Showing papers presented at "American Control Conference in 1997"

A non-divergent estimation algorithm in the presence of unknown correlations

Abstract: This paper addresses the problem of estimation when the cross-correlation in the errors between different random variables are unknown. A new data fusion algorithm, the covariance intersection algorithm (CI), is presented. It is proved that this algorithm yields consistent estimates irrespective of the actual correlations. This property is illustrated in an application of decentralised estimation where it is impossible to consistently use a Kalman filter.

Finite-time stability of homogeneous systems

Abstract: Examines finite-time stability of homogeneous systems. The main result is that a homogeneous system is finite-time stable if and only if it is asymptotically stable and has a negative degree of homogeneity.

State-dependent Riccati equation techniques: an overview

Abstract: State-dependent Riccati equation (SDRE) techniques are rapidly emerging as general design methods which provide a systematic and effective means of designing nonlinear controllers, observers, and filters. This paper provides an overview of several SDRE design techniques including SDRE nonlinear regulation, SDRE nonlinear H/sub /spl infin//, SDRE nonlinear H/sub 2/, and SDRE nonlinear filtering.

Robust, fragile or optimal?

Abstract: We show by examples that optimum and robust controllers, designed by using the H/sub 2/, H/sub /spl infin//, l/sup 1/ and /spl mu/ formulations, can produce extremely fragile controllers, in the sense that vanishingly small perturbations of the coefficients of the designed controller destabilize the closed loop control system. The examples show that this fragility also usually manifests itself as extremely poor gain and phase margins of the closed loop system.

Advanced gain-scheduling techniques for uncertain systems

Abstract: The paper is concerned with the design of gain-scheduled controllers for linear parameter-varying systems. Two alternative LMI characterizations are investigated. Both characterizations are amenable to a finite number of LMI conditions either via a gridding of the parameter range or via grid-free techniques which rely on multi-convexity concepts. Practicality and implementation issues are discussed and examples are provided.

A rule-based energy management strategy for a series hybrid vehicle

Abstract: A rule-based control and energy management strategy for a series hybrid vehicle is presented. The strategy is based on splitting the power demand between the engine and the battery such that these power sources are operated at high efficiency. The power demand is estimated as the output of a high gain PI controller that controls the longitudinal acceleration of the vehicle. The focus was to improve the fuel economy of the vehicle by suitable power assignment to the power sources. This power split (assignment) is implemented under a rule-base frame. The rules depend on the values of selected variables: the power demand itself, the driver's acceleration command and the status of the SOC (state of charge) of the battery. The rules ensure that the engine and the battery operate at high efficiency whenever possible. At high power demand the engine will operate at its maximum rated power. Simulation results of the proposed strategy showed improvement in fuel economy over the "thermostat" strategy. An improvement of 11% in the urban cycle and of 6% in the highway cycle have been achieved for a series hybrid vehicle driven by a 40 KW diesel engine and a 60 kW lead acid battery.

Dynamic surface control of nonlinear systems

Abstract: A method is proposed for designing stable controllers with arbitrarily small tracking error for uncertain, mismatched nonlinear systems. This method is another "synthetic input technique", similar to backstepping and multiple surface control methods, but with an important addition, r-1 low pass filters are included in the design, where r is the relative degree of the output to be controlled. It is shown that these low pass filters allow a design where the model is not differentiated, thus ending the complexity arising due to the "explosion of terms" that has made other methods difficult to implement in practice. This paper presents the method and proves stability via a composite Lyapunov method.

Piecewise linear quadratic optimal control

Abstract: A technique for computation of piecewise quadratic Lyapunov functions is further developed for performance analysis and controller synthesis for nonlinear systems. In this way, degree of observability is estimated, L/sub 2/ induced gain is computed and optimal control problems are solved. The computations are based on convex optimization in terms of linear matrix inequalities.

Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion

Abstract: Develops a methodology for recursive construction of optimal and near-optimal controllers for strict-feedback stochastic nonlinear systems under a risk-sensitive cost function criterion. The design procedure follows the integrator backstepping methodology, and the controllers obtained guarantee any desired level of long-term average cost, for a given risk-sensitivity parameter /spl theta/. Furthermore, they lead to closed-loop system trajectories that are bounded in probability, and in some cases asymptotically stable in the large. These results also generalize to nonlinear systems with strongly stabilizable zero dynamics.

The model-free learning adaptive control of a class of SISO nonlinear systems

Abstract: The model-free learning adaptive control of a class of nonlinear systems is presented in this paper based on a new concept of partial derivative called 'pseudo-partial-derivative'. The BIBO stability of the regulator are proved.

High performance robust motion control of machine tools: an adaptive robust control approach and comparative experiments

Abstract: Studies the high performance robust motion control of machine tools. Instead of the disturbance observer (DOB) design previously tested by many researchers, a newly proposed adaptive robust control (ARC) is applied to make the resulting closed-loop system robust to model uncertainties. Compared to DOB, the proposed ARC has a better tracking performance and transient in the presence of discontinuous disturbances such as Coulomb friction and it is of a lower-order. As a result, time-consuming and costly rigorous friction identification and compensation is alleviated and overall tracking performance is improved. The ARC design can also handle large parameter variations and is flexible in introducing extra nonlinear robust control terms and parameter adaptations to further improve the transient response and tracking performance. An anti-integration windup mechanism is built in the ARC and thus the problem of control saturation is alleviated. Extensive comparative experimental tests are performed and the results show the superior performance of the proposed ARC.

A linear programming characterization of all stabilizing PID controllers

Abstract: The YJBK parametrization characterizes all stabilizing controllers. In industry, most controllers are PID and there is no solution to the problem: can a plant P(s) be stabilized by a PID controller? In this paper, we provide an answer to this question. Besides settling the question of existence, we provide a computationally constructive characterization of all stabilizing PID controllers that stabilize a given plant. Thus this result is essentially an extension of the YJBK characterization restricted to PIDs and opens up the possibility of optimal design using PIDs.

A game theoretic approach to nonlinear robust receding horizon control of constrained systems

Abstract: In this paper, we present an approach to synthesize a nonlinear model predictive controller with guaranteed robust stability, where uncertainty and input constraints are explicitly included in the formulation of the optimization problem. Conceptually, this approach can be viewed as a suitable combination of nonlinear MPC and H/sub /spl infin// control.

LMI for stability and robustness of hybrid systems

Abstract: This paper presents results for stability and robustness of hybrid systems consisting of nonlinear subsystems. Present stability results that are extensions of classical Lyapunov theory are restricted to certain kinds of hybrid systems. For example, it is required that all subsystems have the same equilibrium point. In this paper these results are generalized, but more importantly, it is shown how Lyapunov functions for hybrid systems can be solved by linear matrix inequalities (LMI). Furthermore, it is shown how uncertainties around the nominal switch sets can be handled by introducing acceptable switch regions as additional stability conditions. The theory is illustrated by an example.

Bounded real lemma and H/sub /spl infin// control for descriptor systems

Abstract: The purpose of this paper is to give a necessary and sufficient condition under which for a given plant of descriptor system model there exists a normal, internally stabilizing controller that has an upper limit on its order and that satisfies a closed-loop H/sub /spl infin// norm bound. The approach used in this paper is based on a generalized version of bounded real lemma, thus the proofs are simple.

Input shaped control of a planar gantry crane with hoisting

Abstract: The dynamic behavior of a planar gantry crane with hoisting of the load is investigated. The feedforward technique of input shaping is proposed for reduction of the residual vibration. Several versions of input shaping are evaluated and compared with time-optimal rigid-body commands over a wide range of parameters. Input shaping offers significant reduction in both, the residual and transient oscillation.

Numerical comparison of output feedback design methods

Abstract: This paper aims to provide a fair comparison of several output feedback design methods available in the literature to date. The methods solve a set of benchmark problems which require closed loop stabilization. The comparison and the final classification are made in terms of numerical efficiency. Practical as well as theoretical aspects of convergence are discussed.

Solution of coupled Lyapunov equations for the stabilization of multimodal linear systems

Abstract: The paper discusses stabilization of linear multimodal systems using a control law that selects a particular system mode. The systems considered are similar to jump linear systems. In a jump linear system the active mode is selected by a random process. Here, the controller uses a piecewise quadratic Lyapunov function to select the system mode to activate. The paper relates existence of a stabilizing control law to the solution of a pair of coupled Lyapunov equations. Solution of these equations is discussed and related to the location of the eigenvalues of certain matrix operators derived from the component system matrices and the coupling parameter. Relationships to earlier work by the authors (1994) is discussed.

The use of sliding modes to simplify the backstepping control method

Abstract: We propose a simple sliding mode based controller for nonlinear systems with mismatched uncertainties. The design methodology is similar to backstepping and multiple surface control method but with the inclusion of sliding mode filters for estimating the derivatives of the plant output.

A general framework for automatic steering control: system analysis

Abstract: In this paper, steering control for passenger cars on automated highways is analyzed, concentrating on look-down reference systems. Extension of earlier experimental results for low speed to highway speed is shown to be nontrivial. The limitations of pure output-feedback of lateral vehicle displacement from the road reference are examined under practical constraints and performance requirements such as robustness, maximum lateral error and passenger comfort. The in-depth system analysis directly leads to a new alternative design direction which allows to harness the benefits of look-ahead reference systems for look-down highway speed automatic driving.

Potential benefits of hybrid control for linear time invariant plants

Abstract: A question which has bothered control researchers for some time is whether hybrid control offers any advantage over linear control for linear plants. We show in this paper, via several examples, that hybrid control can indeed overcome certain types of limitation which are unavoidable if linear feedback control is used.

Traffic-responsive signal timing for system-wide traffic control

Abstract: Due to the many complex aspects of a traffic system, it has been difficult to determine the optimal signal timing. Much of this difficulty has stemmed from the need to build extremely complex models of the traffic dynamics as a component of the control strategy. This paper presents a fundamentally different approach for optimal signal timing that eliminates the need for such complex models. The approach is based on a neural network serving as the basis for the control law, with the weight estimation occurring in closed-loop mode via the simultaneous perturbation stochastic approximation (SPSA) algorithm. Since the SPSA algorithm requires only loss function measurements, there is no system-wide model required for the weight estimation.

On the current status of magnetorheological dampers: seismic protection of full-scale structures

Abstract: Because of their mechanical simplicity, high dynamic range, low power requirements, large force capacity and robustness, magnetorheological (MR) fluid dampers have been shown to be semi-active control devices that mesh well with application demands and constraints to offer an attractive means of protecting civil infrastructure systems against severe earthquake and wind loading. Following an overview of the essential features of MR fluids, this paper discusses the current status of this new technology for seismic protection of structures, including presentation of recent laboratory studies employing a seismically-excited, scale-model building and preliminary analyses of a prototype full-scale MR damper.

Experiments and simulations on the nonlinear control of a hydraulic servosystem

Abstract: Presents the derivation, simulation and implementation of a nonlinear tracking control law for a hydraulic servosystem. An analysis of the nonlinear system equations is used in the derivation of a Lyapunov function that provides for exponentially stable force trajectory tracking. This control law is then extended to provide position tracking. The proposed controller is simulated and then implemented on an experimental hydraulic system to test the limits of its performance and the realistic effects of friction.

Optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation

Abstract: The simultaneous perturbation stochastic approximation (SPSA) algorithm has recently attracted considerable attention for optimization problems where it is difficult or impossible to obtain a direct gradient of the objective (say, loss) function. The approach is based on a highly efficient simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo process. The objective is to minimize the mean square error of the estimate. We also consider maximization of the likelihood that the estimate be confined within a bounded symmetric region of the true parameter. The optimal distribution for the components of the simultaneous perturbation vector is found to be a symmetric Bernoulli in both cases. We end the paper with a numerical study related to the area of experiment design.

A review of three PWM techniques

Abstract: Concerns switching power converters for motor drives. Three commonly used PWM techniques, sinusoidal PWM technique, space vector PWM technique and hysteresis (bang-bang) PWM technique, are discussed in this paper with emphasis on implementation. Experimental results are presented for all three PWM techniques.

Steady-state target optimization in linear model predictive control

Abstract: For practical model predictive control applications, a receding horizon regulator must be able to handle nonzero controlled variable targets and nonsquare systems in a consistent manner. This work presents a steady-state target optimization that determines the steady-state state and input targets for a constrained, linear, state-space regulator.

Input shaper designs for minimizing the expected level of residual vibration in flexible structures

Abstract: The method of input shaping has been shown to yield good performance in the control of flexible structures while being insensitive to modeling errors. However, previous studies do not take into account the distributions of the parameter variations. We develop an input shaping method that allows the ranges of system parameter values to be weighted according to the expected modeling errors. Comparisons with previously proposed input shaper designs in terms of shaper length, frequency insensitivity, and expected level of residual vibration are presented, illustrating the qualities of the new input shaper design method.

Models for hysteresis and application to structural control

Abstract: Hysteresis is a phenomenon common to a broad spectrum of physical systems. As such, it is often present in plants for which controllers are being designed, where it introduces a problematic nonlinear multivalued behavior. Continuing research into nonlinear systems is generating an increasing interest in the control of hysteretic plants. Herein, there is a broad twofold focus: to obtain general and tractable models of hysteresis capable of accurately describing a variety of hysteretic phenomena, and then to derive corresponding control designs and supporting analytical results. This paper presents mathematical definitions and illustrative descriptions of four general hysteresis models: the hysteron, Bouc-Wen, Chua-Stromsmoe and Preisach models. Each model is capable of representing a great many forms of hysteretic behavior, and is also mathematically tractable enough for control design. As an example, the Bouc-Wen model is used to develop a semi-active structural control model for a magnetorheological damper attached to a three-story scaled building.

Robust adaptive control of uncertain nonlinear systems using neural networks

Abstract: This paper describes a hybrid approach to the problem of controlling a class of nonlinear systems in the face of both unknown nonlinearities and unmodeled dynamics. In the proposed methodology, neural networks and direct adaptive control compensate for unknown nonlinear mappings while dynamic nonlinear damping provides robustness to unmodeled dynamics. To illustrate the theoretical development, the authors design a longitudinal autopilot for a simplified nonlinear missile aerodynamic model with input unmodeled dynamics. Simulation results demonstrate robustness in the face of this type of uncertainty.