Title: A fresh approach for lyapunov-based control of mechanical systems
Abstract: This dissertation deals with the development of several control design techniques for robotic systems and distributed parameter systems, such as flexible beam and strings. In Chapter 1, we consider the problem of output feedback link position tracking control of robot manipulators. This problem has been a topic of considerable interest over the past several years. A limitation that exists in almost all of the proposed OFB link position tracking controllers is the semi-global nature of the stability results. In contrast, global solutions to the OFB link position setpoint control problem have been presented by several researchers. In this chapter, we design a global, adaptive, OFB tracking controller for uncertain, n DOF's, robot manipulators. The control law is composed of. (i) a desired compensation adaptation law (DCAL) feedforward term to compensate for parametric uncertainty, and (ii) a nonlinear feedback term coupled to a nonlinear, dynamic filter to compensate for the lack of velocity measurements and the difference between the actual system dynamics and the feedforward term based on the desired trajectory. That is, the proposed controller ensures global asymptotic link position tracking while compensating for parametric uncertainty and lack of link velocity measurements.
In Chapter 2, we consider the problem of controlling the displacement and rotation of a cantilevered Timoshenko beam. While the Timoshenko model is more accurate at predicting the beam's response in comparison to the Euler-Bernoulli model, the Timoshenko model is a more difficult model to utilize for control design purposes due to its higher order. In this chapter, a Lyapunov-type design/analysis procedure based on an energy-related function is utilized to first develop an model-based boundary control law which achieves a uniform exponential stability result for the beam displacement and rotation. The proposed model-based control strategy requires measurements of the free-end displacement, slope, rotation due to bending, slope of the rotation due to bending, and the time derivatives of these quantities. We then illustrate how the structure of the model-based controller allows one to synthesize an adaptive controller which stabilizes the beam displacement and rotation asymptotically fast while compensating for uncertainty associated with the mechanical system parameters.
In Chapter 3, we improve on the range of applicability of boundary control for string-like systems by utilizing a more accurate model. Specifically, the model used for control design purposes includes nonlinear terms in the field equation which account for both large amplitude displacements and generic nonlinear tension effects. As one would expect, the nonlinear terms in the field equation also spawn additional nonlinear effects in the actuator boundary dynamics which must be compensated for. Based on the proposed model for the actuator-string system, we design a model based boundary controller which asymptotically stabilizes the total energy of the actuator-string system. The proposed boundary controller is a nonlinear algorithm which requires measurement of. (i) the string's slope (and its time derivative) at the actuated boundary, (ii) the string's velocity at the actuated boundary, and (iii) the tension in the string. We then redesign the model based boundary controller as an adaptive boundary controller which compensates for parametric uncertainty and asymptotically stabilizes the total energy of the system.
Publication Year: 1999
Publication Date: 1999-01-01
Language: en
Type: article
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