Balance control is important for biped standing. Due to the time-varying control bounds induced by the foot constraints, and the lack of tools for analyzing stability of highly nonlinear systems, it is extremely difficult to design balance control strategies for a standing biped with a rigorous stability analysis in spite of large efforts. In this thesis, three important issues are fully considered for a standing biped: maintaining the postural stability, minimizing the energy consumption and satisfying the constraints between the biped feet and the ground. Both the theoretical and the experimental studies on the constrained and energy-efficient control are carried out systematically using the genetic algorithm (GA). The stability for the proposed balancing system is thoroughly investigated using the concept of Lyapunov exponents. On the other hand, the controlled standing biped is characterized by high nonlinearity and great complexity. For systems with such features, in general the Lyapunov exponents are hard to be estimated using the model-based method. Meanwhile the biped is supposed to be stabilized at the upright posture, indicating that the system should possess negative Lyapunov exponents only. However the accuracy of negative exponents is usually poor if following the traditional time-series-based methods. As it is nontrivial to examine the system stability for bipedal robots, the numerical accuracy of the estimated Lyapunov exponents is extremely demanding. In this research, two novel approaches are proposed based upon system approximation using different types of Radial-Basis-Function (RBF) networks. Both the proposed methods can estimate the exponents reliably with straightforward algorithms, yet no mathematical model is required in any newly developed method. The efficacies of both methods are demonstrated through a linear quadratic regulator (LQR) balancing system for a standing biped, as well as several other dynamical systems. The thesis as a whole, has set up a framework for developing more sophisticated controllers in more complex movement for robot models with less conservative assumptions. The systematic stability analysis shown in this thesis has a great potential for many other engineering systems.

This thesis documents the development of a novel nonlinear controller for servo pneumatic actuators that give good reference tracking at low speed motion, where friction has strong effect to the system behaviors. The design of the nonlinear controller presented in this thesis is based on the formalism of Lyapunov stability theory. The controller is constructed through a dynamical adaptive backstepping-sliding mode control algorithm. The conventional Lyapunov-based control algorithm is often limited by the order of the dynamical system; however, the backstepping design concept allows the control algorithm to be extended to higher order dynamical systems. In addition, the friction is estimated on-line via the Lyapunov-based adaptive laws embedded in the controller; meanwhile, the sliding mode control provides high robustness to the system parameter uncertainties. The simulation results clearly demonstrating the improved system performance (i.e., fast response and the reduced tracking error) are presented. Finally, the integration of the controller with a Lyapunov-based pressure observer reduces the state feedback of the servo pneumatic actuator model to only the piston displacement.

Vehicle yaw stabilization and rollover prevention are two key factors in safety of vehicles. Designing a controller that can address both of the above safety concerns is of interest. In addition, it is essential that the performance of such a controller is evaluated properly. This can be done using a proper stability analysis. The above research problem is challenging for two reasons. First, maintaining both of the objectives, yaw stabilization and rollover mitigation, is contradictory at some instances, specifically when the vehicle is close to the verge of wheel lift-off. Second, the complexity of the dynamics of vehicle systems, which mostly arises from tire dynamics, makes the problems of controller design and stability analysis more challenging. In this Ph.D. thesis, a novel method for stability analysis of dynamical systems using the concept of Lyapunov exponents is proposed. The proposed method for stability analysis does not have the limitations of the current methods, and more specifically, can identify boundaries of the whole stability regions of attractors in a dynamical system. Furthermore, this method is computationally efficient and can be applied to general forms of nonlinear systems. The proposed stability analysis scheme is applied to the closed loop systems of ground vehicles with T-S fuzzy controllers for the purpose of evaluating and comparing the performance of the systems. The T-S fuzzy controllers integrate yaw stabilization and rollover avoidance. The ground vehicles that are studied in this research consist of torsionally flexible and torsionally rigid vehicles, which have differences in their dynamics because of the torsional compliance in their frames. The torsional compliance plays an important role in the dynamics, specifically for long vehicles, leading to different rollover indexes in the front and rear axles of the vehicles. The T-S fuzzy controllers are capable of prioritizing the contradictory objectives, and capturing all the essential complexities of dynamics of the systems. / February 2016

Flocking, the collective motion of systems consisting of many agents, is a ubiquitous phenomenon in nature, observed both in biological and artificial systems. The understanding of such systems is important from both a theoretical point of view, as it extends the field of statistical physics to non-equilibrium systems, and from a practical point of view, due to the emergence of applications that are based on the modelling. In the present thesis I numerically investigated several aspects of flocking dynamics, simulating systems consisting of up to millions of particles. One first problem I worked on regarded the flocks response to external perturbations, something that had received little attention so far. The result was a scaling relation, connecting the asymptotic response of a flock to the strength of the external fleld affecting it. Additionally, my preliminary results point towards a generalised fluctuation-dissipation relation for the short-time response, with two different effective temperatures depending on the direction at which the perturbing field is applied. Another aspect I studied was the stability and dynamical properties of non-confined active systems (finite flocks in open space). The results showed that these flocks are stable only when an attracting 'social force' keeps the agents from drifting away from each other. The velocity fluctuations correlations were found to be different than the asymptotic limit predictions of hydrodynamic theories for infinite flocks. Finally, I studied the clustering dynamics of flocking systems. The conclusion was that the non-equilibrium clustering in the ordered phase is regulated by an anisotropic percolation transition, while it does not drive the order-disorder transition, contrary to earlier conjectures. I believe the results of this work answer some important questions in the field of ordered active matter, while at the same time opening new and intriguing ones, that will hopefully be tackled in the near future.

This thesis finds that vortex instabilities are not necessarily a barrier to their potential as sites for planetesimal formation. It is challenging to build planetesimals from dust within the lifetime of a protoplanetary disc and before such bodies spiral into the central star. Collecting matter in vortices is a promising mechanism for planetesimal growth, but little is known about their stability under these conditions. We therefore aim to produce a more complete understanding of the stability of these objects. Previous work primarily focusses on 2D vortices with elliptical streamlines, which we generalise. We investigate how non?constant vorticity and density power law profiles affect stability by applying linear perturbations to equilibrium solutions. We find that non?elliptical streamlines are associated with a shearing flow inside the vortex. A ?saddle point instability? is seen for elliptical?streamline vortices with small aspect ratios and we also find that this is true in general. However, only higher aspect ratio vortices act as dust traps. For constant?density vortices with a concentrated vorticity source we find parametric instability bands at these aspect ratios. Models with a density excess show many narrow bands, though with less strongly growing modes than the constant?density solutions. This implies that dust particles attracted to a vortex core may well encounter parametric instabilities, but this does not necessarily prevent dust?trapping. We also study the stability and lifetime of vortex models with a 2D flow in three dimensions. Producing nearly?incompressible 3D models of columnar vortices, we find that weaker vortices persist for longer times in both stratified and unstratified shearing boxes, and stratification is destabilising. The long survival time for weak, elongated vortices makes it easier for processes to create and maintain the vortex. This means that vortices with a large enough aspect ratio have a good chance of surviving and trapping dust for sufficient time in order to build planetesimals.

No description available.

<p> Flexural vibrations of a shaft mounted at each end on a non - linear spring have been studied. Theoretical analysis is carried out for the cubic non-linear spring. </p> <p> The effect of mountirig of a heavy rotor on the shaft has been considered. The stability analysis of the system is also given in the theoretical analysis.</p> / Thesis / Master of Engineering (ME)

No description available.

No description available.

The object of this study is to incorporate a nonlinear material law for wood in the finite element program ABAQUS to develop effective finite element models of glulam domes, and to investigate the buckling behavior of glulam domes using this finite element program. The material law is implemented with a FORTRAN subroutine. Results from thorough testing of the subroutine are presented. The dome is then modeled with I-DEAS and, analyzed with ABAQUS. The modeling procedure is briefly discussed, and the results from the stability analysis of the dome are presented. Finally, conclusions and further research scope based on this study are presented. / Master of Science