Control of Nonlinear Mechatronic Systems

This dissertation is divided into four self-contained chapters. In Chapter 1, an adaptive nonlinear tracking controller for kinematically redundant robot manipulators is presented. Past research efforts have focused on the end-effector tracking control of redundant robots because of their increased dexterity over their non-redundant counterparts. This work utilizes an adaptive full-state feedback quaternion based controller developed in [1] and focuses on the design of a general sub-task controller. This sub-task controller does not affect the position and orientation tracking control objectives, but instead projects a preference on the configuration of the manipulator based on sub-task objectives such as the following: singularity avoidance, joint limit avoidance, bounding the impact forces, and bounding the potential energy. In Chapter 2, two controllers are developed for nonlinear haptic and teleoperator systems for coordination of the master and slave systems. The first controller is proven to yield a semi-global asymptotic result in the presence of parametric uncertainty in the master and the slave dynamic models provided the user and the environmental input forces are measurable. The second controller yields a global asymptotic result despite unmeasurable user and environmental input forces provided the dynamic models of the master and slave systems are known. These controllers rely on a transformation and a flexible target system to allow the master system\u27s impedance to be easily adjusted so that it matches a desired target system. This work also offers a structure to encode a velocity field assist mechanism to provide the user help in controlling the slave system in completing a pre-defined contour following task. For each controller, Lyapunov-based techniques are used to prove that both controllers provide passive coordination of the haptic/teleoperator system when the velocity field assist mechanism is disabled. When the velocity field assist mechanism is enabled, the analysis proves the coordination of the haptic/teleoperator system. Simulation results are presented for both controllers. In Chapter 3, two controllers are developed for flat multi-input/multi-output nonlinear systems. First, a robust adaptive controller is proposed and proven to yield semi-global asymptotic tracking in the presence of additive disturbances and parametric uncertainty. In addition to guaranteeing an asymptotic output tracking result, it is also proven that the parameter estimate vector is driven to a constant vector. In the second part of the chapter, a learning controller is designed and proven to yield a semi-global asymptotic tracking result in the presence of additive disturbances where the desired trajectory is periodic. A continuous nonlinear integral feedback component is utilized in the design of both controllers and Lyapunov-based techniques are used to guarantee that the tracking error is asymptotically driven to zero. Numerical simulation results are presented for both controllers. In Chapter 4, a new dynamic model for continuum robot manipulators is derived. The dynamic model is developed based on the geometric model of extensible continuum robot manipulators with no torsional effects. The development presented in this chapter is an extension of the dynamic model proposed in [2] (by Mochiyama and Suzuki) to include a class of extensible continuum robot manipulators. First, the kinetic energy of a slice of the continuum robot is evaluated. Next, the total kinetic energy of the manipulator is obtained by utilizing a limit operation (i.e., sum of the kinetic energy of all the slices). Then, the gravitational potential energy of the manipulator is derived. Next, the elastic potential energy of the manipulator is derived for both bending and extension. Finally, the dynamic model of a planar 3-section extensible continuum robot manipulator is derived by utilizing the Lagrange representation. Numerical simulation results are presented for a planar 3-section extensible continuum robot manipulator