Showing papers on "Robust control published in 1982"

Robustness of adaptive control algorithms in the presence of unmodeled dynamics

Abstract: This paper reports the outcome of an exhaustive analytical and numerical investigation of stability and robustness properties of a wide class of adaptive control algorithms in the presence of unmodeled dynamics and output disturbances. The class of adaptive algorithms considered are those commonly referred to as model-reference adaptive control algorithms, self-tuning controllers, and dead-beat adaptive controllers; they have been developed for both continuous-time systems and discrete-time systems. The existing adaptive control algorithms have been proven to be globally assymptotically stable under certain assumptions, the key ones being (a) that the number of poles and zeroes of the unknown plant are known, and (b) that the primary performance criterion is related to good command following. These theoretical assumptions are too restrictive from an engineering point of view. Real plants always contain unmodeled high-frequency dynamics and small delays, and hence no upper bound on the number of the plant poles and zeroes exists. Also real plants are always subject to unmeasurable output additive disturbances, although these may be quite small. Hence, it is important to critically examine the stability robustness properties of the existing adaptive algorithms when some of the theoretical assumptions are removed; in particular, their stability and performance properties in the presence of unmodeled dynamics and output disturbances. A unified analytical approach has been developed and documented in the recently completed Ph.D. thesis by Rohrs [15] that can be used to examine the class of existing adaptive algorithms. It was discovered that all existing algorithms contain an infinite-gain operator in the dynamic system that defines command reference errors and parameter errors; it is argued that such an infinite gain operator appears to be generic to all adaptive algorithms, whether they exhibit explicit or implicit parameter identification. The practical engineering consequences of the existence of the infinite-gain operator are disastrous. Analytical and simulation results demonstrate that sinusoidal reference inputs at specific frequencies and/or sinusoidal output disturbances at any frequency (including d.c.) cause the loop gain of the adaptive control system to increase without bound, thereby exciting the (unmodeled) plant dynamics, and yielding an unstable control system. Hence, it is concluded that none of the adaptive algorithms considered can be used with confidence in a practical control system design, because instability will set in with a high probability.

Robust-resistant spectrum estimation

Abstract: Conventional spectrum estimates of both the smoothed-periodogram and autoregressive variety lack robustness toward outliers in the original data. Outliers and other local perturbations are modeled by non-Gaussian additive noise, which is zero most of the time. Correspondingly, the lack of robustness of the conventional estimates of the spectrum manifest not only inflated variances but also damaging asymptotic biases. This paper discusses robust-resistant methods of spectrum estimation which do not suffer in this way. The main approach involves "data cleaning" by either one-sided or two-sided outlier interpolators based on autoregressive approximations. The autoregressive coefficients are themselves estimated robustly in an iterative loop along with the data-cleaning operation. The well-cleaned data are then used along with the autoregressive model to form smoothed spectral density estimates via prewhitening. Study of the so-called "linear part" of the nonlinear outlier interpolator algorithm shows that considerable bias reduction is realizable through use of the robust procedure. Some examples of applications of the robust methodology are presented. Special considerations for real-time processing and large data sets are discussed. Extensions of the method to cross-spectrum estimation, missing data, and irregularly spaced data problems are briefly mentioned.

Control Algorithm for a Static Phase Shifting Transformer to Enhance Transient and Dynamic Stability of Large Power Systems

Abstract: A robust control algorithm for the control of a static phase shifting or quadrature boost transformer has been developed and tested. This algorithm utilizes the inherent stabilizing ability of a phase shifter to rapidly return the power system to a stable operating point following severe transients. Under normal operating conditions, the controller minimizes power flow deviations and slip fluctuations due to random power demand changes. The control commands are generated using only local measurements (voltage and complex power at the transformer), specified power flow, and imprecise values of equivalent impedances of the power system.

Singular perturbations and robust redesign of adaptive control

Abstract: Effects of unmodeled high frequency dynamics on stability and performance of adaptive control schemes are analyzed. In the regulation problem global stability properties are no longer guaranteed, but a region of attraction exists for exact adaptive regulation. The dependence of the region of attraction on unmodeled parasitics is examined first. Then the general case of model reference adaptive control is considered in which parasitics can destroy stability and boundedness properties. A more robust adaptive law is proposed, guaranteeing the existence of a region of attraction from which all signals converge to a residual set which contains the equilibrium for exact tracking. The size of this set depends on design parameters, the frequency range of parasitics and the reference input signal characteristics.

Robustness of self-tuning controllers

Abstract: The theory of adaptive control usually assumes that the controlled system is linear and of known finite order. The robustness problem examined here is to find the extent to which these conditions may be violated while retaining stability of the adaptive algorithm. Explicit frequency-domain circle-type results are given for certain classes of nonlinear or high-order systems.

Control Logic for Parameter Insensitivity and Disturbance Attenuation

Abstract: An approach to the synthesis of control logic that is both insensitive to system parameters and attenuates response to input disturbances (sometimes called robust control logic) is presented and is applied to a simple system with an uncertain vibration frequency. A conclusion drawn from this study is that the lower the order of the compensator dynamics, the lower the sensitivity of the closed-loop system performance to parameter variations. It follows that estimated-state feedback is undesirable when there are large uncertainties in the system parameters. However, quadratic performance indices are minimized with estimated-state feedback, so the designer must trade off parameter insensitivity against disturbance attenuation. This is done here by minimizing the expected value of a sum of quadratic performance indices, each one of which is evaluated with different values of the system parameters; the decision variables in the minimization are parameters in a compensator of specified order that is less than or equal to the order of the system model.

Performance robustness properties of adaptive control systems

Abstract: Currently available adaptive control algorithms experience difficulties in the presence of unmodeled plant dynamics. In this paper conditions are derived which guarantee that the adaptive controller will have specified performance despite plant uncertainty and unmodeled dynamics. These conditions provide guidelines for the analysis and design of robust adaptive controllers. A combination of results from robust control and adaptive control theory is used to prove the main theorem. The notions of robust and tuned control are discussed.

The Design of Decentralized Controllers for the Robust Servomechanism Problem using Parameter Optimization Methods

Abstract: The problem of designing realistic decentralized controllers to solve the robust decentralized servomechanism problem [1] is considered in this paper. In particular, it is desired to find a decentralized controller for a plant to solve the robust servomechanism problem so that closed loop stability and asymptotic regulation occur, and also so that other desirable properties of the controlled system, such as fast response, low-interaction, integrity, tolerance to plant variations, constraints on gain magnitudes etc. occur. The method of design is based on extending the centralized design method of [2] to deal with the decentralized case. A number of examples are included to illustrate the design method.

A Variable Structure Approach to Robust Control of VTOL Aircraft

Abstract: This paper examines the application of variable structure control theory to the design of a flight control system for the AV-8A Harrier in a hover mode The objective in variable structure design is to confine the motion to a subspace of the total state space The motion in this subspace is insensitive to system parameter variations and external disturbances that lie in the range space of the control A switching type of control law results from the design procedure The control system was designed to track a vector velocity command defined in the body frame For comparison purposes, a proportional controller was designed using optimal linear regulator theory Both control designs were first evaluated for transient response performance using a linearized model, then a nonlinear simulation study of a hovering approach to landing was conducted Wind turbulence was modeled using a 1052 destroyer class air wake model

Robust control strategy for a linear time-invariant multivariable sampled-data servomechanism problem

Abstract: A robust control strategy for a linear sampled-data control system such that the error is asymptotically zero not only at, but also between, the sampling instances, in spite of both continuous and discrete disturbances, is proposed The tracking and the disturbances are assumed to satisfy a linear autonomous differential-difference equation The control strategy consists of an analogue servocompensator driving the process, a digital servocompensator driven by the tracking error and driving the analogue servocompensator, and a digital stabilising compensator regulating an overall augmented discrete system formed by the discretised process and both the digital and analogue servocompensators The analogue servocompensator contains the modes of the reference and the disturbance signals; the digital servocompensator contains the modes of the discrete reference and discretised disturbance signals The tracking error is shown to be asymptotically zero at all times Also, the control input to the analogue servocompensator is zero in the steady state If the exogenous signal mode is at the origin, the analogue servocompensator need not contain a simple mode at the origin However, in this case the control input to the analogue servocompensator is a constant signal in the steady state

Structural Information in Robustness Analysis

Abstract: Two topics on using structural information in the robustness analysis of control feedback systems are presented. First, we describe how to identify sensitive direction for perturbations to individual components (subsystems) of larger systems. This technique is then applied, to parameter variation analysis. Also we discuss the role of the control weighting matrix in the robustness analysis of the linear quadratic (LQ) desigjn, using a 2×2 example. In particular, it is shown that the structure of the control weighting matrix can be used to classify sensitivities of the control system to model uncertainties.

Optimal Control of a Class of Discrete Multivariable Nonlinear Systems. Application to a Fermentation Process

Abstract: The optimal control of a class of discrete multivariable nonlinear systems given by: x k+1 =a(x k )+B(x k )u k , y k =C x k , is analysed. A closed-loop structure is obtained with the proposed performance index. The addition of numerical integrators to the output error and the design of an optimal control law for the resultant augmented system lead to a very robust control structure. The performance of this control law is evaluated by applying it to a simulated continuous culture fermentation process.

Analysis of performance robustness for uncertain multivariable systems

Abstract: Frequency domain measures are developed which quantify the relation between performance robustness and model uncertainty for linear-time-invariant multivariable feedback systems. The measures require that uncertainty, as well as performance robustness, be expressed in terms of conic-sector bounds [6]-[8].

Robust control of unknown discrete multivariable systems

Abstract: Some recent results on controller design for unknown discrete multivariable plant are extended to include quantitative measures of the robustness of the final design.

Zero assignment in the multivariable robust servomechanisms

Abstract: Feedforward of the reference input is introduced to provide another degree of freedom in the overall system optimization of multivariable robust servomechanisms. This provides the designer with substantial control over the shape of the transient response. Introduction of the feedforward matrices has no effect on the pole locations or robustness properties of the system and creates new transmission zeros, the location of which can be influenced by proper selection of feedforward matrices. Loss functions such as the integral square error can be used to determine the feedforward matrices. Explicit formulas are derived for the feedforward matrices in terms of Lyapunov functions.

Robust compensation of optimal control for manipulators

Abstract: In a suboptimally controlled manipulator arm, friction torque variations cause trajectory deviations and performance deterioration. On the other hand, the on-line computation of nonlinear terms in the suboptimal controller is time consuming or requires large memory space when table look-up techniques are used. In order to obtain robustness against variations in open loop dynamics and decrease nonlinear couplings in suboptimal control systems for manipulators with quadratic performance indices, in addition to full state feedback, it is necessary to introduce feedback associated with the derivatives of the state variables. This additional feedback may be implemented as minor compensating loops embedded within the suboptimal controller by analog devices. As an example, torque compensation and acceleration compensation for MIT arm are considered and yield a simple linear controller with improved robustness.

Control of a Spinning Projectile

Abstract: : Powerful multivariable robust control synthesis techniques which have recently been devised (1) are applied to a tracking problem for a spinning projectile. A linearized lateral axis model of the projectile is used to design a reduced order LQG compensator to command angle of attack and sideslip using only fixed plane pitch rate and yaw rate measurements. Singular values of various transfer function matrices are used to explain the design procedure to obtain robust compensation that recovers the full state feedback guaranteed gain and phase margins. (Author)

Frequency-Shaped Penalty Functions for Robust Control Design

Abstract: Modern Control Laws are based on the optimization of a certain performance Index. These control laws behave well for the nominal plant parameters but the performance can be very sensitive to small errors in the plant model. Recently considerable work has been done to evaluate robustness of modern control laws in the presence of plant transfer function uncertainties. This work indicates poor robustness particularly when state estimation is used to derive variables for feedback. This paper discusses an approach to synthesize multivariable control laws which are robust with respect to system errors. The approach is based on the frequency shaping of penalty functionals, and combines good features of modern and classical control approaches.

Robust control of self-adjoint distributed-parameter structures

Abstract: This paper examines the active vibration control-of distributed-parameter structures in which a self-adjoint differential operator expresses the stiffness distribution. For large and complex structures, computational requirements and/or modeling limitations ensure that a reduced-order controller is used. However, although in practice only discrete actuators and discrete sensors are available, spatially distributed control forces and spatially distributed observations are desirable for implementing a reduced-order controller. Therefore a distinction arises among 1) designing distributed control forces for a reduced-order model, 2) implementing the control forces with a number of actuators, and 3) estimating the distributed state from a number of sensors. Herein the distinctions are realized by introducing three appropriate projection operations. The effects of the three projections on the actual closed-loop eigenvalues are investigated in detail. A criterion for the controller to be robust in the stability sense is discussed and illustrative examples are presented.

Dualite : Identification bayesienne — Commande robuste

Abstract: A new duality concept is studied in this paper. The general frame of the conflict between parametric identification and control quality is recalled and then precised step by step. In order to get a rigorous mathematical definition of this duality an inherently parallel bayesian identification method is used ; its convergence properties are set by a theorem. Robust state-estimation through a Kalman filter is linked to the previous bayesian parametric identification ; a first sense of dual-effect clearly appears. Robust control versus identification can then be studied in the last part : the mathematical formulation of duality is given for a class of adaptive control ; robustness and identification qualities are introduced and their theoretical expressions are given with respect to a suitable criterion.

On the robust control of systems with respect to set valued objectives

Abstract: This paper considers an extension of the Target Tube Reachability Problem (TTRP) for discrete-time, linear systems with set-constrained disturbance inputs and observation uncertainties to include set-bounded parametric uncertainty in the state transition matrix. A backwards recursive algorithm, similar in spirit to that developed by Bertsekas & Rohdes [1], is proposed for the determination of Robust Attainability Regions in state space. These guarantee the existence of admissible control actions that maintain possible state trajectories inside a pre-specified Target Tube defined over a finite planning horizon. The basic concepts for this extension are robust direct and inverse images of closed, convex, bounded (CCB) sets through linear maps with uncertain but bounded parameters. Formulae and simple examples are furnished in detail for the ellipsoidal case.

Optimal Control of a Class of Discrete Multivariable Nonlinear Systems: Application to a Fermentation Process

Abstract: The optimal control of a class of discrete multivariable nonlinear systems given by: x k+1 =a(x k )+B(x k )u k , y k =C x k , is analysed. A closed-loop structure is obtained with the proposed performance index. The addition of numerical integrators to the output error and the design of an optimal control law for the resultant augmented system lead to a very robust control structure. The performance of this control law is evaluated by applying it to a simulated continuous culture fermentation process.

Critical parameter selection in the vibration suppression problem of large flexible space structures

Abstract: The paper addresses the application of parameter sensitivity analysis to large flexible space structure models with uncertain parameters such as modal dampings, modal frequencies, mode shape slopes at actuator (sensor) locations. A criterion that allows the specific control objective to influence the parameter selection process is given to delineate the critical parameters in linear regulator problems. The quantitative measure is labeled 'Parameter Error Index (PEI) '. Explicit and simple formulas are obtained in terms of modal data for PEI for the vibration suppression problem of an LSS. The proposed procedure is applied to the 'Purdue Model', a generic two dimensional LSS model. Results are presented which indicate that, for this problem modal frequencies are more critical parameters than mode shapes. This type of information is useful in parameter estimation, robust control design, structure redesign, etc.

Displacement Control of Elastic Structures: Integral Control with a Robustness Property

Abstract: The issue of design of feedback controllers for elastic structures is addressed, where the objective is accurate and robust displacement control of the structure. Motivation for the work arises from study of control of multi-story buildings as part of the pseudo-dynamic-test method. If the force actuators have "fast" dynamics suitable control may be achieved by feedback of structural displacements and velocities, usilng a PID type controller logic. If the force actuators have "slow" dynamics it is suggested that structural accelerations also be fed back to the controller. Locations of the assigned closed loop poles are specified which guarantee robustness to variations in the actuator time constant and to uncertainties in the structural stiffness. Simplifying assumptions are made so that results are obtained using elementary arguments.

Comparative Analysis of a Class of Robust State Estimation Algorithms

Abstract: This paper deals with a problem of robust estimation of the state of discrete, linear, dynamical system in case when measurements are corrupted by non-Gaussian heavy-tailed noise. The solution of a mini-max approach to this problem is outlined. Two types of robust filters - unconditional and conditional - are presented. The results of digital Monte-Carlo simulations show high performance of the proposed robust filters in comparison with the linear Kalman filter.

Approximate error regulation - The robust servomechanism problem for unknown input signals

Abstract: This paper considers the problem of finding a robust servomechanism controller which achieves exact asymptotic tracking and regulation for a given class of reference and disturbance signals, and arbitrarily good approximate asymptotic regulation for other classes of reference and disturbance input signals. Necessary and sufficient conditions for the existence of such a controller, and a characterization of controllers which accomplish this are given. An explicit algorithm for such controllers is also given; in particular, it is shown that the design of such a controller can always be accomplished by using the cheap control design method as used in [1] for the multivariable robust servomechanism problem. A degenerate type of robust servomechanism controller (called a high gain servomechanism controller) consisting of only static feedback gains, is also given, which has the property that it produces arbitrarily good approximate regulation for all tracking/disturbance signals; thus this controller shows that dynamics in the feedback controller are not essential for achieving good approximate error regulation. Some numerical examples are included to illustrate the results.

Constructive Design of Robust Optimal Regulators

Abstract: An algorithm is developed that determines the parameters of a robust dynamic linear regulator which is optimal in the sense that it minimizes a quadratic cost function. Robustness is achieved by constraining the solution to a set of controllers which satisfy an inequality based on the small gain theorem. The resulting closed loop system will remain stable even when plant dynamics deviate from the nominal by perturbations within some prescribed set.