Fakhreddine Karray

On the robust control aspect of a class of systems involving interconnected rigid and flexible appendages: case study

A robust control procedure for precision pointing and tracking of fast moving elastic structures is proposed. Based on a combination of the sliding manifold approach with the theory of optimal interpolation, this design procedure generates a control effort capable of insuring high pointing and tracking performance in the presence of induced disturbances and modelling uncertainties. The uncertainties are handled by sliding control and estimation of the nonlinearly excited elastic elastic dynamics by an interpolator of the structure dynamic response. Chattering behaviour of the controller is avoided at the expense of tolerating a known tracking error. It is shown through analysis that a trade-off has to be set, by taking into account the main requirements of a given mission and the system hardware capabilities. For illustration purposes, a set of numerical simulations is then run to assess the system dynamical performance.

On the nonlinear system identification of a class of bilinear dynamical models

A nonlinear system identification technique based on the functional spline interpolation for dealing with high-dimensional bilinear dynamical models is described. At first, the nonlinear dynamics of a given system are transformed through Carleman bilinearization into a bilinear form. Decoupled bilinear models are then constructed, with input-output mappings expressible in closed form and with dimension determined by the number of training signals used in a prior learning stage. The motivation is given by the need for order reduction and input-output analysis of Carleman bilinearization. For illustration purposes, the technique is then applied to a forced version of Duffings equation.<<ETX>>

Nonlinear robust variable structure control of pointing and tracking with operator spline estimation

Summary form only given. Variable control (VSC) in effect consists of designing a control input based on a simplified or inaccurate dynamic model, to which a variable correction is added, based on estimates of the model errors, sufficient incipiently to overshoot the desired controlled trajectory (sliding manifold). To suppress chattering, an optimally time-varying boundary layer can be generated to contain the sliding surface, within which the corrected control is continuously interpolated. An explicit design rule (tradeoff) can then be established between tracking error tolerance and effective control bandwidth, determined by the imposed model error bounds. For rapid rotation of a deformable body, the elastic response can be moded by oscillators driven by angular acceleration, where stiffness and damping coefficients are also angular-velocity- and acceleration-dependent. Bandwidth-limited VSC has been generated for pointing and tracking with such deformable vehicles, with the operator spline estimate used in the design of the nominal part (the equivalent control estimate), and the operator spline error bound in that of the control correction.<<ETX>>

State vector estimation of high dimensional systems based on functional spline operators

An estimation procedure based on the functional spline interpolation for dealing with high-dimensional bilinear dynamical models is described. At first, the nonlinear dynamics of a given system is transformed through Carleman bilinearization into a bilinear form. Decoupled bilinear models are then constructed, with input-output mappings expressible in closed form and with dimension determined by the number of training signals used in a prior learning stage. Motivation is given by the need for order reduction and input-output analysis of Carleman bilinearization. An illustration of the technique is made to a forced version of Duffings equation and merits and eventual extension of the procedure are also highlighted.<<ETX>>

Nonlinear estimation and robust control by means of optimal interpolation and sliding manifold techniques

The theory of the optimal interpolation of bilinear systems is described. Its potential usefulness in a robust control system design is highlighted. The optimal interpolator is derived from a nonlinear system identification technique based on a Fock space framework. It has the ability of reducing the high dimensionality of the original bilinear system to the one defined by the number of test input-output pairs determined in a prior stage. This offline modeling technique is then used to generate estimates of the system states as well as upper bounds on their error estimates. Based on this, and through an adaptation of the sliding manifold theory, a robust control effort can be generated for the purpose of insuring the high tracking performance of a moving elastic structure subject to parametric uncertainties and induced disturbances

Robust control synthesis of elastic structures based on variable structure control combined with optimal interpolation technique

A variable structure control technique combined with an operator spline for bilinear systems is investigated to control the moving elastic structure for purposes of achieving high performance tracking and precision pointing of a fast moving flexible structure (such as the agile motion of a robot manipulator with flexible links or the slewing maneuvers of a large space structure). The control torque applied to the structure is based on estimates of the structure parameters and on upper bounds of the model errors. It is shown through a simulated example how the chattering behavior of the controller, which involves high actuator activity, is avoided at the expense of tolerating a known tracking error in such a way that the closed loop dynamics in the boundary layer is approximated by the response of a critically damped oscillator with designer-selected bandwidth. A tradeoff is then to be set by the designer by taking into account the main requirements of a given task and the hardware available that is capable of achieving it.<<ETX>>