• Tsypkin
• dual-input describing function

Throughout the last decades, attitude control systems with switching actuators
and discrete sensors have been used in satellites subjected to slowly varying
disturbances. Sun sensors are usually employed. Such sensors are discrete
and, typically, slower than actuators. Several types of on-off thrusters are
employed as actuators, such as hydrazine, cold-gas and pulse plasma thrusters.
These thrusters are typically affected by switching constraints. Due to these
constraints and the disturbances, the system shall operate in limit cycle
conditions. Two types of limit cycles can occur:
• Saturation limit cycles.
• Disturbance limit cycles.
Our purpose is the development of a controller design method which avoids
saturation limit cycles - that are very expensive in terms of fuel consumption -
and produces a disturbance limit cycle which meets amplitude and bandwidth
requirements. A reference scenario will be presented and simulations will be
performed to test potential outcomes.
The first part of the thesis will study the methods used to predict limit
cycles. Particular emphasis will be given to the classical describing function
theory. After that, we will develop the new dual-input describing function
theory which can deal with slowly varying disturbances. In order to address
strange behaviors the classical Tsypkin method will be presented and the hybrid
Tsypkin-dual-input describing function method, which takes into account
disturbances, will be applied to our case.
In the second part, we will focus on the design methods of the controller.
The Kharitonov approach, which is robust and uses the classical describing
function theory, will be studied in detail. In the end we will introduce the new
dual-input Kharitonov approach, developed by using the dual-input describing
function theory and capable of dealing with slowly varying disturbances.