Design and implementation of second-order sliding mode controllers for a CMG-based experimental setup.

The Control of Dynamical System is a subject at the boundary between engineering and applied mathematics. Any satellite put into orbit requires an adequate attitude control system, whether it is for scientific observations, telecommunications or any other service. Over the years, a growing number of powerful, responsive and accurate actuators have been developed, such as thrusters, Control Moment Gyroscopes (CMGs) and reaction wheels. Meanwhile, new control algorithms have been studied, of which the Sliding Mode Controller (SMC) is one of the most popular. For many applications requiring very precise control, an active full three-axis control is used: in this case, the satellite is stabilized by the above mentioned actuators. Using an active control, the satellite is not spinning anymore, so it’s possible to use solar panels and have a more precise pointing, with the disadvantages of being more expensive (fuel and/or actuators) and more complex. The following thesis deals with two different types of sliding mode controllers, a method, characterized by good robustness, for the control of nonlinear systems. Good robustness is a characteristic especially for adaptive controllers, which have the peculiarity of adapting controller gains during operations. The robustness is an important feature for controlling a spacecraft, as it is very difficult to have perfect internal and external disturbance modeling and usually also the knowledge of the plant to control is imprecise. In general, the control consists of defining a sliding surface and following it through a feedback law. The two types of SMC studied are the Super Twisting (STW) and the Adaptive Continuos Twisting (ACTW), both used for the attitude control of a satellite, with simulations on Matlab, followed by experimental testing with a testbed. The testbed consists of a platform for conducting rigorous and replicable experiments: in this thesis the platform is equipped with four Control Moment Gyroscopes arranged in a pyramidal configuration and the goal is to test the two control laws. One important difficulty related to the use of CMGs is their singularity problem in wich, under a certain configuration of CMGs gimbal angles, no control torques can be generated. The geometric singularity problem, solved by a Singular Direction Avoidance (SDA) steering law, will be discussed in this thesis. The Matlab language of the simulations has been converted to C++ in order to use the testbed in the Satoh laboratory at Osaka University.