Joseph W. Jackson

Dynamic interpolation and application to flight control

To simplify the specification of a desired trajectory for some subset of the variables of a dynamic control system, it may be advantageous to designate a set of intercept points that the trajectory is required to pass through. The system controls can then be computed in terms of a spline function to meet these requirements for dynamic interpolation. Optimization of a cost function under continuity constraints can be embedded in the determination of spline coefficients to obtain certain desirable geometric properties of the resulting trajectory.

A Non-Holonomic Dynamic Interpolation Problem

The tracking problem in which certain dynamic variables of a control system are forced to follow a desired path, is a major problem in theory and practice. Another way of attaching the problem is to specify the trajectory in terms of a discrete, ordered set of points through which the dynamic variables must pass. It is natural to impose smoothness constraints on the trajectories. We call this the dynamic interpolation problem. A number of authors have considered the problem, in conjunction with applications to flight paths of aircraft, [6], [7], [8], and path planning for robots [3], [15]. The main emphasis in this work has been to satisfy the many constraints on the state variables to be met in these applications, whilst minimizing natural costs associated with the control. However, the underlying geometry of the resulting trajectories is obscured and not dealt with specifically.

Dynamic interpolation for linear systems (air traffic control)

The authors set out to apply dynamic interpolation to a single-input single-output time-invariant linear system. Optimization of a quadratic cost function is embedded in the method to provide minimization of control effort. These results are applied to the guidance of a linearized aircraft model through a set of 4-D waypoints on final approach into an airport. In a practical implementation of this method, the interaction of an on-board flight management computer and the microwave landing system can be directed to generate smooth steering commands to either the pilot or autopilot. Actuation of such commands would result in a curved path trajectory through the desired waypoints. The proposed configuration was intended to increase air traffic control efficiency by expanding the usage of the controlled airspace of the facility, resulting in reduced congestion at many major airports.<<ETX>>

Curved path approaches and dynamic interpolation

It is shown that to simplify the specification of a desired trajectory for some subset of the variables of a dynamic control system, it may be advantageous to designate a set of intercept points that the trajectory is required to pass through. The system controls can then be computed in terms of a spline function to meet these requirements for dynamic interpolation. Optimization of a cost function under continuity constraints can be imbedded in the determination of spline coefficients to obtain certain desirable geometric properties of the resulting trajectory. The optimal trajectories determined under the additional constraint of constant speed are useful in determining the acceptability of the results of dynamic interpolation.<<ETX>>The method of splines was applied to the control of linearizable dynamical systems such that an affine invariant cost functional (total energy) is minimized subject to discrete path constraints. CAGD (computer-aided geometric design) and optimal control methods were applied to derive reference trajectories for comparison with the dynamic results, and to determine intercept times for the waypoints. An acceptable trajectory was generated by the application of these methods to a difficult aircraft approach problem. It is suggested that a combination of finite element and spline techniques should eventually be suitable for solutions of practical dynamic interpolation problems considered in the literature.<<ETX>>

British Aerospace regional jetliner digital flight guidance certification

The British Aerospace Regional Jetliner (RJ), RJ70, RJ85, RJ100, and RJ115 aircraft will be certified with a Category 3 capable-digital flight guidance system (DFGS). The DFGS system integrates autoland, steep approach, elevator trim, yaw damper, altitude alerting, automatic throttle control, windshear detection, windshear guidance, return-to-service, and fault storage built-in test (BIT) into a single system. An optional dual DFGS configuration is also available. British Aerospace Regional Aircraft Ltd. and Honeywell engineering teams worked in a coordinated effort to develop control and monitoring algorithms to the specific needs to the RJ in meeting CAA and FAA certification requirements including autoland. The authors describe the special design requirements and developments undertaken on the RJ by both parties to satisfy an aggressive and demanding certification schedule while maintaining a solidly performing digital flight control system. Future developments in the operational environment for the RJ aircraft are also discussed.<<ETX>>