Showing papers presented at "American Control Conference in 1994"

Robust H/sup /spl infin// control of uncertain linear systems with structured uncertainty

Abstract: This paper considers a problem of absolute stabilization with a specified level of disturbance attenuation for a class of uncertain systems in which the uncertainty is structured and satisfies a certain integral quadratic constraint. The paper shows that an uncertain system is absolutely stabilizable with a specified level of disturbance attenuation if and only if there exists a solution to a corresponding H/sup /spl infin// control problem. The paper also shows that if an uncertain system can be absolutely stabilized with a specified level of disturbance attenuation via nonlinear output feedback control then it can be absolutely stabilized via linear output feedback control. A key technical result used in this paper is an extension of the "S-procedure" result of Megretsky and Treil (1993).

An approach to model validation in the /spl mu/ framework

Abstract: The problem of model validation of postulated system models when experimental data is available is addressed in this paper. The approach presented requires a /spl mu/ test across frequency and shows that the structure of the model set in terms of the size and type of uncertainty and noise weights plays a central role in the model validation process. In general, increasing the size of the model set increases the ease of validation of a particular model. The proposed model-validation technique is used to synthesize controllers for an experimental structure which significantly out performs poorly selected uncertainty weights.

Self-scheduled /spl Hscr//sub /spl infin// linear parameter-varying systems

Abstract: This paper is concerned with /spl Hscr//sub /spl infin//-like control of a class of linear parameter-varying (LPV) plants. Here the state-space entries of the plant are assumed to depend affinely on a time-varying vector /spl theta/ of real parameters which is measured in real-time. These parameter measurements are incorporated in the control law to optimize the performance and robustness of the closed-loop system. The resulting controller is therefore time-varying and automatically "gain-scheduled" along the parameter trajectories. Complete solvability conditions are obtained for continuous- and discrete-time systems in terms of linear matrix inequalities (LMI) and a physically motivated example demonstrates the advantages and performance of the proposed methodology.

Explicit controller formulas for LMI-based H/sub /spl infin// synthesis

Abstract: The set of H/sub /spl infin// controllers with closed-loop performance /spl gamma/ can be implicitly parametrized by the solutions R, S of a system of linear matrix inequalities (LMI). The matrices R, S play a role analogous to that of the Riccati solutions X/sub /spl infin// and Y/sub /spl infin// in classical state-space H/sub /spl infin// control. Useful applications of this parametrization include reduced-order H/sub /spl infin// synthesis, mixed H/sub 2//H/sub /spl infin// design, H/sub /spl infin// design with a pole placement constraint, etc. This paper is concerned with the computation of H/sub /spl infin// controllers given any solution (R, S) of the characteristic system of LMIs. Explicit and numerically reliable formulas are derived for both full- and reduced-order cases. Remarkably, these formulas turn out to be simple extensions of the usual "central controller" formulas where the LMI solutions R, S replace the Riccati solutions X/sub /spl infin//, Y/sub /spl infin//. In addition, they apply to regular as well as singular H/sub /spl infin// problems. Finally, the LMI-based approach also leads to simple and numerically appealing new formulas for discrete-time H/sub /spl infin// controllers.

Some examples in mixed H/sub 2//H/spl infin/ control

Abstract: It is shown that the H/sub 2/ performance of optimal auxiliary cost mixed H/sub 2//H/sub /spl infin// controllers can sometimes be worse than that of central H/sub /spl infin// controllers.

General-structured unknown input observers

Abstract: Using the framework of the general structured observer, we present a straightforward procedure for designing an unknown input observer (UIO) for a linear system subject to unknown inputs or uncertain disturbances. Necessary and sufficient conditions in terms of the transmission zeros are provided for the existence of a full-order UIO capable of producing an asymptotic estimate of the state. Moreover, an extension of the UIO, called the extended UIO, is developed to estimate both the system state and the unknown input simultaneously. Experimental results for a DC servo motor system demonstrate the applicability of the proposed methodologies.

Synthesis of robust servo compensator based on H/sub /spl infin// control

Abstract: In this paper, we formulate two types of type 1 H/sub /spl infin// servo problems, namely the output regulation type and the disturbance rejection type, to adopt the robust tracking requirement. For continuous-time systems, we show that the Glover-Doyle solution (1988) on H/sub /spl infin// control problem can be directly applied to both cases if we modify the problems appropriately. The order reductions of the Riccati equation to be solved for the optimization and the resultant controller are also investigated. We next investigate the type 1 digital control system synthesis by sampled-data H/sub /spl infin// technique. We show that the output regulation type problem has no solution while the disturbance rejection type problem is well defined. We develop a method of type 1 digital controller synthesis based on the sampled-data H/sub /spl infin// control.

Nonlinear H/sub /spl infin// control of a missile's roll axis

Abstract: This paper describes the application of a new method for generating the optimal H/sub /spl infin// controller for a nonlinear system. It is a three step approach: modeling (using the describing function approach), synthesis (using the H/sub /spl infin// loop shifting technique), and robustness analysis (using the labelling technique of simplicial algorithms). The method is demonstrated by designing an optimal H/sub /spl infin// controller for a cruise missile's roll axis. The actuator is a first order servo with deadband and command limiting.

Low-order H/sub /spl infin// synthesis via LMIs

Abstract: The existence of low-order H/sub /spl infin// controllers can be fully characterized by a system of linear matrix inequalities (LMI) together with a rank constraint. Due to this rank constraint, the corresponding optimization problem is nonconvex and much harder than pure LMIs. Nevertheless, it can be attacked by a number of optimization techniques. One possible approach is discussed in this paper. Here adequate solutions are sought by solving a smooth constrained optimization problem. Numerical experiments show that this scheme often succeeds in significantly reducing the controller order.

An /spl alpha/-/spl beta/ target tracking approach to the benchmark tracking problem

Abstract: This paper considers the /spl alpha/-/spl beta/ target tracking approach to the benchmark tracking problem for beam steering of an array radar system with highly maneuvering targets Since /spl alpha/-/spl beta/ target trackers are widely used in practical radar systems, this investigation/design considers the implementation problems such practical trackers experience, ie the various benchmark radar/target cases introduce rate variations, track lags and noise characteristics One objective of the /spl alpha/-/spl beta/ tracking approach is to develop fundamental /spl alpha/-/spl beta/ 'rules-of-thumb' and outline countermeasures to variations in track rate, maneuvers, measurement noise and system changes It is expected that the overall tracking performance of the /spl alpha/-/spl beta/ approach will be inferior to other design techniques such as extended Kalman filtering, fault detection and multiple model However, the simplicity and computational savings of the /spl alpha/-/spl beta/ target tracker are engineering advantages

The design of helicopter flight control systems using advanced H/sup /spl infin// control

Abstract: This paper reports on the experience gained when a multivariable helicopter flight control law was tested on the Large Motion Simulator (LMS) at DRA Bedford. This was part of a study into the application of multivariable control theory to the design of full-authority flight control systems for high-performance helicopters. Results are presented that were obtained during the piloted simulation trial. The performance provided by the control law led to level 1 handling quality ratings for all of the mission task elements assessed, both during the real-time and off-line analysis.

H/sub /spl infin// control and estimation problems with delayed measurements: state space solutions

Abstract: Necessary and sufficient conditions for existence of estimators and controllers meeting desired H/sub /spl infin// performance criterion are given for the case where the finite sensor delays exist A complete characterization of such controllers is also presented The necessary and sufficient conditions are computable and are framed in terms of two algebraic Riccati equations and one finite-horizon Riccati differential equation The controllers and estimators that are obtained here have a linear periodic structure and are easily implementable At the foundation of these results lies a modified Nehari problem, the state space solution for which may be of independent interest

Reduced order H/sub /spl infin// filtering

Abstract: A overview of H/sub /spl infin// filtering, estimation, deconvolution approaches is presented. The problem of reduced order H/sub /spl infin// estimation filter design is considered. The method is illustrated by examples for several order H/sub /spl infin// filters.

On robust performance in H

Abstract: Abstract In this paper we consider the robust performance problem in H ∞ with scalar perturbations. We illustrate how the worst case H ∞ performance can be regarded as an H ∞ norm of a function of several complex variables. Based on this characterization we show how the worst case performance can be obtained from the H ∞ norm of a single system. This system is constructed from the original nominal system with the perturbations replaced by certain all-pass functions. We show that as the order of the all-pass functions goes to infinity, this H ∞ norm converges to the worst case performance. The implications of this characterization for computing the complex structured singular value and robust synthesis are discussed, though at present, this method does not seem to provide an efficient algorithm for this computation.

Design of H/sub 2/ and H/sub /spl infin// controllers with two degrees of freedom

Abstract: The tracking behavior of many feedback control systems can be improved by using a compensator with two degrees of freedom which processes the reference signal independently of the plant output signal, e.g., the reference signal can be processed by a static prefilter. This is described in the first part of this paper dealing with LQG/LTR and H/sub 2/ controllers. With H/sub /spl infin// methods, it is easy to design more sophisticated, dynamic feedforward controllers. They can be developed either in a second step, when the loop is already closed by a feedback compensator, or in one step together with the H/sub /spl infin// feedback part of the compensator. This latter possibility has the advantage that only one observer is needed for the two parts of the controller, thus the number of states of the complete compensator is minimized. An application of these design configurations to a helicopter is shown. Step responses without overshoot are achieved for position control.

Input shaping for vibration-damped slewing of a flexible beam using a heavy-lift hydraulic robot

Abstract: An input shaping scheme originally used to slew flexible beams via a tabletop D.C. motor is modified for use with an industrial-type, hydraulic-drive robot. This trajectory generation method was originally developed to produce symmetric, rest-to-rest maneuvers of flexible rotating rods where the angular velocity vector and gravitational vector were collinear. In that configuration, out-of-plane oscillations were excited due to centripetal acceleration of the rod. The bang-coast-bang acceleration profile resulted in no oscillations in either plane at the end of the symmetric slew maneuver. In this paper, a smoothed version of the bang-coast-bang acceleration is used for symmetric maneuvers where the angular velocity vector is orthogonal to the gravitational vector. Furthermore, the hydraulic robot servo dynamics are considered explicitly in determining the input joint angle trajectory. An instrumented mass is attached to the tip of a flexible aluminum rod. The first natural frequency of this system is about 1.0Hz. Joint angle responses obtained with encoder sensors are used to identify the servo actuator dynamics.

Tracking maneuvering targets using H/sub /spl infin// filters

Abstract: Develops, tests and evaluates H/sub /spl infin// algorithms for tracking maneuvering targets as an alternative to traditional approaches based on Kalman filter extensions and modifications. A crucial property of H/sub /spl infin// filters is an automatic increase of the filter bandwidth. The authors further explore this property versus appropriate artificial increases of the bandwidth of a Kalman filter and the H/sub /spl infin// filter itself. H/sub /spl infin// and Kalman filters are compared for RMSE performance as well as performance robustness to different maneuvering trajectories. Simulation results are presented showing the performance and robustness of the two filters for different maneuvering trajectories, data rates and bandwidth adjustments.

An algorithm and data structure for approximately computing nonlinear H/sub /spl infin// control laws

Abstract: An algorithm and data structure are developed for finding Taylor series solution of the Hamilton-Jacobi-Isaacs equation associated with the nonlinear H/sub /spl infin// control problem. This algorithm yields a set of linear algebraic equations, which not only lead to a transparent solvability condition of the Hamilton-Jacobi-Isaacs equation in the form of Taylor series, but also furnish a systematic procedure to generate the coefficients matrices of the Taylor series. This algorithm is illustrated on a missile pitch autopilot design.

Positive real controller design with H/sub /spl infin// norm performance bound

Abstract: This paper considers the positive real controller design for strictly positive real plants subject to a general H/sub /spl infin// norm performance bound. This problem is shown to be equivalent to a pair of small gain problems. A sufficient condition for their solutions is a standard H/sub /spl infin// small gain problem which can be readily solved. This procedure has been applied to the control of an experimental rotating flexible beam with good results.

Pseudorational functions and H/sup /spl infin// theory

Abstract: ©1994 IEEE Personal use of this material is permitted However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE This material is presented to ensure timely dissemination of scholarly and technical work Copyright and all rights therein are retained by authors or by other copyright holders All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright In most cases, these works may not be reposted without the explicit permission of the copyright holder

Reduced order mixed H/sub 2//H/sub /spl infin// optimization with a singular H/sub /spl infin// constraint

Abstract: A general mixed H/sub 2//H/sub /spl infin// optimal control problem is considered. The system consists of a plant and stable weights on the H/sub 2/ and H/sub /spl infin// transfer functions, and is linear time-invariant. The controller order can be reduced to that of the plant augmented with the H/sub 2/ weights only. A solution allowing a feedforward term in the H/sub /spl infin// problem and a singular H/sub /spl infin// constraint is developed. An F-16 longitudinal controller is designed to demonstrate the new method.

Time-varying problems of H/sup /spl infin// control and absolute stabilizability of uncertain systems

Abstract: This paper considers an absolute stabilization problem for a class of time-varying uncertain systems in which the uncertainty satisfies an integral quadratic constraint. The main result of the paper shows that a state feedback absolute stabilization problem has a solution if and only if there exists a solution to a corresponding infinite horizon, time-varying, state feedback H/sup /spl infin// control problem. The paper also shows that if either of these problems can be solved via the use of nonlinear state feedback control then it can also be solved via the use of linear state feedback control. Furthermore, the required controller can be constructed by solving a Riccati differential equation. The paper also considers the special case of periodic time-varying systems.

Mixed L/sup 1//H/sub /spl infin// suboptimal controllers for continuous-time systems

Abstract: A successful controller design paradigm must take into account both model uncertainty and design specifications. Model uncertainty can be addressed using either H/sub /spl infin// or L/sup 1/ robust control theory, depending upon the uncertainty characterisation. However, these frameworks cannot accommodate the realistic case where the design specifications include both time and frequency domain constraints. In this paper we present a design procedure for suboptimal L/sup 1//H/sub /spl infin// controllers. These controllers allows for minimizing the worst-case peak output due to bounded persistent disturbances, while, at the same time, satisfying an H/sub /spl infin//-norm constraint upon some closed-loop transfer function of interest. The main result of the paper shows that rational mixed L/sup 1//H/sub /spl infin// suboptimal controllers can be obtained by solving a sequence of problems, each one consisting of a finite-dimensional convex optimization and a standard, unconstrained H/sub /spl infin// problem.

/spl Hscr//sub /spl infin// control of nonlinear systems: a convex characterization

Abstract: The nonlinear /spl Hscr//sub /spl infin//-control problem is considered with an emphasis on developing machinery with promising computational properties. The solutions to /spl Hscr//sub /spl infin//-control problems for a class of nonlinear systems are characterized in terms of nonlinear matrix inequalities which result in convex problems. The computational implications for the characterization are discussed. >

H/sub 2//H/sub /spl infin// filtering: theory and an aerospace application

Abstract: In many filtering problems of practical interest, some of the noise signals satisfy the assumptions of H/sub 2/ (Kalman-Bucy) filtering, while others can be more accurately modeled as bounded energy signals (hence more amenable to an H/sub /spl infin// filtering approach) These problems may be addressed by considering a mixed H/sub 2//H/sub /spl infin// filtering problem In this paper the authors present a novel theory which solves the mixed problem exactly and in a computationally efficient way The applicability of the theory is illustrated by designing a filter to estimate the states of an aircraft flying through a downburst

Hybrid H 2 H ∞ Estimation for Phase-Locked Loop Filter Design

Abstract: A method of combining Kalman filtering and minimax filtering is proposed and demonstrated in an application to phase-locked loop design. Kalman filtering suffers from a lack of robustness to departures from the assumed noise statistics. But minimax filtering has the drawback of ignoring the engineer's (admittedly incomplete) knowledge of the noise statistics. It is shown in this paper that hybrid Kalman/minimax filtering can provide the best of both worlds. Phase-locked loop filter design is used in this paper to demonstrate an application of hybrid estimation.

/spl mu/ meets Bode

Abstract: This paper considers a simple control problem for a plant with large variations in gain The problem is solved using a classical approach, and also modern robust control approaches, that assume either dynamic or real parametric uncertainty The results of the different techniques are compared

Nonlinear H/sub /spl infin// control of periodic orbits

Abstract: Studies nonlinear state feedback H/sub /spl infin// control of periodic orbits. The authors develop a nonlinear analogy of the current state space theory of H/sub /spl infin// control, namely the solution of the state feedback H/sub /spl infin// control problem, for nonlinear systems having periodic orbits. The authors use a new set of coordinates proposed in Hauser and Chung Choo Chung (1994) to develop nonlinear state feedback H/sub /spl infin// control of periodic orbits.

/spl Hscr//sub /spl infin// identification for robust control

Abstract: In this paper, the role that frequency domain model identification performs in the controller design for single input, single output systems is developed. /spl Hscr//sub /spl infin// control design methods can guarantee the stability of a closed loop system with the plant only partially known, provided the controlled nominal plant as well as the uncertainty are stable and the frequency response of the plant uncertainty can be bounded. The nominal performance of such a closed loop system is critically dependent on the class of uncertainty that must be designed for, as well as the actual (but often unknown) accuracy of the model. Thus it is a primary aim of this paper to address conservatism in the modelling error bounds in order to enhance the ultimate performance of the controlled plant. The techniques for experiment design, frequency response estimation, model identification, estimation of priors and bound calculation that are developed are demonstrated in the case study which identified a model and bound for the vertical plasma dynamics of a tokamak fusion reactor.