Showing papers on "Robust control published in 1991"

Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics

Abstract: Continuing the development of the structured singular value approach to robust control design, the authors investigate the problem of computing mu in the case of mixed real parametric and complex uncertainty. The problem is shown to be equivalent to a smooth constrained finite-dimensional optimization problem. In view of the fact that the functional to be maximized may have several local extrema, an upper bound on mu whose computation is numerically tractable is established; this leads to a sufficient condition of robust stability and performance. A historical perspective on the development of the mu theory is included. >

Robust speed control of DC servomotors using modern two degrees-of-freedom controller design

Abstract: The authors propose a robust speed control system for DC servomotors based on the parametrization of two-degree-of-freedom controllers. The servosystems can dramatically improve the characteristics of the closed loop systems, i.e. the disturbance torque suppression performance and the robustness to system parameter variations, without changing the command input response. The excellent control performances obtained during laboratory experiments by using a microprocessor-based controller are shown. >

One-cycle control of switching converters

Abstract: A new large-signal nonlinear control technique is proposed to control the duty-ratio d of a switch such that in each cycle the average value of a switched variable of the switching converter is exactly equal to or proportional to the control reference in the steady-state or in a transient. One-cycle control rejects power source perturbations in one switching cycle; the average value of the switched variable follows the dynamic reference in one switching cycle; and the controller corrects switching errors in one switching cycle. There is no steady-state error nor dynamic error between the control reference and the average value of the switched variable. Experiments with a constant frequency buck converter have demonstrated the robustness of the control method and verified the theoretical predictions. This new control method is very general and applicable to all types of pulse-width-modulated, resonant-based, or soft-switched switching converters for either voltage or current control in continuous or discontinuous conduction mode. Furthermore, it can be used to control any physical variable or abstract signal that is in the form of a switched variable or can be converted to the form of a switched variable. >

Survey of robust control for rigid robots

Abstract: Current approaches to the robust control of the motion of rigid robots are surveyed, and the available literature is summarized. The five major design approaches discussed are the linear-multivariable approach, the passivity approach, the variable-structure approach, the saturation approach, and the robust-adaptive approach. Some guidelines for choosing a method are offered. >

Uncertain Models and Robust Control

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On a convex parameter space method for linear control design of uncertain systems

Abstract: This paper presents a new procedure for continuous and discrete-time linear control systems design. It consists of the definition of a convex programming problem in the parameter space that, when solved, provides the feedback gain. One of the most important features of the procedure is that additional design constraints are easily incorporated in the original formulation, yielding solutions to problems that have raised a great deal of interest within the last few years. This is precisely the case of the decentralized control problem and the quadratic stabilizability problem of uncertain systems with both dynamic and input uncertain matrices. In this last case, necessary and sufficient conditions for the existence of a linear stabilizing gain are provided and, to the authors’ knowledge, this is one of the first numerical procedures able to handle and solve this interesting design problem for high-order, continuous-time or discrete-time linear models. The theory is illustrated by examples.

A collection of robust control problems leading to LMIs

Abstract: The authors consider four control-related problems, all of which involve reformulation into linear matrix inequalities (LMIs). The problems are: structured singular value ( mu ) upper bound synthesis for constant matrix problems; robust-state-feedback problem with quadratic stability criteria for uncertain systems; optimal, constant, block diagonal, similarity scaling for full information and state feedback H/sub infinity / problem; and a partial theory for optimal performance in systems which depend on several independent variables. >

Robust adaptive control: a unified approach

Abstract: A complete tutorial review of the entire field is presented, beginning with simple instability examples to identify the causes of nonrobust behavior in adaptive control. Some of the mathematical groundwork is presented, and the theory for the design and analysis of adaptive laws is developed. Commonly used adaptive controller structures are discussed, highlighting their particular robustness properties. Particular attention is paid to model reference, pole placement, and linear quadratic controller structures. Designs and analyses of model reference, pole placement, and linear quadratic controllers, based on combining the corresponding controller structures with the various robust adaptive laws, are presented. Suggestions for future research are given. >

Reinforcement Learning is Direct Adaptive Optimal Control

Abstract: Control problems can be divided into two classes: 1) regulation and tracking problems, in which the objective is to follow a reference trajectory, and 2) optimal control problems, in which the objective is to extremize a functional of the controlled system's behavior that is not necessarily defined in terms of a reference trajectory. Adaptive methods for problems of the first kind are well known, and include self-tuning regulators and model-reference methods, whereas adaptive methods for optimal-control problems have received relatively little attention. Moreover, the adaptive optimal-control methods that have been studied are almost all indirect methods, in which controls are recomputed from an estimated system model at each step. This computation is inherently complex, making adaptive methods in which the optimal controls are estimated directly more attractive. Here we present reinforcement learning methods as a computationally simple, direct approach to the adaptive optimal control of nonlinear systems.

Robust control design for interconnected systems with time-varying uncertainties

Abstract: We consider a design of decentralized control for a class of interconnected non-linear dynamical systems having uncertainty. This uncertainty is (possibly fast) time-varying, and it may appear in each system as uncertain parameter and input disturbance. It also may appear in the interconnections. No statistical information about the uncertainty is imposed; only its possible bound is assumed to be known. The two control schemes proposed here, namely the linear and the non-linear, take the bounds of the interconnections into account. The use of the non-linear control requires more assumptions than the use of linear control. In applications where these assumptions are met, the designers have both controls at their disposal, and depending on the particular application, one may be preferable to the other.

Adaptive control of flexible joint robots

Abstract: The problem of designing a robust adaptive control strategy for flexible joint robot manipulators is considered. By utilising the concept of integral manifolds, reduced-order models of the flexible system are obtained. This makes it possible to develop adaptive control schemes for the flexible full-order system at the reduced-order level, which otherwise would be difficult due to ill-conditioning and the curse of dimensionality. Two common adaptive control strategies are examined: (i) the adaptive inverse dynamics and (ii) the Slotine and Li algorithm. It is shown how these standard rigid adaptive control techniques can be generalized and improved for successful application to flexible joint manipulators. The result is robust adaptive control laws which take both parametric and dynamic uncertainties into account. Numerical simulations for a two-link flexible joint manipulator illustrate the potential and advantages of the new adaptive schemes as compare to the two standard algorithms in the literature. >

Robust identification and Galois sequences

Abstract: Worst-case l1 identification is studied for BIBO stable linear shift-invariant systems. It is shown that the Chebyshev identification method when used with Galois input designs satisfies a certain robust convergence property and provides l1 model error bounds in worst-case identification of BIBO stable systems with a uniformly bounded noise set-up. The robust identification methodology developed is compatible with the modelling requirements of modern robust control design.

Robust hybrid impedance control of robot manipulators

Abstract: The objective of hybrid impedance control is defined, and a robust hybrid impedance control method is proposed. The task space is split into force-controlled and position-controlled subspaces based on the concept of hybrid control. Desired inertia and damping are introduced in the force control subspace to improve the dynamic behavior, and impedance control is used in the position-controlled subspace. In the proposed control scheme, the hybrid impedance control is equivalent to tracking a desired acceleration trajectory, which is generated in real-time. The computed torque technique and a PI control law are used to reduce the influence of model uncertainties. Experimental results obtained with a two-degree-of-freedom direct drive robot have shown the effectiveness of the proposed hybrid impedance control method. >

H/sub 2/ iterative model refinement and control robustness enhancement

Abstract: Many practical applications of control system design based on input-output measurements permit the repeated application of a system identification procedure operating on closed-loop data together with successive refinement of the designed controller. A paradigm is developed for such an iterative design. The key to the procedure is to account for evaluated modeling error in the control design and, equally, to allow for the requirements of the closed-loop controller in performing the identification. With an H/sub 2/ control problem, this is achieved by frequency weighting the linear quadratic control criterion and by filtering the identifier signals in a logical fashion. >

Stability of SISO quadratic dynamic matrix control with hard output constraints

Abstract: The inclusion of output constraints in the on-line optimization problem solved by quadratic dynamic matrix control (QDMC) can result in a unstable, closed-loop system, even when the corresponding unconstrained algorithm is stable. The presence of constraints in the optimization problem produces a nonlinear, closed-loop system, although the plant and model dynamics are assumed linear. This article quantifies the effect of output constraints on both nominal and robust stability for single-input/single-output processes. Stability conditions provided can be used to select the QDMC parameters and constraint window. Examples demonstrate that these conditions can capture the nonlinear effect of the constraints and that tuning rules developed for the unconstrained case should not be used with output constraints. An example with dead time error illustrates the use of this framework to guarantee the robustness of constrained QDMC with respect to modeling error.

The control of switching DC-DC converters-a general LWR problem

Abstract: The control of switching DC-DC converters is reviewed. It is regarded as a general linear quadratic regulator (LQR) problem, and an innovative optimal and robust digital controller is proposed. The control strategy adopted can achieve good regulation, rejection of modest disturbances, and the ability to cater to switching converters with RHP zeros. This controller design is a general approach that is applicable to all PWM-type DC-DC converters with their circuit topologies known or unknown. Modern CAD techniques are used to reach the final control law. Application to a published Cuk converter is used as an example, and the performance is evaluated. >

Performance weight selection for H-infinity and μ-control methods

Abstract: The paper discusses, from a process control perspective, different approaches to performance weight selection when using H-infinity objectives. Approach A considers direct bounds on important trans...

An H/sub infinity / approach to two degree of freedom design

Abstract: The authors introduce a novel design procedure for two-degree-of-freedom controllers. The technique will be used to design a control system for the distillation column design case study described by D.J.N. Limebeer (1991). The feedback controller and the prefilter are designed in a single step in an H/sub infinity / optimization framework. The feedback controller is used to meet the robust stability and disturbance rejection specifications, while the prefilter is used to shape the time responses of the closed loop. This approach has the advantage that no additional controller states are required for the prefilter; the feedback controller and prefilter share the same state space. It is proved that the state estimator part of the controller is a Kalman filter, which is a property inherited from the normalized coprime factorization design procedure given by D. McFarlane and K. Glover (1990). >

Parameter-dependent Lyapunov functions, constant real parameter uncertainty, and the Popov criterion in robust analysis and synthesis. 1

Abstract: A framework for parameter-dependent Lyapunov functions, a less conservative refinement of 'fixed' Lyapunov functions, is developed. An immediate application of this framework is a reinterpretation of the classical Popov criterion as a parameter-dependent Lyapunov function. This observation is exploited to obtain conditions for robust controller synthesis with full-state, full-order, and reduced-order controllers in H/sub 2/ and H/sub 2//H/sub infinity / settings. >

Robust approximation and identification in H

Abstract: Robust approximation and identification of stable shiftinvariant systems is studied in the H∞ sense using a stable perturbation set-up. Issues of model set selection tion are addressed using the n-width concept: a concrete result establishes a priori knowledge for which a certain rational model set is optimal in the n-width sense. A general construction of interest to identification theory using ϵ-nets provides near-optimal identification methods tuned to the a priori knowledge about the system. A notion of robust convergence is defined so that any untuned identification method satisfying it has a generic well-posedness property for systems in the disk algebra. The existence of robustly convergent identification methods based on any complete model set in the disk algebra is established. It is also shown that the classical Fejer and de la Vallee-Poussin polynomial approximation operators provide robustly convergent identification methods. Furthermore, a result is given for optimal Hankel norm model reduction from experimentally obtained models.

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 degrees 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.

Robust H(infinity) control design for the Space Station with structured parameter uncertainty

Abstract: A robust H-infinity control design methodology and its application to a Space Station attitude and momentum control problem are presented. This new approach incorporates nonlinear multi-parameter variations in the state-space formulation of H-infinity control theory. An application of this robust H-infinity control synthesis technique to the Space Station control problem yields a remarkable result in stability robustness with respect to the moments-of-inertia variation of about 73% in one of the structured uncertainty directions. The performance and stability of this new robust H-infinity controller for the Space Station are compared to those of other controllers designed using a standard linear-quadratic-regulator synthesis technique.