. Numerical simulations are provided to show the effectiveness of the approach.

Uncertainty Modeling and Fixed-Order Controller Design for a Hypersonic Vehicle Model

Abstract: Control system design for hypersonic vehicles will be complicated by coupling effects between aerodynamics, propulsion, and structure. Using H1 and π-synthesis techniques, these features can be modeled as uncertainties and incorporated into the design procedure of a e ight control system. However, modern control theory techniques generallyleadtohigh-ordercontrollers.Thetimedelays,whicharecreatedwhenthesecontrollersareimplemented, may not be acceptable. A technique to constrain controller dimension a priori in the design process is used to design e xed-order π controllers that are robust to mixed real/complex uncertainties. Typical hypersonic effects such as propulsion system perturbations and aeroelastic fuselage bending are modeled as uncertainties in a robust control design framework. Three different e xed-order controllers are synthesized for a hypersonic vehicle model accelerating through Mach 8. A comparison with full-order and reduced-order designs is conducted and the results illustrate that the e xed-order controllers exhibit robustness properties similar to full-order designs while considerably reducing controller complexity.

Voltage control strategy for maximum torque operation of an induction machine in the field-weakening region

Abstract: In this paper, a novel field-weakening scheme for the induction machine is presented. The proposed algorithm, based on the voltage control strategy, ensures the maximum torque operation over the entire field-weakening region without using the machine parameters. Also, by introducing the direct field-oriented (DFO) control, which is insensitive to the variation of machine parameters in the field-weakening region, the drive system can obtain robustness to parameter variations. Moreover, the speed sensorless control can be achieved in the very-high-speed range, where the utilization of the speed sensor is limited. Experimental results for the laboratory induction motor drive system confirm the validity of the proposed control algorithm.

Robust nonlinear H/sub /spl infin// synchronization of chaotic Lur'e systems

Abstract: We propose a method of robust nonlinear H/sub /spl infin// master-slave synchronization for chaotic Lur'e systems with applications to secure communication. The scheme makes use of vector field modulation and either full static state or linear dynamic output error feedback control. The master-slave systems are assumed to be nonidentical and channel noise is taken into account. Binary valued continuous time message signals are recovered by minimizing the L/sub 2/-gain from the exogenous input to the tracking error for the standard plant representation of the scheme. The exogenous input takes into account the message signal, channel noise and parameter mismatch. Matrix inequality conditions for dissipativity with finite L/sub 2/-gain of the standard plant form are derived based on a quadratic storage function. The controllers are designed by solving a nonlinear optimization problem which takes into account both channel noise and parameter mismatch. The method is illustrated on Chua's circuit.

Using wave variables for system analysis and robot control

Abstract: Wave variables were originally introduced in the context of time delayed force reflecting teleoperation. Their use provides significant benefits for control, including robustness to arbitrary delays and an inherent hybrid construction, well suited for handling unknown passive environments. They also suggest a new perspective for analysis, presenting information from an alternative viewpoint. In this paper we explore the concept of wave variables in a more general robotic and mechanical setting, leading to alternate control approaches.

Fuzzy PID control of a flexible-joint robot arm with uncertainties from time-varying loads

Abstract: This paper presents the design and experiment of a fuzzy proportional integral derivative (PID) controller for a flexible-joint robot arm with uncertainties from time-varying loads. Experimental results have shown remarkable tracking performance of this fuzzy PID controller, and have convincingly demonstrated that fuzzy logic control can be used for flexible-joint robot arms with uncertainties and it is quite robust. In this paper, the fuzzy PID controller is first described briefly, using a simple and practical PD+I controller configuration. This configuration preserves the linear structure of the conventional PD+I controller, but has nonconstant gains: the proportional, integral, and derivative gains are nonlinear functions of their input signals, which have self-tuning (adaptive) capabilities in set-point tracking performance. Moreover, these variable gains make the fuzzy PID controller robust with faster response time and less overshoot than its conventional counterpart. The proposed design was tested using a flexible-joint robot arm driven by a DC motor in a laboratory, where the arm was experienced with time-varying loads. Control performance by the conventional and fuzzy PID controllers for such a laboratory robotic system are both included in this paper for comparison.

Design and analysis of the nonlinear feedback linearizing control for an electromagnetic suspension system

Abstract: This paper presents some results on the robust stabilization of a class of feedback linearizable nonlinear single-input/single-output (SISO) systems exhibiting parametric uncertainty. We characterize a class of nonlinear systems with bounded uncertain parameters which can be transformed into a linear interval matrix robustness problem. We also present some analysis and implementation of nonlinear feedback linearizing control for an electromagnetic suspension (EMS) system. We show that the EMS system is nonlinear feedback linearizable and satisfies the proposed condition, and hence that the proposed nonlinear feedback controller for an EMS system is robust against mass parameter perturbation and force disturbance. Some tests are performed for making an experimental comparison between feedback linearizing control and classical state feedback control using linearization by small perturbation analysis.