AUTOMATIC CONTROL SYSTEM FOR AN UNMANNED AIR VEHICLE - A MARKOVIAN MODEL APPROACH

摘要

The synthesis problem of wing deployment of an Unmanned Air Vehicle was considered via the Jump Markovian Systems approach. The change in the vehicle's dynamics duo to wing deployment was given a probabilistic interpretation, where the probability of deploying the wings from a folded position increases exponentially with time. However, once deployed, the wings remain open and , therefore, have a zero probability of switching back to a folded position. This description may even be closer to reality than the more intuitive deterministic one whereby the instant of wing deployment is selected according to a set of a-priori defined conditions on the angle attack and its derivative (e.g. small absolute value of the angle of attack combined with a small absolute derivative of the angle of attack). Even in the deterministic case, the first moment during which the above conditions are satisfied may depend on random parameters such as the angle of attack of the host vehicle at release, its velocity, etc. giving rise, in a very natural way, to a probabilistic interpretation of the switching time. For the situation where wing deployment timing is defined a-priori, the transition probabilities may be considered to be design parameters tuned to maximizing closed loop bandwidth, minimizing control effort, etc. The results achieved by the Markovian Jump Systems approach are quite encouraging. For very short duration wing deployment, the Markov Jump theory based disturbance attenuation factor is markedly less than those obtained with the more common approaches of simply treating each wing state separately or requiring quadratic stability. The latter uses a single gain matrix to control the plant during its two different phases and, therefore, does not utilize the information about the parameter .jumps, thus resulting in poor performance with a large control effort. Separately treating the closed and open wing systems does utilize the jump information, but does not account for the transient, thus leading to good disturbance attenuation but at the cost of large controls. The Markovian Jump approach uses different gain vectors for each phase while accounting for the jump. Although the probabilistic modeling of the jump may seem somewhat artificial in the case of a single shot wing deployment operation, where no folding back of the wings is possible, the approach suggested in the present paper can be thought of as a "gain scheduling" approach for systems with discrete operating points. This approach loses it's advantage when the transition between these operating points is slow. The suggested procedure of comparing performance levels using both deterministic and stochastic frame-works may be a useful addition to the overall control design process. Although the application presented for the Markov Jump approach - wing deployment in an Unmanned Air Vehicles - is not very common in the aerospace industry, the design, analysis and simulation procedure suggested here may be relevant for other applications where possibly fast enough transitions occur between discrete operating points.