Frequency domain data-driven robust and optimal control

The goal of this thesis is to propose pragmatic solutions to real challenges faced in the industry. The scope of this thesis encompasses two subjects: frequency-based structured controller synthesis for linear time-invariant (LTI) systems on one side, and its application to real robots on the other side. The first part of the thesis deals with the development of a novel data-driven synthesis approach, which can be used to design controllers for a closed-loop described by a linear fractional transform. One important advantage of the proposed method is that fixed-structure controllers can be designed using only the frequency response of the plant by solving a series of convex optimisation problems. It is shown, through examples, that this method is competitive with state-of-the-art model-based structured controller approaches. Then, it is shown that this method can also be used to design controllers arbitrarily close to the global optimum, by increasing the order of the controller. Finally, two chapters are dedicated to improving the robustness of the proposed method: first, by studying the behaviour between two consecutive frequency points in the SISO case, and second, by addressing the root cause leading to the synthesis of destabilizing controllers. The second part of this thesis deals with applications of the method proposed in the first. Real systems are all non-linear to a certain extent, but the synthesis method developed in the first part is aimed at linear systems. As ever-increasing performance is required to retain a competitive edge, new methods must be developed. In particular, the applications are presented under the unifying theme of linear parameter varying (LPV) control. The framework of LPV controller synthesis offers a transparent way of carrying out nonlinear control design while using the formalism of LTI systems. In this thesis, three different systems are studied: a Cartesian coordinate measuring robot where three decoupled LPV SISO controllers are designed, a rotary table where an uncertain LPV controller is designed, and finally, a robotic arm where a two-degree-of-freedom LPV controller is designed.