Computation of the safe set: Jammed Actuators or stuck Elevators

This section adds to the design process, an offline reconfigured model once a jammed actuators is being detected and it also well known from Suba et al [16] that not all stuck positions of deflection surfaces uses smooth reconfigured controllers. In this particular approach, we monitored stuck positions incrementally in a sense that a stuck position partition the state space into a safe and an unsafe regions and addresses the smooth reconfiguration offline with respect to a known safe region of the state space. The novelty of this section comes with the computation of the safe set, illustration and then uses the design strategy of the reconfigure controller when a stuck elevator or jammed actuators is been detected [16]. Along with this novelty, we incrementally addressed the

impaired safe set with stuck elevator by reducing the range of operations of the allowable deflection surfaces. It’s true that in the impaired aircraft case, the stuck elevator ceased to function properly, but in our approach, we can deduced the safe region where the reconfigurable controller should restore the flight vehicle. All this comes with the need of sophisticated control systems where safety requirements and performance goals should be achievable. The outline of this section started with a few approaches to reconfigurable systems, the computations of the safe set associated and finally a reconfiguration strategy that will restore the aircraft within the safe set. The reconfigured strategies restore the aircraft with the knowledge of the deduced impaired safe set. The reconfigured model would be embedded in AHFTCS with knowledge of the impaired safe set.

3.3.1 Hardware Reconfiguration based Redundancy Limit

This particular subsection of the section underlines previous techniques of reconfiguration and their limitations. Then focuses on finding solutions to those limitations first by computing the safe set under failure or stuck elevator within a certain range of operations and second by attempting to examine the safe set if there exists an equilibrium point that can be reached from trajectories which start within the shrink safe set and third manage to reconfigure the unimpaired aircraft that restore the flight vehicle within the impaired safe set. As we would observe, as the aircraft deflection surfaces get stuck at a particular position, the geometry nature of the safe set changes as well. This particular section uses the knowledge of the impaired safe set obtained by reducing the range of operation of the deflection surfaces.

Hardware Reconfiguration based Redundancy Limit

Reconfiguration based redundancy of components (hardware and software) has been at the heart of flight fault tolerant systems for decades. With the development of flight-by-wire,computers have become one of the most critical part of automate advanced flight control system. Because of ad- vanced processing speed, analytical redundancy becomes the subject of major research in the flight community as opposed to hardware redundancy. Also with the advent of big commercial aircrafts and flexible military aircrafts,hardware redundancy becomes less important than the software re- dundancy [65]. With that in mind,careful measures must be taken into consideration for the optimal reconfiguration of the complete aircraft architecture for better performance and optimal reliability. Thinking in that trends before reconfiguring the system as does Kwatny et al [16], we first compute the allowable safe set within the initial allowable envelope then initiated an offline recovery strategy

that restore the aircraft within the compute safe set. Analytical and quantitative measure would be taken to ensure that the reconfigurable aircraft remains in the safe set or can recover to the safe once jammed actuators are observed in the system.

3.3.2 Computation of the Safe Set with Jammed Actuators

In this particular set up, we are using the algorithm outline in the previous section to address the computation of the impaired safe set. Set in which there would always exist a reconfigurable controller that would help us to stay within the maneuverable domain even reduce. At first we use the exact the set up of the previous section with the only difference being that the bounds on elevator control input are reduced either symmetrically or asymmetrically. The reduction is seen here as a stuck position of a deflection surface or a jammed actuator. In our attempt to present the problem, we assume that we have a symmetrically jammed actuators, a meaning of that particular set up is that the deflection surfaces may not be controlled independently as it will be in the asymmetric case. Sofar, we have a set up for the symmetric case which allows us to assess the problem and show what would happen if a particular failure is observed. In this particular set up, we may also determine the controller that allows us to reach the impaired safe set of the aircraft system.

For illustration purposes, we use the simplify model already describe above to compute the impaired reachable safe set. A room for computing the reconfigurable controller is then opened that would restore the flight vehicle within the shrink maneuverable domain obtained by reducing the range of operation of the deflection surfaces.Here no assumption is made with the nominal flight path at straight level flight. For the example below, there may be a scaling issues but enough regarding the model can be found in [46].

An observation can be made by looking at the geometry structure of the unimpaired safe set. It shrinks from outside to inside as the elevator gets stuck from outside to inside as well. Which means that at a particular position, there may be no safe trajectories that can reach the unimpaired safe set. The question that should be raised is what do we do next or how do we manage to maintain the aircraft safe. Further investigation in that direction is a subject for future research.

(a) Nominal Safe Set for reduce Aircraft phugoid Model 100 150 200 -0.4 -0.2 0.0 0.2 0.4 V, ftsec Γ , rad

(b) Impaired Safe Set with elevator by reducing the range of operation to (-0.456 rd)

Figure 3.2: Unimpaired and Impaired Safe Set Computation with reduced aircraft Model