LPRS Analysis of Oscillations in Discontinuous Systems with Application to Controller Tuning in Robotic Systems

Abstract

This doctoral thesis deals with two subjects of control engineering related to Relay Feedback Systems (RFSs).

The first subject is about the analysis of oscillations in RFSs. We deal with the oscillations that occur in a system in the presence or absence of parasitic dynamics. In sliding mode control the oscillations, in the presence of parasitic dynamics, are called as chattering. We investigate these oscillations in particular forms of Homogeneous Sliding Mode Controllers (HSMCs) using the Locus of Perturbed Relay Systems (LPRS). Through the LPRS, we determine periodic solutions of HSMC system. We investigate orbital stability, and other realizability conditions of the periodic solutions. Apart from periodic chattering, we discover and analyze another form of chattering which we named as chaotic chattering. We find that the chaotic chattering occurs in only a particular case of the HSMC system under a specific combination of controller and actuator parameters. We discuss how bifurcation points can be found that differentiate the parameter ranges corresponding to the periodic chattering from those revealing chaotic chattering. These bifurcation points are identified based on the eigenvalues of the linearized Poincare maps in the vicinity of periodic solutions, open-loop and closed-loop simulations.

The second subject that this thesis deals with is the application of RFS in the context of control tuning. Two problems are considered in this perspective. The first issue is the development of PID tuning rules for the shapes of oscillations under a test for RFSs. This work is based on the observation that RFSs exhibit few different kinds of shapes in self-excitation modes. Based on such shapes, we develop Tuning Rules (TRs) of PID using the Optimization Under Uncertainty (OUU) principle and the Modified Relay Feedback Test (MRFT). The considered systems are categorized into integrating and non-integrating system and then a corresponding TR is developed for each shape accordingly. The second issue is the development of an autotuning method for the tuning of PIDs in robotic manipulators. We again use the OUU and the MRFT to develop the TR for such a purpose. The actuator dynamics are considered and so, a combined model of the Brushless DC motor and an n-link manipulator is derived and used for the development of the TR. A design process is presented to formulate situational parameters and to create candidate models to be used in the OUU optimization process. The developed tuning approach is tested on different manipulator models in simulations as well as experiments.

Date of Award	Apr 2023
Original language	American English
Supervisor	IGOR Boiko (Supervisor)