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Showing papers presented at "American Control Conference in 1987"


Journal Article•DOI•
10 Jun 1987
TL;DR: Among the problems solved are: simultaneous arbitrary pole assignment for a finite number of systems by a single GSHF controller, exact model matching, and decoupling, and optimal noise rejection.
Abstract: This paper investigates the use of generalized sampled-data hold functions (GSHF) in the control of linear time-invariant systems. The idea of GSHF is to periodically sample the output of the system, and generate the control by means of a hold function applied to the resulting sequence. The hold function is chosen based on the dynamics of the system to be controlled. This method appears to have several advantages over dynamic controllers: it has the efficacy of state feedback without the requirement of state estimation; it provides the control system designer with substantially more freedom; and it requires few on-line computations. This paper focuses on four questions: pole assignment, specific behavior, noise sensitivity, and robustness. Among the problems solved are: simultaneous arbitrary pole assignment for a finite number of systems by a single GSHF controller, exact model matching, decoupling, and optimal noise rejection. Examples are given.

444 citations


Proceedings Article•DOI•
01 Jan 1987

420 citations


Proceedings Article•DOI•
10 Jun 1987
TL;DR: It is shown that the required minimax optimization can be recast as a linear program for uncertainty descriptions which provide impulse response models as affine functions of uncertain parameters.
Abstract: Concepts of model predictive control are extended to uncertain linear systems. An on-line optimizing control scheme is developed which has as its objective the minimization of the worst-case tracking error for a family of linear plants. For uncertainty descriptions which provide impulse response models as affine functions of uncertain parameters, it is shown that the required minimax optimization can be recast as a linear program. Situations which lead to such an uncertainty description are discussed. An example is presented to demonstrate the properties of the proposed control scheme.

340 citations


Proceedings Article•DOI•
10 Jun 1987
TL;DR: This paper considers control design for systems with input magnitude saturation by using four examples, 2 SISO and 2 MIMO, to illustrate the properties of several existing schemes.
Abstract: This paper considers control design for systems with input magnitude saturation Four examples, 2 SISO and 2 MIMO, are used to illustrate the properties of several existing schemes A new method based on a modification of conventional antiwindup compensation is introduced It is assumed that the reader is familiar with the problem of integral windup for saturating plants and conventional schemes for dealing with it

205 citations


Proceedings Article•DOI•
10 Jun 1987
TL;DR: In this paper, the authors used stochastic approximation (SA) to construct maximum likelihood estimates of system parameters, and showed that this SA procedure is, relative to a Kiefer-Wolfowitz procedure, most efficient for large-scale systems.
Abstract: This paper shows how stochastic approximation (SA) can be used to construct maximum likelihood estimates of system parameters. The procedure described here relies on a derivative approximation other than the usual finite-difference approximation associated with a Kiefer-Wolfowitz SA procedure. This alternative derivative approximation requires fewer, by a factor equal to the dimension of the parameter vector being estimated, computations than the standard finite-difference approximation. Numerical evidence presented in the paper indicates that this SA procedure is, relative to a Kiefer-Wolfowitz procedure, most efficient when considering large-scale systems.

170 citations


Journal Article•DOI•
01 Jul 1987
TL;DR: It is shown that the bound for the residual tracking error depends on the speed of the plant parameter variations in such a way that as these parameters become constant the bound reduces to zero.
Abstract: In this paper we consider the Model Reference Control and Model Reference Adaptive Control problem of a class of linear time-varying plants with bounded, piecewise smooth parameters. We first introduce a new controller structure that solves the Model Reference Control problem, with zero tracking error, in the case of smooth slowly time-varying plant parameters. When the plant parameters are unknown we use the robust adaptive law, proposed in [12], to adjust the controller parameters and establish boundedness of all signals in the adaptive loop and good tracking properties, provided that the smooth time-variations of the plant parameters are sufficiently slow and the minimum time between discontinuities is large enough. Furthermore, we show that when the plant parameters become constant, the tracking error converges asymptotically to zero.

132 citations


Journal Article•DOI•
10 Jun 1987
TL;DR: In this article, a method for designing Smith predictor controllers that provide robust performance despite real parameter uncertainties in the process model is presented, and an exact bound for the magnitude of multiplicative uncertainty used to approximate simultaneous uncertainties in process gain, time-constant, and time-delay is derived.
Abstract: A method is outlined for designing Smith predictor controllers that provide robust performance despite real parameter uncertainties in the process model Insight into the design process is gained by viewing the Smith predictor from the perspective of Internal Model Control Performance requirements are written in terms of a frequency-domain weight restricting the magnitude of the closed-loop sensitivity function A general method for approximating multiple parameter uncertainties by a single multiplicative uncertainty is developed - an exact bound is derived for the magnitude of multiplicative uncertainty used to approximate simultaneous uncertainties in process gain, time-constant, and time-delay Three controller design methods are demonstrated The first method locates loop transfer-function uncertainty regions to test for robust performance - real parameter uncertainties are considered exactly The second tuning method approximates real parameter uncertainties by multiplicative uncertainty and uses structured singular value analysis to guarantee robust performance Finally, the Smith predictor controller is compared with the Structured-Singular-Value-optimal controller

128 citations


Proceedings Article•DOI•
10 Jun 1987
TL;DR: In this paper, the effects of contact forces required to maintain satisfaction of the constraints are used to develop explicit conditions for stabilization and tracking using feedback, which provide a guarantee that the closed loop controlled robot is stable when performing tasks defined by the specified constraints.
Abstract: Mathematical models for constrained robot dynamics, incorporating the effects of contact forces required to maintain satisfaction of the constraints, are used to develop explicit conditions for stabilization and tracking using feedback. The control structure allows feedback of displacements, velocities and the contact forces. Global conditions for tracking based on a modified computed torque controller are presented. These conditions provide a guarantee that the closed loop controlled robot is stable when performing tasks defined by the specified constraints.

126 citations


Proceedings Article•DOI•
10 Jun 1987
TL;DR: In this article, three methods are presented for achieving stable force control compliant coverings or soft sensors, sell-tuning of force gains after estimation of environmental impedance, and reliance on fast open-loop joint torque control and using tip force sensor feedback in a slow loop to maintain accuracy.
Abstract: Robots in force control mode often become unstable during contact with stiff environments, due mainly to the high gain nature of wrist force-sensor feedback. Three methods are presented for achieving stable force control compliant coverings or soft sensors, sell-tuning of force gains after estimation of environmental impedance, and reliance on fast open-loop joint torque control and using tip force sensor feedback in a slow loop to maintain accuracy. The latter method is proposed as the best one. Dynamic stability is analysed with a simple model of the robot and its environment. The analyses are verified by single-link experiments on the MIT Serial Link Direct Drive Arm.

117 citations


Proceedings Article•DOI•
10 Jun 1987
TL;DR: In this paper, a bibliography and discussion of recent activity in nonthermodynamic (low frequency) internal combustion engine model development where spark advance, fuel, throttle, and exhaust gas recirculation are the elected control variables are discussed.
Abstract: The paper contains a bibliography and discussion of recent activity in nonthermodynamic (low frequency) internal combustion engine model development where spark advance, fuel, throttle, and exhaust gas recirculation are the elected control variables. Modeling considerations are delineated and the modeling relationship to experimental verification is discussed. Examples with explicit methods of parameter determination and dynamic validation are presented.

97 citations


Proceedings Article•DOI•
10 Jun 1987
TL;DR: In this article, a nonlinear port fuel injected automotive engine model is developed which can be used for the design of engine control algorithms, or within an algorithm for real time control.
Abstract: A nonlinear port fuel injected automotive engine model is developed which can be used for the design of engine control algorithms, or within an algorithm for real time control. The model is being validated using a sequential fuel injection V-6 engine, and includes: ? intake manifold dynamics, ? fuel dynamics, and ? process delays inherent in the four stroke engine cycle. The model is compact enough to run in real time and can be used as an embedded model withim a control algorithm or an observer. Although developed for a specific engine, the model can be adapted to represent various types of automotive engines with a limited amount of engine data. Preliminary validation results look very promising.

Proceedings Article•DOI•
10 Jun 1987
TL;DR: In this article, the root locations of all polynomials of the entire family can be determined by examining only the roots of the polynomial contained in the exposed edges of the polytope.
Abstract: The presence of uncertain parameters in either a state space or frequency domain description of a linear, time-invariant system manifests itself as variations in the coefficients of the characteristic polynomial. If the family of all such polynomials is polytopic in coefficient space, we'll show that the root locations of the entire family can be completely determined by examining only the roots of the polynomials contained in the exposed edges of the polytope. These results are computationally feasible and this crterion goes beyond the presently available stability tests for uncertain systems by being less conservative in all cases and by explicitly determining all root locations. Equally important is the fact that these results are also applicable to discrete-time systems

Proceedings Article•
10 Jun 1987
TL;DR: Under ideal conditions APTOS is shown to be uniformly asymptotically stable and an algorithm is proposed for adapting the PTOS to improve performance in the face of uncertain plant parameters.
Abstract: A Proximate Time-Optimal Servo (PTOS) is developed, along with conditions for its stability. An algorithm is proposed for adapting the PTOS (APTOS) to improve performance in the face of uncertain plant parameters. Under ideal conditions APTOS is shown to be uniformly asymptotically stable. Simulation results demonstrate the predicted performance.

Proceedings Article•
10 Jun 1987
TL;DR: A frequency-domain estimator which can identify both a nominal model of a plant as well as a frequency- domain bounding function on the modeling error associated with this nominal model can be used in conjunction with a robust control-law redesign algorithm to form a robust adaptive controller.
Abstract: The paper presents a frequency-domain estimator which can identify both a nominal model of a plant as well as a frequency-domain bounding function on the modeling error associated with this nominal model. This estimator, which we call a robust estimator, can be used in conjunction with a robust control-law redesign algorithm to form a robust adaptive controller.

Proceedings Article•DOI•
Stephen Richter1•
10 Jun 1987
TL;DR: In this paper, the authors present a homotopy algorithm for solving the optimal projection equation (OPE) problem, where the number of inputs or outputs to the system is less than or equal to the dimension of the compensator.
Abstract: The purpose of this paper is to present a homotopy algorithm for solving the Optimal Projection Equations. Questions of existence and the number of solutions will also be examined. It will be shown that the number of stabilizing solutions to the given Optimal Projection Equations can be determined and that all solutions can be computed via a homotopic continuation from a simple problem. For an important special case, where the number of inputs or the number of outputs to the system is less than or equal to the dimension of the compensator, there is only one solution to the OPE, thus guaranteeing that globally optimum reduced order controller can be computed.

Journal Article•DOI•
10 Jun 1987
TL;DR: In this paper, a unified theory of control synthesis for generalized linear (i.e. descriptor) systems using constant-ratio proportional and derivative (CRPD) feedback is presented, which includes the theory of static state feedback and output feedback.
Abstract: We present a unified theory of control synthesis for generalized linear (i.e. descriptor) systems using constant-ratio proportional and derivative (CRPD) feedback. Our framework includes the theory of static state feedback and output feedback for regular state-space systems as a special case. The main elements of this theory include (1) a covering of the space of all systems, both regular and singular, by a family of open and dense subsets indexed by the unit circle; (2) a group of transformations which may be viewed as symmetries of the cover; (3) an admissible class of feedback transformations on each subset which is specifically adapted to that subset. We obtain a general procedure of control synthesis of CRPD feedback for generalized linear systems which uses the symmetry transformations to systematically reduce each synthesis problem to an ordinary static state feedback (or output feedback) synthesis problem for a corresponding regular system. We apply this approach to obtain natural generalizations of the Disturbance Decoupling Theorem, the Pole Assignment Theorem, and the Brunovsky Classification Theorem.

Proceedings Article•DOI•
10 Jun 1987
TL;DR: In this paper, the authors introduce some extensions of? analysis for LTI systems with structured uncertainty to time varying and nonlinear systems, and they introduce some new extensions of LTI analysis for non-linear systems as well.
Abstract: This paper introduces some new extensions of ? analysis for LTI systems with structured uncertainty to time varying and nonlinear systems.

Journal Article•DOI•
10 Jun 1987
TL;DR: In this paper, certain quantitative relationships between Euclidean condition number and block relative gains are established. And an as yet unproven relation of this type is conjectured, and the control theoretic implications of the established relations are briefly discussed, clarifying the role of the block relative gain concept in control theory.
Abstract: Given an arbitrary nonsingular complex matrix, certain quantitative relationships between its Euclidean condition number and its associated block relative gains are established. In addition, an as yet unproven relation of this type is conjectured. The control theoretic implications of the established relations are briefly discussed, clarifying the role of the block relative gain concept in control theory.

Proceedings Article•DOI•
01 Jan 1987

Proceedings Article•DOI•
10 Jun 1987
TL;DR: Model Reference Control Using Time Delay (MRC/TD) as mentioned in this paper is a control method for nonlinear plants with unknown dynamics that uses time delay to estimate the unknown dynamics and the unexpected disturbance.
Abstract: The control of systems with unknown dynamics is an important issue, particularly in applications where large parameter variations and unexpected disturbances are possible. Several methods have been developed for such cases. These include adaptive control, variable structure control and learning control. This paper first defines this control problem and then proposes a new method - Model Reference Control Using Time Delay (MRC/TD) for nonlinear plants with unknown dynamics. This method will not requireparameter identification, unnecessary discontinuous control or repetative actions. The main feature of the MRC/TD is the direct estimation of the unknown dynamics and the unexpected disturbance. This is accomplished using time delay. This estimation is then used by the controller to cancel both the undesired dynamics and disturbance and to insert the desired dynamics into the plant. The MRC/TD control law for nonlinear plants is presented and the stability analysis and design procedure are given for SISO linear plants. Finally, the validity of MRC/TD is verified through both simulations and experiments.

Journal Article•DOI•
10 Jun 1987
TL;DR: In this article, the stability of nonlinear multiparameter singularly perturbed systems is analyzed and sufficient conditions for existence of a Lyapunov function and uniform asymptotic stability are derived.
Abstract: Asymptotic stability of nonlinear multiparameter singularly perturbed systems is analyzed. Sufficient conditions for existence of a Lyapunov function and uniform asymptotic stability are derived. The new feature of these conditions over earlier results is that there is no restriction on the relative magnitudes of the small singular perturbation parameters. Moreover, the class of systems under consideration can be nonlinear in both the slow and fast variables, while earlier results were limited to systems linear in the fast variables.

Journal Article•DOI•
10 Jun 1987
TL;DR: Two expert systems are used to monitor two industrial processes, looking for problems, and experience with these expert systems has led to practical results and to some lessons for using expert systems for process control.
Abstract: Two expert systems are used to monitor two industrial processes, looking for problems. The processes are an adipic acid reactor and a heat exchanger. When a problem occurs, the process operator is alerted and is told the problem and its probable cause. Expert systems have also been used to tune proportional-integral-derivative controllers and to help select flow meters to suit customer requirements. Experience with these expert systems has led to practical results and to some lessons for using expert systems for process control. The lessons form the bulk of the paper and deal with limits to expert systems, how and where expert systems fit in, knowledge-base engineering, and software engineering for expert systems.

Journal Article•DOI•
10 Jun 1987
TL;DR: In this article, a robust stability and performance analysis technique for harmonic oscillators with uncertain but constant natural frequency was developed. And the authors proved that the majorant Lyapunov equation predicts unconditional stability.
Abstract: A new robust stability and performance analysis technique is developed. The approach involves replacing the state covariance by its block-norm matrix, i.e., the nonnegative matrix whose elements are the norms of subblocks of the covariance matrix partitioned according to subsystem dynamics. A bound (i.e., majorant) for the block-norm matrix is given by the majorant Lyapunov equation, a Lyapunov-type nonnegative matrix equation. Existence, uniqueness, and computational tractability of solutions to the majorant Lyapunov equation are shown to be completely characterized in terms of M matrices. Two examples are considered. For a damped simple harmonic oscillator with uncertain but constant natural frequency, the majorant Lyapunov equation predicts unconditional stability. And, for a pair of nominally uncoupled oscillators with uncertain coupling, the majorant Lyapunov equation shows that the range of nondestabilizing couplings is proportional to the frequency separation between the oscillators, a result not predictable from quadratic or vector Lyapunov functions.

Journal Article•DOI•
Fred Daum1•
10 Jun 1987
TL;DR: In this article, an exact expression for the unnormalized conditional density is derived for certain nonlinear estimation problems using separation of variables, which is a generalization of the Kalman-Bucy filter, the Benes filter and other nonlinear filters within a unified framework.
Abstract: An exact expression for the unnormalized conditional density is derived for certain nonlinear estimation problems. The basic method is to solve the Zakai equation using separation of variables. The new filter is a generalization of the Kalman-Bucy filter, the Benes filter, and other nonlinear filters within a unified framework.

Proceedings Article•DOI•
10 Jun 1987
TL;DR: In this paper the decentralized control problem is formulated as a series of independent designs, and simple bounds on these individual designs are derived, which when satisfied, guarantee robust performance of the overall system.
Abstract: Decentralized control systems have fewer tuning parameters, are easier to understand and tune, and are more easily made failure tolerant than general multivariable control systems. In this paper the decentralized control problem is formulated as a series of independent designs. Simple bounds on these individual designs are derived, which when satisfied, guarantee robust performance of the overall system. The results provide a generalization of the ?-Interaction Measure introduced by Grosdidier and Morari (1986).

Proceedings Article•DOI•
10 Jun 1987
TL;DR: A method for control employing rule-based search is reviewed, and a Rule-Based Controller achieving economical real-time performance is described, applicable to a large class of complex control problems.
Abstract: A method for control employing rule-based search is reviewed, and a Rule-Based Controller achieving economical real-time performance is described. Code optimization, in the form of LISP-to-Pascal knowledge base translation, provides real-time search execution speed and a processing environment enabling highly integrated symbolic and numeric computation. With a multiprocessor software architecture specifying rule-based protocol for control task communication, and a hardware architecture providing concurrent implementation within a multi-microprocessor system, the controller realizes a set of cooperating real-time expert systems. Based on experience gained through the design and implementation of a Rule-Based Flight Control System, the proposed approach appears applicable to a large class of complex control problems.

Proceedings Article•DOI•
10 Jun 1987
TL;DR: In this article, a model reference adaptive control scheme for nonlinear systems in a pure-feedback canonical form with unknown parameters is presented, where the presence of parameter uncertainty in the system causes imperfect linearization, i.e., it introduces nonlinear additive terms in the transformed coordinates.
Abstract: We present a model reference adaptive control scheme for nonlinear systems in a pure-feedback canonical form with unknown parameters. The presence of parameter uncertainty in the system causes imperfect linearization, i.e., it introduces nonlinear additive terms in the transformed coordinates. Provided that these nonlinear terms are dominated by the norm of the transformed state, we establish global convergence of the output error for all initial estimates of the parameter vector lying in an open neighborhood of the true parameters in the parameter space.

Proceedings Article•DOI•
10 Jun 1987
TL;DR: Taking the Bayesian approach in solving the discrete-time parameter estimation problem has two major results: the unknown parameters are legitimately included as additional system states, and the computational objective becomes calculation of the entire posterior density instead of just its first few moments.
Abstract: Taking the Bayesian approach in solving the discrete-time parameter estimation problem has two major results: the unknown parameters are legitimately included as additional system states, and the computational objective becomes calculation of the entire posterior density instead of just its first few moments. This viewpoint facilitates intuitive analysis, allowing increased qualitative understanding of the system behavior. With the actual posterior density in hand, the true optimal estimate for any given loss function may be calculated. While the computational burden may preclude on-line use, this provides a clearly justified baseline for comparison. These points are demonstrated by analyzing a scalar problem with a single unknown, and by comparing an established point estimator's performance to the true optimal estimate.

Proceedings Article•DOI•
10 Jun 1987
TL;DR: In this article, an adaptive pulse width control (PWC) scheme was developed based on the relationship between the displacement of a control object due to a single pulse input and the pulse width.
Abstract: The conventional linear digital control fails to provide precise positioning of a control object under the influence of static friction, Coulomb friction and backlash. This paper presents an adaptive pulse width control (PWC) scheme. This scheme is developed based on the relationship between the displacement of a control object due to a single pulse input and the pulse width. The coefficient appearing in this relationship is estimated by a parameter adaptation algorithm. Sufficient conditions for asymtotic stability of this adaptive scheme is developed using Popov hyperstability theorem. This adaptive PWC is tested on a laboratory positioning table and is shown to be effective.

Proceedings Article•DOI•
10 Jun 1987
TL;DR: An approach is presented to the problem of designing a robust control using on-line measurements and an analysis is presented which establishes conditions under which the proceedure will actually converge to a satisfactory robust design.
Abstract: An approach is presented to the problem of designing a robust control using on-line measurements The idea is to use standard methods of parametric system identification to obtain a nominal estimate of the plant transfer function Non-parametric spectral methods are then used to obtain a frequency domian expression for model uncertainty If the model uncertainty exceeds a specified frequency bound, which has been predetermined from the nominal model and the performance criteria, then data filters used in the system identification are modified and the proceedure is repeated An analysis is presented which establishes conditions under which the proceedure will actually converge to a satisfactory robust design An example is provided which illustrates the method and supporting analysis