An adaptive decentralized nonlinear controller for a robot manipulator is presented in this thesis. Based on the adaptive control schemes designed by Seraji [18], Dai [30], and Jimenez [31], we redesigned and further simplified the control algorithm and, as a consequence, we achieved better path tracking performance. The proposed adaptive controller is made of a PD feedback controller which has time varying gains, a feedforward compensator based on the idea of inverse dynamics, and an auxiliary signal. Due to its adaptive structure, the controller shows robustness against disturbances and unmodeled dynamics. In order to ensure asymptotic tracking we select a Lyapunov function such that the controller forces the negative definiteness of the time derivative of such a Lyapunov function. To do this, the tracking position and velocity error are penalized and used as a part of the adaptive control gain. The main advantages of this scheme are the comparably faster convergence of tracking error, relatively simpler structure, and smoother control activity. This controller only requires the position and angular speed measurement, it does not require any knowledge about the mathematical model of the robot manipulator. Simulation shows the capacity of this controller and its robustness against disturbances. / Graduation date: 1993

Command Generation has been shown to be a practical and effective control scheme for eliminating payload swing on industrial cranes. However, this technology has not been used to its full potential. One reason is that nonlinear crane dynamics degrade the performance of current command generators, making them challenging to use. A second reason is that few crane operators are aware of this technology. Therefore, this thesis strives to alleviate these problems through the completion of three major tasks. First, new command generation algorithms are developed that compensate for nonlinear crane dynamics. Two major sources of non-linear dynamics are targeted: nonlinear drive dynamics, and non-linear physical dynamics of tower cranes. Second, command generation are examined from an educational perspective; both in the classroom and in the working field. Third, three experimental crane devices were built to fulfill the two prior tasks.

This paper presents the Lie-Backlund symmetry method to give the equivalence between differential equations and describe the equivalent transformation procedure of nonlinear control systems of partial differential equations. The equivalent linear systems found by solving the infinitesimal generator of one-parameter Lie groups with prolongations and the infinitesimal generator are used to construct the parameters of invertible mapping u. And the equivalence linear form of the nonlinear system is constructed via u. Some necessary conditions for mapping a nonlinear control system of PDE¡¦s to a linear control system of PDE¡¦s are discussed, and application of Lie-Backlund symmetries and invertible mapping u constructed linear time-invariant control system of partial differential equations.

Thesis (Ph. D.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2004. / Habetler, Thomas, Committee Member ; Sadegh Nader, Committee Member ; Taylor David, Committee Member ; Tsiotras Panagiotis, Committee Co-Chair ; Heck-Ferri Bonnie, Committee Co-Chair. Vita. Includes bibliographical references (leaves 319-326).

Thesis (Ph. D.)--University of Texas at Austin, 2003. / Vita. Includes bibliographical references. Available also from UMI Company.

The Reaction Wheel Pendulum (RWP) is an interesting nonlinear system. A prototypical control problem for the RWP is to stabilize it around the upright position starting from the bottom, which is generally divided into at least 2 phases: (1) Swing-up phase: where the pendulum is swung up and moves toward the upright position. (2) Stabilization phase: here, the pendulum is controlled to be balanced around the upright position. Previous studies mainly focused on an energy method in swing-up phase and a linearization method in stabilization phase. However, several limitations exist. The energy method in swing-up mode usually takes a long time to approach the upright position. Moreover, its trajectory is not controlled which prevents further extensions. The linearization method in the stabilization phase, can only work for a very small range of angles around the equilibrium point, limiting its applicability. In this thesis, we took the 2nd order state space model and solved it for a constant torque input generating the family of phase-plane trajectories (see Appendix A). Therefore, we are able to plan the motion of the reaction wheel pendulum in the phase plane and a sliding mode controller may be implemented around these trajectories. The control strategy presented here is divided into three phases. (1) In the swing up phase a switching torque controller is designed to oscillate the pendulum until the system’s energy is enough to drive the system to the upright position. Our approach is more generic than previous approaches; (2) In the catching phase a sliding surface is designed in the phase plane based on the zero torque trajectories, and a 2nd order sliding mode controller is implemented to drive the pendulum moving along the sliding surface, which improves the robustness compared to the previous method in which the controller switches to stabilization mode when it reaches a pre-defined region. (3) In the stabilization phase a 2nd order sliding mode integral controller is used to solve the balancing problem, which has the potential to stabilize the pendulum in a larger angular region when compared to the previous linearization methods. At last we combine the 3 phases together in a combined strategy. Both simulation results and experimental results are shown. The control unit is National Instruments CompactRIO 9014 with NI 9505 module for module driving and NI 9411 module for encoding. The Reaction Wheel Pendulum is built by Quanser Consulting Inc. and placed in UT’s Advanced Mechatronics Lab. / text

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In the past decades there has been onsiderable commercial and academic interest in methods for monitoring control system performance for linear systems. Far less has been written on control system performance for nonlinear dynamic / stochastic systems. This thesis presents research results on three control performance monitoring topics for the nonlinear systems: i) Controller assessment of a class of nonlinear systems: The use of autoregressive moving average (ARMA) models to assess the control loop performance for linear systems is well known. Classes of nonlinear dynamic / stochastic systems for which a similar result can be obtained are established for SISO discrete systems. For these systems, the performance lower bounds can be estimated from closed-loop routine operating data using nonlinear autoregressive moving average with exogenous inputs (NARMAX) models. ii) Variance decomposition of nonlinear systems / time series: We develop a variance decomposition approach to quantify the effects of different sources of disturbances on the nonlinear dynamic / stochastic systems. A method, called ANOVA-like decomposition, is employed to achieve this variance decomposition. Modifications of ANOVA-like decomposition are proposed so that the NOVA-like decomposition can be used to deal with the time dependency and the initial condition. iii) Parameter uncertainty effects on the variance decomposition: For the variance decomposition in the second part, the model parameters are assumed to be exactly known. However, parameters of empirical or mechanistic models are uncertain. The uncertainties associated with parameters should be included when the model is used for variance analysis. General solutions of the parameter uncertainty effects on the variance decomposition for the general nonlinear systems are proposed. Analytical solutions of the parameter uncertainty effects on the variance decomposition are provided for models with linear parameters. / Thesis (Ph.D, Chemical Engineering) -- Queen's University, 2007-10-17 16:02:26.376 / This work was sponsored by NSERC Discovery, NSERC Equipment, Shell Global Solutions, OGSST and QGA