Showing papers presented at "American Control Conference in 1989"

Integrator Windup and How to Avoid It

Abstract: This paper describes the phenomenon of integrator windup and various ways of avoiding it. It first covers a number of ad hoc schemes. A general procedure to avoid windup which admits a unification of the ideas is given and the results are illustrated on a number of examples.

Digital Control Of Repetitive Errors In Disk Drive Systems

Abstract: Tracking errors in disk drive systems have a significant repetitive component that is not explicitly taken into account in conventional servo controllers. Three specialized digital controllers applied as plug-in modules to a winchester disk drive with a pre-existing analog feedback controller to demonstrate their efficacy in the reduction of this periodic component. These controllers include the discrete time repetitive controller which is based on the internal model principle and feedforward cancellation controllers based on an adaptive prediction algorithm and on input and output measurements of the system.

Use of Neural Nets For Dynamic Modeling and Control of Chemical Process Systems

Abstract: Neural nets are inherently parallel and they hold great promise because of their ability to "learn" nonlinear relationships This paper discusses the use of backpropagation neural nets for dynamic modeling and control of chemical process systems The backpropagation algorithm and its rationale are reviewed The algorithm is applied succesfully to model the dynamic response of pH in a CSTR The use of backpropagation models for control is briefly discussed

Controlled Impedance Test Apparatus for Studying Human Interpretation of Kinesthetic Feedback

Abstract: Many feedback control systems, especially those for complex applications, involve humans in the control loop. Visual information traditionally has been presented to human controllers who make manual responses (i.e., via keyboard, joystick, or other interfaces). To expand system bandwidth, other information channels can be presented so human operators. Kinesthesis, the perception of body positions and forces, represents an attractive supplementary form of human-machine communication, since the limbs (e.g., an operator's hand) can be used both for input and output of information in the control loop. Although psychophysical studies have measured perception of isolated mechanical properties, limited work has been conducted to study human kinesthetic abilities in the context of control. The research described here assesses judgement of coupled properties, including the superposition of linear stiffness, damping, and inertia. Quantitative perception of these properties may depend upon correct models of the mechanical system with which a user interacts. Similarly, perception of fundamental mechanical properties may be influenced by system delays (on the order of magnitude of human reaction time). This paper describes both an apparatus for understanding kinesthetic interaction with mechanical systems and an approach for studying human perception of mechanical properties.

Neural Network Control of Unknown Nonlinear Systems

Abstract: A method for using neural networks to control unknown dynamic systems is presented. The method can be regarded as an adaptive controller for time-invariant nonlinear systems with completely unknown dynamics, except for the system order. A backpropagation neural network is used to model the unknown nonlinear system on-line, based on a functional representation relating plant inputs to plant outputs. The same neural network is used to generate the control signals given the measurements of the current states and the desired values of future states. Although a backpropagation network with supervised learning is used, the training is based on measurement data obatined during the system operation, so that there is no need for an outside "teacher" telling the neural controller about the correct control signals.

Multivariable Anti-Windup and Bumpless Transfer: A General Theory

Abstract: A general theory is developed to address the anti-windup/bumpless transfer (AWBT) problem. Analysis results applicable to any linear time invariant system subject to plant input limitations and substitutions are presented. Quantitative performance objectives for AWBT compensation are outlined and several proposed AWBT methods are evaluated in light of these objectives. A synthesis procedure which highlights the performance trade-offs for AWBT compensation design is outlined.

Closed-Loop Identification via the Fractional Representation: Experiment Design

Abstract: An important aspect of system identification is the problem of experiment design. This paper uses a fractional representation approach to state and solve the closed-loop experiment design problem in terms of variables which are at the designer's disposal: the closed-loop inputs and the initial controller. Results of computer simulations are presented which compare optimal versus several non-optimal identification experiments.

Neural Networks for System Identification

Abstract: Recent advances in the software and hardware technologies of neural networks have motivated new studies in architecture and applications of these networks. Neural networks have potentially powerful characteristics which can be utilized in the development of our research goal, namely, a true autonomous machine. Machine learning is a major step in this development. This paper presents the results of our recent study on neural-network-based machine learning. Two approaches for learning and identification of dynamical systems are presented. A Hopfield network is used in a new identification structure for learning of time varying and time invariant systems. This time domain approach results in system parameters in terms of activation levels of the network neurons. The second technique, which is in frequency domain, utilizes a set of orthogonal basis functions and Fourier analysis network to construct a dynamic system in terms of its Fourier coefficients. Mathematical formulations of each technique and simulation results of the networks are presented.

Modelling and Self-Tuning Control of a Multivariable pH Neutralization Process Part I: Modelling and Multiloop Control

Abstract: This paper describes the design, modelling and control of a multivariable pH neutralization process. The experimental facility consists of two stirred tank reactors with an acid-base neutralization taking place in each tank. The process has been designed as a demonstration unit for the evaluation of advanced Control strategies such as adaptive and multivariable control. The neutralization process has four controlled variables, pH and liquid level in each of the two tanks. This strong acid, strong base neutralization poses a difficult multivariable problem because each manipulated variable has a significant effect on each controlled output. This process is also highly nonlinear and time varying due to the inherent nonlinearity associated with pH control and the shifts in the titration curve that occur when the amount of buffering agent changes in an unpredictable fashion. A physical model of the neutralization process has been developed which is in good agreement with experimental step response data over a wide range of experimental conditions. A multiloop control system consisting of four PID controllers was tedious to tune and had difficult coping with changes in the amount of buffering. In a companion paper (Hall and Seborg, 1989), self-tuning control resulted in improved control especially when only the process gain was estimated on-line, assuming that the dynamics were not changing significantly.

Optimal control with mixed H 2 and H ∞ performance objectives

Abstract: This paper considers the analysis and synthesis of control systems subject to two types of disturbance signals: signals with bounded power spectral density and signals with bounded power. The resulting control problem involves minimizing a mixed H2 and H∞ norm of the system. It is shown that the controller shares a separation property similar to those of pare H2 or H∞. controller. It is also shown that the mixed problem reduces naturally to H2 and H∞ problem in special cases. Some necessary and sufficient conditions are obtained for the existence of a solution to the mixed problem. Explicit state space formulae are given for the optimal controllers.

Steady-state kalman filtering with an H ∞ error bound

Abstract: An estimator design problem is considered which involves both L2 (least squares) and H∞ (worst-case frequency-domain) aspects. Specifically, the goal of the problem is to minimize an L2 state-estimation error criterion subject to a prespecified H∞ constraint on the state-estimation error. The H∞ estimation-error 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 the L2 state-estimation error. The principal result is a sufficient condition for characterizing fixed-order (i.e., full- and reduced-order) estimator with bounded L2 and H∞ estimation error. The sufficient condition involves a system of modified Riccati equations coupled by an oblique projection, i.e., idempotent matrix. When the H∞ constraint is absent, the sufficient condition specializes to the L2 state-estimation result given in [2]. The full version of this paper can be found in [10].

Robust Controller Design for a Nonlinear CSTR

Abstract: A design methodology is presented for the analysis and synthesis of robust linear controllers for a nonlinear continuous stirred tank reactor. Regions are defined in the phase plane in which the maintenance of robust stability and the achievement of robust performance levels are guaranteed. The results are based upon new extensions of the structured singular value theory to a class of nonlinear and time-varying systems.

Optimal control with mixed H2 and H¿ performance objectives

Abstract: This paper considers the analysis and synthesis of control systems subject to two types of disturbance signals: signals with bounded power spectral density and signals with bounded power. The resulting control problem involves minimizing a mixed H₂ and H_∞ norm of the system. It is shown that the controller shares a separation property similar to those of pare H₂ or H_∞. controller. It is also shown that the mixed problem reduces naturally to H₂ and H_∞ problem in special cases. Some necessary and sufficient conditions are obtained for the existence of a solution to the mixed problem. Explicit state space formulae are given for the optimal controllers.

Robust Control of Robotic Manipulators

Abstract: This paper introduces a new control system design methodology that allows the use of linearly controlled manipulators in fast, more complex maneuvers. This is made possible by guaranteeing a prescribed degree of relative stability while constraining the system state variables and inputs. The closed-loop linear system is also assigned desirable eigenvectors. The robustness of the system is evaluated using a new measure of robustness. The design methodology is applied to a 2-D.O.F. robotic manipulator. Simulation results demonstrate that the final design must be a compromise between robustness, relative stability, and other considerations.

Control of Constrained Multivariable Systems using the Conditioning Technique

Abstract: The conditioning technique is first reviewed as a particular case of Astrom and Wittenmark's anti-windup method [11]. Then it is reformulated in terms of a "realizable" reference signal. Using this notion, a method to handle limitations on the manipulated variables of a multivariable control system is presented. The basic idea is to introduce a mapping between the space of manipulated variables and the space of reference signals, using the conditioning technique. The limits on the manipulated variables can be translated into limits on the reference signals. Thus a domain of achievable reference signals corresponds to the domain of achievable control signals. When the control signals issued by the controller yield a point outside the corresponding achievable domain, this point must be projected on the domain boundary. In the proposed method, this projection is performed so as to follow a desired strategy in the corresponding achievable space of reference signals.

Feedback Control of Nonstandard Singularly Perturbed Systems

Abstract: This paper studies feedback control of linear time-invariant singularly perturbed systems of the form ? = A 11 x + A 12 z + B 1 u ? = A 21 x + A 22 z + B 2 u y = C 1 x + C 2 z + Eu. where A 22 may be singular. It is shown that, under stabilizability-detectability assumptions on the slow and fast models, the theory of feedback control of singularly perturbed systems can be extended to the case of singular A 22 . Both state and output feedback results are given.

Model Invalidation: A Connection between Robust Control and Identification

Abstract: This paper begins to address the gap between the models used in robust control theory and those obtained from identification experiments by considering the connection between uncertain models and data. The model invalidation problem considered here is: given experimental data and a model with both additive noise and norm-bounded perturbations, is it possible that the model could produce the input/output data?

End-Point Control of a Two-Link Manipulator with a Very Flexible Forearm: Issues and Experiments

Abstract: An important consideration when designing a control system is where to place sensors. For mechanical manipulators, a logical sensor location is at the manipulator end-point where tasks are performed. Unfortunately, when bending flexibility exists between an end-point sensor and a joint actuator, stability and performance are achieved only through a sophisticated control design. Some of the issues involved in utilizing end-point sensing for two-link flexible manipulators are addressed in this paper. First, a modelling technique is presented that properly represents the foreshortening of a flexible link undergoing deflections, as are the resulting terms that appear in the equations of motion. An example illustrates how this technique corrects a simulation that otherwise incorrectly predicts that the manipulator end-point will exceed workspace limits. Next, in order to realize fully the advantages of the assumed-modes modelling method, mode shapes are selected that allow a low-order model to be used effectively for simulation and control purposes. Then, a nonlinear controller, incorporating state feedback and a constant gain extended Kalman filter driven by end-point measurements, is designed and compared to a conventional proportional-plus-derivative controller that uses collocated sensors. Finally, the results are presented from implementing these controllers on the experimental Stanford Multi-Link Flexible Manipulator configured with a rigid upper arm and a very flexible forearm.

Design of Optimal Dynamical Experiments for Parameter Estimation

Abstract: Measurement errors often lead to large uncertainties in parameter estimation for dynamical systems. However, a considerable improvement of the preciseness may be obtained by a suitable choice of the experimental conditions. An approach is given to calculate optimal input functions by solving a minimization problem, based on a calculation of the Fisher information matrix. This approach is applied to a model describing the growth of plant cells in suspension culture in a stirred tank reactor. The simple model is based on the metabolic structure, limiting rates, mass and energy balances of the cells as well as the reactor equations. A significant increase in the accuracy of the parameter estimations is shown to be possible by fed batch experiment design using the method indicated above, compared to the accuracy which could be obtained using batch experimental data.

Polytopes of Nonnegative Polynomials

Abstract: Algebraic, recursive, and finite tests are proposed to verify if a convex polytope in the parameter space contains only axis or circle nonnegative polynomials. An extraordinary numerical simplicity of the tests is a consequence of the fact that the nonnegativity regions in the parameter space are shown to be convex, and it suffices to check only the vertex polynomials of the polytope. The tests are applied to robustness analysis of absolute stability of nonlinear continuous and discrete systems, optimality of LQ regulators, positive realness of rational functions and matrices, and positivity of polynomial matrices appearing in stability criteria for 2-D polynomials.

Minimal complexity control law synthesis, part 2: problem solution via H 2 /H ∞ optimal static output feedback

Abstract: In part 1 of this two-part paper [1] it was shown that a large class of fixed-structure control laws can be recast as static output feedback controllers for a suitably modified plant. Accordingly, we develop here a comprehensive theory for designing static output feedback controllers. Our results go beyond earlier work by addressing both H 2 and H∞ performance criteria and by accounting fully for all of the singularities in the problem formulation. The results are applied to the fixed-order problem (FoP) [1] to obtain a major unification of prior results, namely: the Bernstein-Haddad H2/H∞ fixed-order dynamic compensator theory, the Glover-Doyle full-order H∞ dynamic compensator theory, the Hyland-Bernstein H2 fixed-order dynamic compensator (optimal projection) theory, and the classical LQG theory.

Vibration Control of a Large Flexible Manipulator by a Small Robotic Arm

Abstract: The vibration of a large flexible manipulator is suppressed by inertial forces induced by the joint torques of a small arm which is located at the tip of the large manipulator. The control of the small arm is studied based on a slow and fast submodel which are derived by applying the singular perturbation technique. A composite controller is designed to control the slow and fast motion.

H ∞ identification of stable LSI systems: a scheme with direct application to controller design

Abstract: In this paper several techniques are given for the identification of stable LSI discrete time systems from input-output data. Explicit H∞ norm error bounds are given and convergence in the noise free and the uniformly bounded deterministic noise case are established. The assumptions made on the unknown system are minimal and are limited throughout the paper to a lower bound on the decay rate of the unknown system and an upper bound on the gain of the unknown system. Given this information an experiment and a construction are specified: the experiment involves obtaining a specified number of frequency measurements of the unknown systems at a set of specified frequencies; the construction uses this experimental data to generate an identified model with prescribed H∞ norm error tolerance to the unknown system. The resulting model identification process is highly efficient from a computational point of view.

Nonlinear Predictive Control of a Semi Batch Polymerization Reactor by an Extended DMC

Abstract: In this paper a new nonlinear model predictive control law is applied to a semi-batch polymerization reactor. The particular model used in this study is the free radical polymerization of polymethylmethacrylate. The principal nonlinearities are due to the reaction rates and the gel effect. Two cases are considered: jacket temperature controlling the reaction temperature, and a MIMO structure where both the reaction temperature and the molecular weight are controlled by the jacket temperature and the initiator feed. The proposed control algorithm uses an explicit nonlinear process model and some of the elements of the classical DMC to solve the nonlinear input-output operator equation without computing the derivatives of the states and output equations. Constraints are not included in the present method.

Idle Speed Control Design using an H-Infinity Appoach

Abstract: This paper considers the design of an idle speed control law for a fuel injected engine. The modelling procedure, including the use of System Identification techniques, is discussed and then emphasis is placed on the control law design using an H-Infinity approach. The choice of appropriate weighting functions is crucial in H-Infinity design and design iterations are discussed. The final control law is shown to have good performance in simulation and to be robust to parameter perturbations: it represents a good starting point for future implementations.

Quantification of Uncertainty in Estimation using an Embedding Principle

Abstract: In this paper a new method to quantify uncertainty due to undermodelling is presented The unmodelled dynamics are embedded in a general class of systems which is defined using realistic a priori information This embedding principle can be formalized in several different ways; the one presented in this paper involves the setting of a stochastic framework, where the unmodelled dynamics are taken to be a particular realization of a Stochastic Embedding Process (SEP) A priori knowledge is used to choose suitable statistics for this process This approach allows one to quantify the effect of the modelling errors on the estimated transfer function in the frequency domain The principal advantage of this approach is that it allows one to consider robust and adaptive control within the same conceptual framework

Observer-based Control of Uncertain Linear Systems: Recovering State Feedback Robustness Under Matching Condition

Abstract: In this paper we study the problem of observer design for a class of state-feedback controllers that includes high-gain linear control, continuous approximations of min-max control and continuous approximations of variable structure control. Assuming that the state-feedback controller robustly stabilizes the system in the presence of matched parametric uncertainties, we are to design the observer such that the observer-based control recovers the stability robustness of the state-feedback-control. We will show that it is possible to design such an observer, if the nominal, system is left-invertible and minimum-phase.