Thomas A. W. Dwyer

Variable structure control of globally feedback-decoupled deformable vehicle meneuvers

The use of Cayley-Rodrigues attitude parameters as kinematic variables is shown to yield a globally linearized and decoupled model of the equations of motion of a deformable body, wherein the structural deformation state appears only in the coefficients of the inverse transformation. It is then shown how commanded multi-axial attitude maneuvers can be encoded as switching surfaces for a variable structure control implementation of the corresponding computed slew torques, automatically modulated in response only to detected angular rate error signs, for accurate tracking in the presence of separately damped or even uncontrolled (but stable) structural deformations.

Sliding Regimes on Slow Manifolds of Systems with Fast Actuators

In this article the slow manifold of a system with actuator parasitics is used as a sliding surface on which a Variable Structure Controller recovers the qualitative properties of the reduced order, closed loop system obtained from an ideal actuator-based feedback controller design. Illustrative examples are presented, where 1) the simplicity of reduced order singular perturbation design methods; and 2) the robustness of Variable Structure sliding modes, are advantageously combined.

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>>

Slew-induced deformation shaping

Computed torques for pointing and tracking require compensation for slew-induced structural, forebody/aftbody, or optical train alignment deformations. Thus even if only line-of-sight variables are to be commanded, full state feedback is needed. The solution proposed is to decouple by feedforward of the line-of-sight slew dynamics into the deformation control loop. It is shown how arbitrarily few actuators are needed for such deformation shaping, at the cost of higher differentiability of the reference line-of-sight dynamics. The low-rate, single-axis case is developed in detail, and its extension to high rates and multiple axes by global feedback linearization is outlined.<<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>>

Automatically reconfigurable control for rapid retargeting of flexible pointing systems

A reconfigurable nonlinear control system design methodology is proposed in this report, to automatically correct computed slew torque commands of space-based pointing systems, for the effects of slew-induced structural deformations. The torque corrections can be generated either from structural sensors, or else from higher derivatives of commanded boresight angular rates. In the latter case, structural control forces must be likewise generated from higher angular slew rates, to shape the slew-induced structural excitation. Automatic selection of slew torque. and structural actuator correction signals, as well as automatic correction for tracking error gains can be managed by a supervisory controller that tests required effort levels against actuator ratings. It is also indicated how translations during slews can be likewise corrected. The simulated implementation of such a control system for a space-based laser beam expander has been implemented on a Silicon Graphics IRIS computer system. A videotape of such a simulation as well as hardcopy are available.

Real-Time Collision Avoidance Manipulator Transfer Movements

Collision free robot manipulator maneuvers for transferring a payload from one location to another in the presence of obstacles are discussed. Such maneuvers are executed by means of two algorithms running in parallel. The first algorithm performs an on-line, one step ahead acceleration optimization, with an adaptive N-step ahead precaution measure to prevent overshooting the specified forbidden joint coordinates. The second algorithm, an on-line planning algorithm, at the same time, selects the current target state and the current forbidden joint coordinates for the first algorithm. Since the task is a point to point transfer movement, the problem is dealt in robot joint space directly and the kinematic problem can be bypassed completely. A simulation example using a 2 degree-of-freedom planner robot is given.

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