This dissertation demonstrates that a magnetic-levitation (maglev) stage has the capabilities to control movements and reject vibration simultaneously. The mathematical model and vibration control scheme with a 6-degree-of-freedom (6-DOF) maglev stage for nanoscale positioning are developed for disturbance rejection. The derived full nonlinear dynamic equation of motions (EOMs) of the maglev stage include translational and rotational motions with differential kinematics. The derived EOMs and the magnetic forces are linearized to design a multivariable controller, a Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR), for vibration disturbance rejection in a multi-input multi-output (MIMO) system. For a more accurate model, the dynamics of an optical table with a pneumatic passive isolation system is also considered. The model of the maglev stage with the optical table is validated by experiments. Dual-loop controllers are designed to minimize the influence of the vibration disturbance between the moving platen and the optical table in the x-, y-, and z-axes motions. The inner-loop compensator regulates the velocity to reject vibration disturbance and the outer-loop compensator tracks positioning commands. When the vibration disturbances of 10 to 100 Hz are applied, the vibration-reduction ratios are about 30 to 65 percent in horizontal motion and 20 to 45 percent in vertical motion. In addition, the vibration disturbances of 45.45 Hz are attenuated by about 4 to 40 percent in angular motions. The vibration control schemes are effective in not only translational but rotational motions. In step responses, the vibration control schemes reduce the wandering range in the travel from the origin to another location. Positioning and tracking accuracies with the vibration controller are better than those without the vibration controller. In summary, these dual-loop control schemes with velocity feedback control improved the nanopositioning and vibration/disturbance rejection capabilities of a maglev system.

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We use the adaptive probabilities of crossover and mutation, elitist strategy, and extinction and immigration strategy to improve the simple genetic algorithm in this study. We expect that the search technique can avoid falling into the local maximum due to the premature convergence, and the chance of finding the near-optimal parameter in the larger searching space could be obviously increased. The accelerometer is then taken as the sensor for output measurement, and the designed actuator and digital PID controller is implemented to actively suppress the vibration of the plain that is due to the excitation effect of the high-speed and precision positioning of the linear motor. From the computer simulations and the experimented results, it is obvious that the near-optimal digital PID controller designed by modified genetic approach can improve the effect of vibration suppression; the settling time is also decrease. For the vibration suppressions of high-speed precision positioning problems, the vibrating plain system can fastly be stabilized.

Biodynamic feedthrough occurs in many types of operator controlled machines where the operator is a passenger and the motion of the controlled machine excites motion of the human operator, creating unwanted feedback. It is a significant cause for control performance degradation in backhoes. In this research, the problem of biodynamic feedthrough is investigated in a backhoe control system. For simplification, the system is limited to a single degree of freedom. Several controller based approaches are investigated to reduce cab vibration, while maintaining cylinder tracking performance. These controllers are tested in hardware, with and without the human operator and associated biodynamic feedthrough. The effect of this cab vibration reduction on biodynamic feedthrough is tested in a small set of human subject tests. The results indicate that some vibration reduction and improvement in the operator's control performance can be achieved by adding cab vibration compensation.

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Models, modelling and control design play important parts in automatic control. The contributions in this thesis concern topics in all three of these concepts. The poles are of fundamental importance when analyzing the behaviour of a system, and pole placement is an intuitive and natural approach for control design. A novel parameterization for state feedback gains for pole placement in the linear multiple input case is presented and analyzed. It is shown that when the open and closed loop poles are disjunct, every state feedback gain can be parameterized. Other properties are also investigated. Hammerstein models have a static non-linearity on the input. A method for exact compensation of such non-linearities, combined with introduction of integral action, is presented. Instead of inversion of the non-linearity the method utilizes differentiation, which in many cases is simpler. A partial differential equation (PDE) can be regarded as an infinite order model. Many model based control design techniques, like linear quadratic Gaussian control (LQG), require finite order models. Active damping of vibrations in a viscoelastic beam, modelled as a PDE, is considered. The beam is actuated by piezoelectric elements and its movements are measured by strain gauges. LQG design is used, for which different finite order models, approximating the PDE model, are constructed. The so obtained controllers are evaluated on the original PDE model. Minimization of the measured strain yields a satisfactory performance, but minimization of transversal deflection does not. The effect of the model accuracy of the finite order model approximations is also investigated. It turns out that a model with higher accuracy in a specified frequency interval gives controllers with better performance. The wave equation is another PDE. A PDE model, with one spatial dimension, is established. It describes wave propagation in a tube perforated with helical slots. The model describes waves of both extensional and torsional type, as well as the coupling between the two wave types. Experimental data are used for estimation of model parameters, and for assessment of the proposed model in two different cases. The model is found adequate when certain geometrical assumptions are valid.

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