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A common problem in developing new gimbal products is predicting performance. At the beginning of the design stage, typically the proposal writing stage, it is critical to be able to anticipate the performance of a design, which may still be very roughly defined. Static performance metrics such as pointing accuracy are easier to predict and can be related to position sensor resolution and compliance in the structure and drive. Dynamic performance metrics such as rate tracking and bandwidth are much more difficult to estimate. These dynamic parameters will serve as the results of this paper. A gimbal model is usually developed in this early stage of design. A model is built for each axis as cross-coupling is not usually significant. The development of each model is inherently dependent on the integrity of the parameters used. Some parameters may be easily accessible and clearly defined, such as manufacturer specifications for commercial-off-the-shelf (COTS) components. An example of these would be motors. A motor datasheet will usually include specifications such as winding resistance, torque constant, etc. Some parameters have to estimated such as drive friction, structural rigidity and drive parameters. There is also much less certainty in these estimates due to their dependence on the integrated, final system. Building an accurate and sufficient model of the system is a challenging task. This thesis developments and validates a single axis gimbal model. Following this is a recursion on the model parameters based upon empirical data. Finally, application of different control laws are evaluated in simulation on the model. First, a classical output feedback law is implemented. Secondly, a state observer is implemented with state feedback. State feedback coefficients are found using both pole placement (PP) algorithms and linear quadratic regulation (LQR) optimal control formulas.

ii) An adaptive output regulation design is proposed for the systems with ISS inverse dynamics and an uncertain exosystem. When the exosystem contains uncertain parameters, the direct approach can not be implemented any longer. To deal with this issue in the general case, by introducing an observer, we first derive an extended system composed of the plant and the observer. Then the output regulation problem of the extended system is solved. It is further shown that the unknown parameter vector of the exosystem can be exactly estimated if a controller containing a minimal internal model is employed., iii) A sufficient solvability condition of the global output regulation for the systems with iISS inverse dynamics is proposed. Since the concept of iISS is strictly weaker than the ISS one, the result allows us to handle a much larger class of nonlinear systems., In the past ten years or so, the output regulation of the strict output feedback systems has attracted a lot of attention. In contrast with the strict output feedback systems, the output feedback systems is more general since it not only involves the nonlinearity of the system output but also the unmodeled dynamics. Therefore, the usual design method is not applicable, which motivates us to develop some new methodology for the output regulation design of the output feedback systems., One of the motivations of the case study is to deal with the output regulation problem of a shunt-connected DC motor whose inverse dynamics is iISS but not ISS. As an illustration, a disturbance rejection problem of the shunt-connected DC motor is solved., The application of the result leads to the solution of several interesting control problems such as the global disturbance rejection of the FitzHugh-Nagumo (FHN) system and the robust output synchronization of the generalized third and fourth-order Lorenz system and the Harmonic system., The main results of the thesis are outlined as follows. i) A direct approach is proposed for the output regulation of the systems with ISS inverse dynamics and unknown control directions. The internal model is first designed for the control input. The output feedback control design is further achieved based on a type of partial state observer which is designed for the transformed augmented system. The Nussbaum function technique is successfully incorporated in the stabilization design to deal with the case of unknown control directions., The nonlinear output regulation is a central control problem that involves nonlinear stabilization, tracking control and disturbance rejection as special cases. The control objective is to find a feedback controller to achieve asymptotic tracking and/or disturbance rejection while maintaining closed-loop stability. The output regulation study has experienced rapid developments in the past two decades or so. It is now well known that the problem can be systematically approached according to the general framework of tackling nonlinear output regulation that is composed of the following two steps. The first step is the problem conversion: from nonlinear output regulation to stabilization. The output regulation is generally more complicated than the stabilization problem. Therefore the problem conversion indeed reduces the complexity and makes it possible to be handled. In this step, the output regulation is converted into the stabilization of an augmented system consisting of the original plant and a suitable dynamic compensator called internal model. The second step is the stabilization of the augmented system whose solvability implies solvability of the output regulation problem., The result is applied to solve a tracking control problem associated with the well known Lorenz system and a class of generalized fourth-order Lorenz systems. By certain system decomposition, it is proved that the Lorenz system contains certain ISS inverse dynamics and the output feedback control is successfully realized., The thesis is concerned with the global robust output regulation for nonlinear systems in the output feedback form by using output feedback control. For the nonlinear output feedback systems, we mainly study three typical output regulation problems. The first one is the output regulation problem with unknown control directions and input-to-state stable (ISS) inverse dynamics using a direct approach. The second one is the adaptive output regulation problem with an uncertain exosystem and ISS inverse dynamics. The third one is a case study on the solvability of the systems with integral input-to-state stable (iISS) inverse dynamics., Xu, Dabo., Adviser: Jie Huang., Source: Dissertation Abstracts International, Volume: 72-01, Section: B, page: ., Thesis (Ph.D.)--Chinese University of Hong Kong, 2010., Includes bibliographical references (leaves 107-113)., Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web., Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web., also in Chinese., isbn: 9781124357676, Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Despite the fact that significant progress has been made on the research of these two problems for nonlinear systems for over two decades, many problems are still open. In particular, so far the output regulation problem is mainly handled by robust control approach. This approach has certain fundamental limitations and cannot handle the following three cases. (1) The control direction is unknown. (2) The boundaries of system uncertainties are unknown. (3) The exosystem is not known precisely., Stabilization and output regulation are two fundamental control problems. The output regulation problem aims to design a feedback controller to achieve asymptotic tracking of a class of reference inputs and rejection of a class of disturbances in an uncertain system while maintaining the internal stability of the closed-loop system. Thus the output regulation problem is more demanding than the stabilization problem. Nevertheless, under some assumptions, the output regulation problem can be converted into a stabilization problem for a well defined augmented system and the solvability of the stabilization problem for this augmented system implies that of the output regulation problem for the original plant. Therefore, to a large extent, the study of the stabilization problem will also lay a foundation for that of the output regulation problem., To handle these problems and overcome the shortcomings of the robust control approach, in this thesis, we have incorporated the adaptive control approach with the robust control approach. Both stabilization problem and output regulation problem are considered for two important classes of nonlinear systems, namely, the output feedback systems and lower triangular systems. The main contributions are summarized as follows. (1) The adaptive output regulation problem for nonlinear systems in output feedback form is addressed without knowing the control direction. The Nussbaum gain technique is incorporated with the robust control technique to handle the unknown control direction and the nonlinearly parameterized uncertainties in the system. To overcome the dilemma caused by the unknown control direction and the nonlinearly parameterized uncertainties, we have adopted a Lyapunov direct method to solve the adaptive output regulation problem. (2) The adaptive stabilization problem for nonlinear systems in lower triangular form is solved when both static and dynamic uncertainties are present and the control direction is unknown. Technically, the presence of dynamic uncertainty has made the stabilization problem more difficult than the previous work. We have managed to combine the changing supply rate technique and the Nussbaum gain technique to deal with this difficulty. The result is also applied to solve the output regulation problem for lower triangular systems with unknown control direction. (3) The adaptive output regulation problem for nonlinear systems in output feed-back form with unknown exosystem is studied. The adaptive control technique is applied to estimate the unknown parameter results from the unknown exosystem. The condition under which the parameter estimation converges to its real value is also discussed. Further, the global disturbance rejection problem for nonlinear systems in lower triangular form is solved by formulating the unknown external disturbanc, Liu, Lu., Adviser: Jie Huang., Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3693., Thesis (Ph.D.)--Chinese University of Hong Kong, 2008., Includes bibliographical references (leaves 204-214)., Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web., Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web., s in English and Chinese., School code: 1307., isbn: 9781109226423, Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)