In real life feedback control applications of mechanical systems, friction and time delays are two important issues that might have direct effects on the performance of systems. Hence, an adaptive nonlinear observer based friction compensation for a special time delayed system is presented in this thesis. Considering existing delay, an available Coulomb observer is modified and closed loop system is formed by using a Smith predictor based controller as if the process is delay free. Implemented hierarchical feedback system structure provides two-degree of freedom and controls both velocity and position separately. For this purpose, controller parametrization method is used to extend Smith predictor structure to the position control loop for different types of inputs and disturbance attenuation. Simulation results demonstrate that without requiring much information about friction force, the method can significantly improve the performance of a control system in which it is applied.

Spring Loaded Inverted Pendulum (SLIP) model has a long history in describing running behavior in animals and humans as well as has been used as a design basis for robots capable of dynamic locomotion. Anchoring the SLIP for lossy physical systems resulted in newer models which are extended versions of original SLIP with viscous damping in the leg. However, such lossy models require an additional mechanism for pumping energy to the system to control the locomotion and to reach a limit-cycle. Some studies solved this problem by adding an actively controllable torque actuation at the hip joint and this actuation has been successively used in many robotic platforms, such as the popular RHex robot. However, hip torque actuation produces forces on the COM dominantly at forward direction with respect to ground, making height control challenging especially at slow speeds. The situation becomes more severe when the horizontal speed of the robot reaches zero, i.e. steady hoping without moving in horizontal direction, and the system reaches to singularity in which vertical degrees of freedom is completely lost. To this end, we propose an extension of the lossy SLIP model with a slider-crank mechanism, SLIP-SCM, that can generate a stable limit-cycle when the body is constrained to vertical direction. We propose an approximate analytical solution to the nonlinear system dynamics of SLIP-SCM model to characterize its behavior during the locomotion. Finally, we perform a fixed-point stability analysis on SLIP-SCM model using our approximate analytical solution and show that proposed model exhibits stable behavior in our range of interest.

Application performance of mechanical positioning systems might not coincide with the theory, mainly due to nonlinearities or imperfections of system models. Although it is sometimes possible to ignore these mismatches, systems generally suffer from performance degradation or even instability eventually. Especially, friction force and time delay are two major factors of these undesired effects. Hence, in this paper, Smith predictor-based controllers and an adaptive Coulomb friction observer are designed to enhance position tracking performance of a mechanical system including time delay. In fact, implemented hierarchical control scheme provides two-degree of freedom to control both velocity and position separately. The proposed observer structure is mainly motivated by the Friedland-Park observer but could be considered as an extension of it which characterizes a general class of nonlinear functions for friction estimation. To assure its functionality with delayed measurements, different velocity predictor schemes are designed and their performances are compared. As a guideline for observer design, some conditions for exponential stability and robustness analysis are presented. Simulation results demonstrate that the proposed control system enhances the tracking performance even when the actual friction is a compound of various static and dynamic terms.

No abstract