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.

Thesis (M.S.)--University of Missouri--Rolla, 2007. / Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed November 28, 2007) Includes bibliographical references.

Thesis (Ph. D.)--West Virginia University, 2005. / Title from document title page. Document formatted into pages; contains xiii, 187 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 165-172).

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Based on the Lypunov stability theorem, a design methodology of adaptive backstepping control is proposed in this thesis for a class of multi-input systems with matched and mismatched perturbations to solve regulation problems. The systems to be controlled contain blocks¡¦ dynamic equations, hence virtual input controllers are firstly designed so that the state variables of first blocks are asymptotically stable if each virtual control input is equal to the state variable of next block. The control input is designed in the last block to ensure asymptotic stability for each state even if the perturbations exist. In addition, adaptive mechanisms are embedded in each virtual input function and control input, so that the upper bound of perturbations is not required to be known beforehand. Finally, a numerical example and a practical application are given for demonstrating the feasibility of the proposed control scheme. ­^¤åºK­n(keyword)¡Gadaptive block backstepping controller, mismatched parameter uncertainty, virtual input controller, Lyapunov stability .

A methodology of designing an adaptive sliding mode controller for a class of nonlinear systems with matched and mismatched perturbations is proposed in this thesis. A specific designed sliding surface function is presented first, whose coefficients are determined by using Lyapunov stability theorem and linear matrix inequality (LMI) optimization technique. Without requiring the upper bounds of matched perturbations, the controller with adaptive mechanisms embedded is also designed by using Lyapunov stability theorem. The proposed control scheme not only can drive the trajectories of the controlled systems reach sliding surface in finite time, but also is able to suppress the mismatched perturbations when the controlled systems are in the sliding mode, and achieve asymptotic stability. In addition, the proposed control scheme can be directly applied to a class of underactuated systems. A numerical example and a practical experiment are given for demonstrating the feasibility of the proposed control scheme.

In this thesis an adaptive backstepping control scheme is proposed for a class of multi-input perturbed systems with time-varying delays to solve regulation problems. The systems to be controlled contain n blocks¡¦ dynamic equations, hence n-1 virtual input controllers are designed from the first block to the (n-1)th block, and the backstepping controller is designed from the last block. In addition, adaptive mechanisms are embedded in each virtual input controllers and proposed controller, so that the least upper bounds of perturbations are not required to be known beforehand. Furthermore, the dynamic equations of the systems to be controlled need not satisfy strict-feedback form, and the upper bounds of the time delays as well as their derivatives need not to be known in advance either. The resultant controlled systems guarantee asymptotic stability in accordance with the Lyapunov stability theorem. Finally, a numerical example and a practical application are given for demonstrating the feasibility of the proposed control scheme.

Based on the Lyapunov stability theorem, a decentralized adaptive backstepping tracking control scheme for a class of perturbed large-scale systems with non-strict feedback form is presented in this thesis to solve tracking problems. First of all, the dynamic equations of the plant to be controlled are transformed into other equations with semi-strict feedback form. Then a decentralized tracking controller is designed based on the backstepping control methodology so that the outputs of controlled system are capable of tracking the desired signals generated from a reference model. In addition, by utilizing adaptive mechanisms embedded in the backstepping controller, one need not acquire the upper bounds of the perturbations and the interconnections in advance. The resultant control scheme is able to guarantee the stability of the whole large-scale systems, and the tracking precision may be adjusted through the design parameters. Finally, one numerical and one practical examples are demonstrated for showing the applicability of the proposed design technique.

Based on the Lyapunov stability theorem, a sliding mode control design methodology is proposed in this thesis for a class of perturbed switched systems. The control of the systems is rest restricted to switching between two different constant values. New sliding mode reaching conditions are proposed for the controllers so that the controlled systems can enter the sliding mode in finite time. Once the switched control system is in the sliding mode, the stability of the system is guaranteed by choosing a suitable sliding surface. In addition, a method for alleviating the infinite switching phenomenon is also provided in this thesis. Finally, a numerical and a practical example with computer simulation results are given for demonstrating the feasibility of the proposed control scheme.