Showing papers presented at "Mediterranean Conference on Control and Automation in 1999"

2-Sliding Mode with Adaptation *

Abstract: Sliding mode is used in order to retain a dynamic system accurately at a given constraint and is the main operation mode in variable structure systems. Such mode is a motion on a discontinuity set of a dynamic system and features theoretically-infinite-frequency switching. The standard sliding modes are known to feature finite-time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. In realization their sliding precision is proportional to the time interval between measurements. Having generalized the notion of sliding mode, higher order sliding modes preserve or generalize its main properties and remove the chattering effect. With discrete measurements they may provide for up to the rth order of sliding precision with respect to the measurement interval. The main implementation problem of these modes is the information demand growing with the sliding order. If the aim is to nullify some output variable σ then r-sliding mode realization generally requires measurements of the time derivatives of up to the ( r-2)th order of σ to be available. A new approach demonstrated in the paper provides for 3-sliding accuracy realization while only σ itself is available. That is the first controller of such kind.

Stable Inversion of MIMO Linear Discrete Time Non-Minimum Phase Systems

Abstract: A novel technique to achieve output tracking via stable inversion of non-minimum phase linear systems is presented wherein the desired signal is obtained from field measurements, and hence corrupted by noise. The earlier approach to stable inversion does not take into account the noise in the system. The unknown input decoupled observer approach is applicable only to minimum phase systems. Moreover, the unobservable states are inadequately constructed resulting in inferior output tracking in the presence of noise. In this paper we extend this procedure to non-minimum phase systems. We present the novel Stable Dynamic model Inversion (SDI) approach which is applicable to non-minimum phase systems, and takes into account the presence of noise in target time histories.

Initialization and Model Reduction for Wiener Model Identification

Abstract: The identification of nonlinear systems by the minimization of a predictionerror criterion suffers from the problem of local minima. To get a reliableestimate we need good initial values for the parameters. In this paper wediscuss the class of nonlinear Wiener models, consisting of a linear dynamicsystem followed by a static nonlinearity. By selecting a parameterizationwhere the parameters enter linearly in the error, we can obtain an initialestimate of the model via linear regression. An example shows that thisapproach may be preferential to trying to estimate the linear system directlyform input-output data, if the input is not Gaussian. We discuss some of theusers choices and how the linear regression initial estimate can be convertedto a desired model structure to use in the prediction error criterionminimization. The method is also applied to experimental data.

Improving Efficiency in the Computation of Piecewise Quadratic Lyapunov Functions

Abstract: In a series of papers, the authors have developed a method for analysis of piecewise linear systems. The idea is to use Lyapunov functions that are piecewise quadratic. Such Lyapunov functions can be computed via convex optimization in terms of linear matrix inequalities. This paper presents two approaches for improving the efficiency of these computations. It is shown that by splitting the analysis computations into two distinct steps, one can decrease the computations with roughly 50% essentially without introducing conservatism. By using ellipsoidal boundings rather than polyhedral descriptions of the operating regimes, it is possible to reduce the computations even further. Combined, the two approaches allow the computation times to be reduced with an order of magnitude compared to previous formulations. However, it is shown that the use of ellipsoidal cell boundings in the S-procedure introduces conservatism in comparison with analysis based on polytopic region descriptions. An explicit formula for the minimal volume ellipsoid containing a simplex is also given, together with a complete proof.

A Feedforward-Feedback Interpretation of a Sliding Mode Control Law

Abstract: In this paper we provide a feedforward-feedback interpretation of a sliding mode control scheme. Given a desired trajectory, the feedforward signal is generated using a stable inversion method, and the feedback signal includes the switching term of the sliding mode control law. In this manner, we introduce robustness into the stable inversion technique. This approach is motivated by the need to replicate time signals typically in the automobile industry. The application of such an interpretation to a quarter car benchmark model yields encouraging results. Special attention will be given to non-minimum phase systems illustrated by a simulation example of the lunar roving vehicle.

Deep Space Control Challenges of the New Millennium

Abstract: The exploration of deep space presents a variety of significant control challenges. Long communication delays coupled with challenging new science objectives require high levels of system autonomy and increasingly demanding pointing and control capabilities. Historically, missions based on the use of a large single spacecraft have been successful and popular since the early days of NASA. However, these large spacecraft missions are currently being displaced by more frequent and more focused missions based on the use of smaller and less expensive spacecraft designs. This trend drives the need to design smart software and good algorithms which together with the miniaturization of control components will improve performance while replacing the heavier and more expensive hardware used in the past. NASA's future space exploration will also include mission types that have never been attempted before, posing significant challenges to the underlying control system. This includes controlled landing on small bodies (e.g., asteroids and comets), sample return missions (where samples are brought back from other planets), robotic exploration of planetary surfaces (e.g., intelligent rovers), high precision formation flying, and deep space optical interferometry, While the control of planetary spacecraft for traditional flyby and orbiter missions are based on well-understood methodologies, control approaches for many future missions will be fundamentally different. This paradigm shift will require completely new control system development approaches, system architectures, and much greater levels of system autonomy to meet expected performance in the presence of significant environmental disturbances, and plant uncertainties. This paper will trace the motivation for these changes and will layout the approach taken to meet the new challenges. Emerging missions will be used to explain and illustrate the need for these changes.

Nonlinear Identification of the Position Sled Dynamics of a CD Player

Abstract: Abstract This contribution concerns the identification of the dynamics of a sled carrying the optics housing of a CD player. The memory access time of the CD player depends, among other factors, on the settling time of the sled after a step change. This contribution focusses on the oscillations at the end of a step response. Measured closed-loop data are used to identify different types of black-box models of the sled dynamic. First linear models are concerned, and then different types of nonlinear models. The different types of models are compared and discussed. Due to poor excitation of the plant, some conclusions are uncertain. However, it is clear that the nonlinear models give better simulation performance on validation data than the linear ones. Also, the oscillations at the end of a step response seem to be controller induced. Therefore, it seems appropriate to use different models, and then also different controllers, at different parts of a step response.