Showing papers presented at "American Control Conference in 1988"

State-space solutions to standard H 2 and H ∞ control problems

Abstract: Simple state-space formulas are presented for a controller solving a standard H∞-problem. The controller has the same state-dimension as the plant, its computation involves only two Riccati equations, and it has a separation structure reminiscent of classical LQG (i.e., H2) theory. This paper is also intended to be of tutorial value, so a standard H2-solution is developed in parallel.

Stability theory for linear time-invariant plants with periodic digital controllers

Abstract: This paper considers the control of a linear time-invariant plant by a digital controller composed of a sampler. a periodic discrete-time component, and a zero-order hold. The stability of such a configuration is analyzed in detail. It is shown how closed-loop zeros can be placed using such a scheme. As a consequence. it is proved that the gain margin can be arbitrarily assigned by suitable choice of sampling time and digital controller. The design procedure is constructive, using state-space methods.

LQG control with an H ∞ performance bound: a riccati equation approach

Abstract: An LQG control-design problem involving a constraint on H∞ disturbance attenuation is considered. The H∞ performance constraint is embedded within the optimization process by replacing the covariance Lyapunov equation by a Riccati equation whose solution leads to an upper bound on L2 performance. In contrast to the pair of separated Riccati equations of standard LQG theory, the H∞-constrained gains are given by a coupled system of three modified Riccati equations. The coupling illustrates the breakdown of the separation principle for the H∞-constrained problem. Both full- and reduced-order design problems are considered with an H∞ attenuation constraint involving both state and control variables. An algorithm is developed for the full-order design problem and illustrative numerical results are given. A more complete version of this paper is given in [41].

Discrete-Time Domain Analysis and Synthesis of Repetitive Controllers

Abstract: Repetitive control is formulated and analyzed in the discrete-time domain. Sufficiency conditions for the asymptotic convergence of a class of repetitive controllers are given. The "plug-in" repetitive controller is introduced and applied to track-following in a disk-file actuator system. Inter-sample ripples in the tracking error were present when the "plug-in" repetitive controller was installed. The performance is enhanced, however, when the zero-holding device is followed by a low-pass filter or replaced by a delayed first-order hold.

On the Controllability and Observability of Hybrid Systems

Abstract: This paper considers a special class of hybrid systems, whose state space is a cross-product space of an Euclidean space and a finite-state space. Such models may be used to represent systems subject to known abrupt parameter variations, such as commutated networks. They may also be used to approximate some types of time-varying systems. The paper investigates controllability, observability, and stability of hybrid systems. In particular, it derives a necessary and sufficient algebraic condition, a simple algebraic criterion, and a computationally simple algebraic sufficient test for controllability and observability. Moreover, it provides a simple sufficient stability condition.

A Schur Method for Balanced Model Reduction

Abstract: The calculation of the balancing transformation required in Moore's "balanced-transformation" model reduction procedure tends to be badly conditioned, especially for non-minimal models that stand to benifit the most from model reduction. In this paper it is shown that the Moore reduced model can be computed directly without balancing via projections defined in terms of arbitary bases for the left and right eigenspaces associated with the "large" eigenvalues of the product PQ of the reachability and controllablility grammians. Two methods for computing these bases are proposed, one based on the ordered Schur decomposition of PQ and the other based on the Cholesky factors of P and Q. The algorithms perform reliably even for non-minimal models.

An Integrated Approach to Controls and Diagnostics: The 4-Parameter Controller

Abstract: In this paper we present a theoretical basis for an integrated approach to the design of reliable control systems. In this approach, the control and diagnostic modules of a reliable control system are designed together, instead of independently, thereby accounting for the interactions which occur between these two modules in a functioning reliable control system. The approach makes use of a significant generalisation of the familiar 2-parameter controller known as the 4-parameter controller. This controller has two vector inputs and not one, but two vector outputs; correspondingly, this controller is comprised of not two, but four matrix parameters. The additional controller output is monitored to detect and isolate sensor and actuator faults, thereby providing the controller with diagnostic capabilities, or "intelligence," in addition to its control capabilities. Using a parameterization of all stabilising 4-parameter controllers, the fundamental limitations and inherent tradeoffs governing the design of reliable control systems are clarly delineated, with special attention given the issues of uncertainty and control/diagnostic interaction. Several means for resolving these desig tradeoffs are proposed, and illustrated by way of non-trivial examples. These results are expected to pave the way for the achievement of improved overall control/dignostic performance in reliable control systems, and also to pave the way for the achivement of significant complexity reductions in both the design and implementation of reliable control systems.

Adaptive And Repetitive Digital Control Algorithms for Noncircular Machining

Abstract: This paper presents experimental results of digital tracking control algorithms applied to a hydraulic linear actuating system for tool positioning in noncircular machining. Noncircular machining is accomplished by controlling the tool position in the direction normal to the surface of the rotating workpiece. Implementation of two robust tracking controllers is presented: one is the adaptive zero phase error tracking controller for tracking arbitrary shaped desired signals, and the other is the digital repetitive controller for tracking periodic desired signals.

Model Reduction for Robust Control: A Schur Relative-Error Method

Abstract: A numerically robust Relative Error Method (REM) for state-space model order reduction is described. Our algorithm is based on Desai's Balanced Stochastic Truncation (BST) technique for which M. Green has obtained an L? relative-error bound. However, unlike previous methods, our Schur method completely circumvents the numerically delicate initial step of obtaining a minimal balanced stochastic realiztion (BSR) of the the power spectrum matrix G(s)GT(-s).

Unconstrained and Constrained Mode Expansions for a Flexible Slewing Link

Abstract: The linear equations of motion of a uniform flexible slewing link which were derived via Hamilton's Extended Principle are considered. These equations account for the coupling between bending and rigid modes. Unconstrained and constrained mode expansions are investigated and a quantitative comparison is made between the frequency equations and associated mode shapes. A finite dimensional model is derived using the assumed modes method and the theoretical frequencies are verified with an experimental counterbalanced aluminum beam.

Augmented Object and Reduced Effective Inertia in Robot Systems

Abstract: The paper investigates the dynamic characteristics and control of robot systems involving combinations of parallel and serial mechanical structures, e.g. multiple manipulators and macro/micro-manipulators. A framework for the analysis and control of multiple manipulator systems with respect to the dynamic behavior of the manipulated object is developed. A multi-effector/object system is treated as an augmented object representing the total masses and inertias perceived at some operational point. This system is actuated by the total effector forces acting at that point. The allocation of forces is based on the minimization of the total joint actuator efforts. For serial structures, the effective inertial characteristics of a combined macro/micro-manipulator are shown to be dominated by the inertial characteristics of the micro-manipulator. A new approach for a dextrous dynamic coordination of such mechanisms based on treating the combined system as a single redundant manipulator while minimizing of the deviation from the neutral (mid-range) joint positions of the micro-manipulator is proposed.

Controller Design for Uncertain Systems via Lyapunov Functions

Abstract: We present a controller design methodology for uncertain systems which is based on the constructive use of Lyapunov functions The uncertainties, which are deterministic, are characterized by certain structural conditions and known bounds As a consequence of the Lyapunov approach, the methodology is not restricted to linear systems The robustness of these controllers in the presence of singular perturbations is considered The situation in which the full state of the system is not available for measurement is also considered These controllers are illustrated by application to the tracking control of a Manutec r3 robot which has an uncertain payload

A Time Delay Controller for Systems with Unknown Dynamics

Abstract: This paper focuses on the control of systems with unknown dynamics and deals with the class of systems described by ?=f(x,t)+h(x,t)+B(x,t)u+d(t) where h(x,t) and d(t) are unknown dynamics and unexpected disturbances, respectively. A new control method, Time Delay Control (TDC), is proposed for such systems. Under the assumption of accessibility to all the state variables and their derivatives, the TDC is characterized by a simple estimation technique of the effect of the uncertainties. This is accomplished using time delay. The control system's structure, stability and design issues are discussed for linear time-invariant and single-input- single-output systems. Finally, the control performance was evaluated through both simulations and experiments. The theoretical and experimental results indicate that this control method shows excellent robustness properties to unknown dynamics and disturbances.

Receding Horizon Tracking Control as a Predictive Control and its Stability Properties

Abstract: The receding horizon tracking control for the discrete time invariant system is presented in this paper. This control law is derived by using the receding horizon concept from the standard tracking problems. Stability properties of this control law are analyzed and it is shown that there exists a finite horizon for which the closed loop systems are always asymptotically stable. It is also shown that the receding horizon tracking control with integral action provides zero offset for a constant command input.

A Generalization of Kharitonov's Four Polynomial Concept for Robust Stability Problems with Linearly Dependent Coefficient Perturbations

Abstract: From a systems-theoretic point of view, Kharitonov's seminal theorem on stability of interval polynomials suffers from two fundamental limitations: First, the theorem only applies to polynomials with independent coefficient perturbations. Note that uncertainty in the physical parameters of a linear system typically results in dependent perturbations in the coefficients of the characteristic polynomial. Secondly, Kharitonov's Theorem only applies to zeros in the left half plane?more general zero location regions are not accommodated. In view of this motivation, the main result of this paper is a generalization of Kharitonov's four polynomial concept to the case of linearly dependent coefficient perturbations and more general zero location regions.

Strict Global Lyapunov Functions for Mechanical Systems

Abstract: This paper presents a strict, global Lyapunov function for the class of dissipative mechanical systems defined on a configurtion space which admits a trivial tangent bundle.

Load Balancing and Closed Chain Multiple Arm Control

Abstract: We give the general dynamical equations for several rigid link manipulators rigidly grasping a commonly held rigid object. It is shown that the number of lost arm configuration degrees of freedom due to imposing the closed loop kinematic constraints is the same as the number of degrees of freedom gained for controlling the internal forces of the closed chain system. This number is equal to the dimension of the kernel of the Jacobian operator which transforms contact forces to the net forces acting on the held object, and it is shown that this kernel can be identified with the subspace of controllable internal forces of the closed chain system. Control of these forces allows one to regulate the grasping forces imparted to the held object or to control the load taken by each arm. It is shown that the internal forces can be influenced without affecting the control of the configuration degrees of freedom, and that this fact is independent of control law choice and involves only kinematical information about each arm. Control laws of feedback linearization type are shown to be useful for controlling the location and attitude of a frame fixed with respect to the held object, while simultaneously controlling the internal forces of the closed chain system. Since the kernel describing the internal forces subspace depends only on the relative location of arm tip contact points, force feedback can be used to feedback linearize and control the system even when the held object has unknown mass properties.

Quantitative Feedback Theory (QFT)

Abstract: In QFT, the feedback design problem has always been that of achieving defined performance over specified range of plant uncertainty, with minimum "cost of feedback". Eigenvalue realization was always considered an incidental problem. Two benchmark problems are presented. The first is a 2×2 highly uncertain nonlinear plant. The second is a 3×7 digital (60 Hz) flight control problem with uncertainty consisting of 36 possible effector failure cases with no failure detection and identification, i.e. a fixed compensation design. Both problems were solved by QFT with satisfactory results.

On a Fractional Representation Approach to Closed-Loop Experiment Design

Abstract: In this paper we propose a plant model, based on a fractional representation of the loop, which is uniquely suited to the closed-loop experiment design problem. The advantage of this model is that it substitutes a open-loop problem (for which there has been extensive work) for the original closed-loop problem. We also present the results of Monte Carlo simulations which suppport the utility of this approach.

Robust Observer Design with Application to Fault Detection

Abstract: A new scheme for robust estimation of the partial state of linear time-invariant multivariable systems is presented, and it is shown how this may be used for the detection of sensor faults in such systems. We consider an observer to be robust if it generates a faithful estimate of the plant state in the face of modelling uncertainty or plant perturbations. Using the Stable Factorization approach we formulate the problem of optimal robust observer design by minimizing an appropriate norm on the estimation error. A logical candidate is the 2-norm, corresponding to an H? optimization problem, for which solutions are readily available. In the special case of a stable plant, the optimal fault diagnosis scheme reduces to an internal model control architecture.

An Assessment of Air-to-Air Missile Guidance and Control Technology

Abstract: This paper provides an assessment of current air-to-air missile guidance and control technology. Areas explored include target state estimators, advanced guidance laws, and bank-to-turn autopilots. The assumptions, benefits, and limitations of recent applications of nonlinear filtering, adaptive filtering, modern control, adaptive control, dual control, differential game theory, and modern control design techniques to the air-to-air missile problem are discussed.

Robustness in the Presence of Joint parametric Uncertainty and Unmodeled Dynamics

Abstract: It is shown that, in the case of joint real parametric and complex uncertainty, Doyle's structured singular value can be obtained as the solution of a smooth constrained optimization problem. While this problem may have local maxima, an improved computable upper bound to the structured singular value is derived, leading to a sufficient condition for robust stability and performance.

Robust stabilization of normalized coprime factors: an explicit H ∞ solution

Abstract: The problem of robustly stabilizing a linear system subject to H∞ bounded perturbations in the Numerator, N, and denominator, M, of its normalized left coprime factorization is explicitly solved Although this is a particular H∞ optimization problem which would normally require an iterative solution, it can in fact be solved directly giving the optimal stability margin 1 - ||M , N||2H

H ∞ robust control synthesis for a large space structure

Abstract: In a design study involving the use of H∞ optimal control theory, an 11-state control law is generated for a 116-state model of a large flexible space structure. A combination of co-located rate feedback, modal truncation, and optimal Hankel-norm model techniques is found to lead to a vastly simplified four-state model for the structure which, by singular-value theory, is proved to be satisfactory for design of a controller whose bandwidth exceeds the natural frequencies of all of the modes of the original 116-state model. Specifications regarding disturbance attenuation, bandwidth, and stability robustness are quantitatively expressed as weighting functions in a mixed-sensitivity H∞ optimal control synthesis problem, the solution to which is computed by the authors' program LINF.

A Fractional Approach to Model Reduction

Abstract: A new method for the model reduction of finite-dimensional, linear, time-invariant (FDLTI) plants is given. The method uses fractional representation theory to extend balance and trancate model reduction to unstable plants without requiring the ad-hoc division of the plant into stable and completely unstable parts. The new method, dubbed fractional balanced reduction or FBR, applies balance and truncate to a special representation of the graph operator of the plant. This operation yields an object readily recognized as the graph operator of a reduced order plant. The method has nice properties including existence of an a priori error bound in the graph metric, and preservation of sector containment which is useful for deciding system stability when nonlinearities are present.

Adaptive Control Systems for Machining

Abstract: In CNC systems of metal-cutting processes the machining variables (e.g., the cutting speed and feedrate) are prescribed by the part programmer. The determination of these variables depends on experience and knowledge regarding the workpiece and tool materials, coolant conditions, and other factors. The main idea in adaptive control is the improvement in production rate and of part quality by calculation and setting of the optimal variables during the machining itself. This calculation is based upon measurements of process variables in real time and is followed by a subsequent on-line adjustment of the machining variables subject to constraints with the objective to optimize the performance of the overall system.

Joint-Based Control of a Nonlinear Model of a Flexible Arm

Abstract: In this paper the control problem for a one-link flexible arm described by a nonlinear model is considered. Based on the input-output inversion algorithm, a state-feedback control law is designed which enables exact reproduction of any desired smooth joint trajectory. In the closed loop an unobservable dynamics naturally arises, related to the varables describing the arm distributed flexibility. Open vs. closed-loop strategies are developed and compared. Simulation results are included. Finally, extensions of this approach to end-point based trajectory control are suggested.

Considerations for Automated Nap-of-the-Earth Rotorcraft Flight

Abstract: In this paper, we consider nap-of-the-earth (NOE) rotorcraft flight as one of the applications in which obstacle avoidance plays a key role, and investigate the prospects of automating the guidance functions of NOE flight. Based on a proposed structure for the guidance functions, we identify obstacle detection and obstacle avoidance as the two critical components requiring substantial advancement before an automatic guidance system can be realized. We discuss the major sources of difficulties in developing these two components, including sensor requirements for which we provide a systematic analysis.