The stabilization of unmanned aerial vehicles and its orientation in a given direction is provided by the orientation system. One of the important stages in the development of UAV orientation systems is the development of object orientation algorithms. The problem of orientation of objects in the magnetic field is based on the estimation of the discrepancies between the model Bmod and the measured Bmeas components of the Earth's magnetic field. Accordingly, the paper discusses some algorithms related to the orientation of satellites and unmanned aerial vehicles. It is shown that limiting the model to the first 13 harmonics can lead to errors in the representation of the Earth's main magnetic field of about 15 nT. A mathematical proof of this fact is carried out based on the consideration of the equation of an ideal magnetic field meter. The work analytically proves that the Jacobian matrix of the magnetic field measurement vector in the earth's coordinate system has a determinant equal to zero, which means that, having knowledge of the magnetic field measurement vector H-1, it is impossible to uniquely determine the vector of the orientation angles of the meter {f, o, y }t-. Thus, the paper shows an algorithm for calculating the orientation angles depending on the values of the measured and model values of the Earth's magnetic field.
Adaptive control techniques are often avoided in aerospace systems due to stringent plant structural requirements and validation difficulties. This dissertation seeks to broaden the range of aerospace engineering applications that can utilize an adaptive controller through the development of an extended model reference adaptive control (MRAC) design. First, a partitioned control framework is presented that permits the combined use of an adaptive control law and a nonadaptive control law. The partitioned framework is used to shift full control authority away from the adaptive portion of the system. Next, two MRAC variations that can accommodate the nonminimum phase zeros often seen in aerospace applications are discussed for use as the adaptive system. The parallel feedforward compensator approach proposes inclusion of a user--defied fictitious model in parallel with the plant that is designed to make the plant appear nonminimum phase. The surrogate tracking error approach modifies the typical MRAC structure to handle nonminimum phase plants by requiring knowledge of its nonminimum phase zeros. A tracking error convergence proof is provided for this continuous-time MRAC variant. The partitioned design using the surrogate tracking error approach is applied to the control tasks of an experimental, flexible wing aircraft. A simulation is used to demonstrate much improved flight path angle command tracking when compared to use of the aircraft's existing nonadaptive control law, even in the presence of large--scale modeling error. A second simulation is used to show the design applied to flexible motion control of the same aircraft model and exhibits similarly improved performance.
A review of optimal control theory for linear systems with quadratic cost functions is presented. Some of the theoretical and practical limitations are discussed with special reference to distributed parameter systems. First a procedure is described for finding the optimal control by constructing a sequence of controllers that converges to the optimal; this method is valid for systems of infinite dimension provided that the operators in the state differential equation satisfy certain conditions. The proof is carried out both for the finite and infinite time interval and the connection is shown with the Riccati equation. The main problem in implementation is that one needs complete knowledge of the state at all times in order to build the optimal controller, this is almost certainly impossible for distributed parameter systems. When the state cannot be measured completely it is proved that an optimal control is realisable for time invariant finite dimensional systems. \n \nThe problems of finding this control are then investigated and computational methods discussed. If the optimal control with complete knowledge of the state cannot be implemented, a method is presented whereby one can find bounds on the possible increase in the value of the cost function arising from the use of some sub-optimal control; several examples are considered. The constrained optimal control depends on the initial state and new optimisation criteria must be put forward to deal with the case in which the initial state is unknown; the most common consist of minimising the cost that can result from the worst initial state. It is then shown how the controllers designed according to these criteria may be improved by using one's limited observation at time zero to place some constraints on the initial state. The Liapunov matrix equation plays an important part in calculating the cost of any control so reducing the computational effort in its solution is useful. It is shown how this can be done and it is of special relevance for distributed parameter systems with their states expressed as an infinite series of eigenfunctions; the results are applied to a diffusion equation example. \n \nFinally, it is shown how optimal control theory may be applied to the design of proportional-integral-derivative controllers. This is done from two standpoints and the resulting controllers are shown to be identical, though the second method of proof is valid for infinite dimensional systems. The results are then applied to a simple example and to a distributed population dynamics system. The practicality of the methods of the thesis are applied to a system with realistic parameters; recommendations are made as to the best approaches. \n