Manual Control of Unstable Systems

Automatic control is increasingly used in mission critical applications. The reason for this is the potential benefits and the fact that control engineering is now able to deal with complex systems. Control of high performance aircrafts is a typical example. Considerable benefits can be obtained by having an aircraft that is unstable in certain flight conditions and providing stability with a control system. The unstable flight conditions typically include the low speed conditions that occur during take off and landing. The aircrafts have hydraulic actuators that saturate for large signals or signal rates. Since the feedback loop is broken in saturation the unstable states may diverge to situations which cannot be recovered. The presence of a pilot is yet another complication because the pilot may also drive the system unstable through manual control actions. Design of control systems for such situations is a significant challenge. Aircraft manufacturers have encountered severe difficulties because of this problem which has led to severe delays of projects. The design of control laws for unstable systems that make it impossible for the pilot to drive the system unstable while maintaining good handling qualities is a challenging problem. The goal of this thesis is to develop insight into this problem. A strongly simplified case that captures the key elements of the problem is first solved to get some insight. This shows that it is possible to develop a hybrid strategy which has interesting problems. A more realistic problem is simultaneous stabilization and control of the pivot of an inverted pendulum. This problem is nice because it also allows easy verification in the laboratory. The problem is investigated and control strategies are designed by combining several different strategies using the hybrid approach. The properties of the strategies are illustrated by simulation. Finally we make a preliminary attempt at applying the ideas to the flight control problems. The conclusion of the work is that the approach taken appears promising and worthy of further studies