Abstract
Feedback loops designed using the ideas of sliding mode control are known to exhibit a number of appealing features. A very prominent characteristic is their insensitivity against bounded matched disturbances and model uncertainties. However, it is wellknown that improper discretetime realizations of sliding mode based algorithms cause socalled discretization chattering, i.e., undesired oscillations in the control signal. These oscillations typically deteriorate the closedloop performance or even cause damages.
This thesis deals with the analysis and development of tools for the characterization of chattering effects as well as with the development of discretization schemes that entirely avoid this effect. The theoretical results are supported by simulations and experiments.
For the characterization of chattering effects, i.e., the determination of frequency and amplitude of oscillations, frequency domain techniques such as the describing function method and the locus of perturbed relay system approach and their extension to the sampled data configuration are studied. The socalled sampled describing function approach is revisited and a formula for the computation of the locus of perturbed relay system approach is derived. In contrast to the describing function method, the locus of perturbed relay system approach yields exact results for the oscillation frequency. Stability properties of limit cycles and the basin of attraction of periodic solutions are discussed.
Then, novel discretetime variants of the supertwisting algorithm are presented. In contrast to the commonly employed explicit Euler discretized supertwisting dynamics, the proposed schemes are exact in the sense that in the unperturbed case the controllers ensure convergence to the origin. Discretization chattering effects are avoided whilst the robustness properties are preserved. The approach is extended to a family of homogeneous differentiators, including the wellknown arbitraryorder robust exact differentiator.
Finally, exploiting the notion of homogeneous eigenvalues, a new family of continuoustime arbitraryorder homogeneous state feedback controllers is derived. A formula that allows to design controllers for all combinations of the system's relative degree and the desired homogeneity degree of the closedloop system is presented. The structure of the resulting controllers permits realization in a discretetime environment straightforwardly using the developed ideas.
This thesis deals with the analysis and development of tools for the characterization of chattering effects as well as with the development of discretization schemes that entirely avoid this effect. The theoretical results are supported by simulations and experiments.
For the characterization of chattering effects, i.e., the determination of frequency and amplitude of oscillations, frequency domain techniques such as the describing function method and the locus of perturbed relay system approach and their extension to the sampled data configuration are studied. The socalled sampled describing function approach is revisited and a formula for the computation of the locus of perturbed relay system approach is derived. In contrast to the describing function method, the locus of perturbed relay system approach yields exact results for the oscillation frequency. Stability properties of limit cycles and the basin of attraction of periodic solutions are discussed.
Then, novel discretetime variants of the supertwisting algorithm are presented. In contrast to the commonly employed explicit Euler discretized supertwisting dynamics, the proposed schemes are exact in the sense that in the unperturbed case the controllers ensure convergence to the origin. Discretization chattering effects are avoided whilst the robustness properties are preserved. The approach is extended to a family of homogeneous differentiators, including the wellknown arbitraryorder robust exact differentiator.
Finally, exploiting the notion of homogeneous eigenvalues, a new family of continuoustime arbitraryorder homogeneous state feedback controllers is derived. A formula that allows to design controllers for all combinations of the system's relative degree and the desired homogeneity degree of the closedloop system is presented. The structure of the resulting controllers permits realization in a discretetime environment straightforwardly using the developed ideas.
Original language  English 

Qualification  Doctor of Technology 
Awarding Institution 

Supervisors/Advisors 

Award date  23 Aug 2019 
Publication status  Published  2019 