Ball and beam

Abstract: We consider the application of a formulation of passivity-based control (PBC), known as interconnection and damping assignment (IDA) to the problem of stabilization of underactuated mechanical systems, which requires the modification of both the potential and the kinetic energies. Our main contribution is the characterization of a class of systems for which IDA-PBC yields a smooth asymptotically stabilizing controller with a guaranteed domain of attraction. The class is given in terms of solvability of certain partial differential equations. One important feature of IDA-PBC, stemming from its Hamiltonian formulation, is that it provides new degrees of freedom for the solution of these equations. Using this additional freedom, we are able to show that the method of "controlled Lagrangians"-in its original formulation-may be viewed as a special case of our approach. As illustrations we design asymptotically stabilizing IDA-PBCs for the classical ball and beam system and a novel inertia wheel pendulum.

Abstract: Approximate input-output linearization of nonlinear systems which fail to have a well defined relative degree is studied. For such systems, a method for constructing approximate systems that are input-output linearizable is provided. The analysis presented is motivated through its application to a common undergraduate control laboratory experiment-the ball and beam-where it is shown to be more effective for trajectory tracking than the standard Jacobian linearization. >

Abstract: Presents a recurrent neural network for solving the Sylvester equation with time-varying coefficient matrices. The recurrent neural network with implicit dynamics is deliberately developed in the way that its trajectory is guaranteed to converge exponentially to the time-varying solution of a given Sylvester equation. Theoretical results of convergence and sensitivity analysis are presented to show the desirable properties of the recurrent neural network. Simulation results of time-varying matrix inversion and online nonlinear output regulation via pole assignment for the ball and beam system and the inverted pendulum on a cart system are also included to demonstrate the effectiveness and performance of the proposed neural network.

Abstract: An analysis of the nonlinear servomechanism problem by the authors (1992) is shown to lead naturally to a straightforward and practical method for solving the problem in an approximate sense. The results are based on a kth-order approximate solution for the plant zero-error manifold, and corresponding control law constructions are shown to yield kth-order asymptotic tracking and disturbance rejection properties for the closed-loop system. The approach is illustrated by application to the ball and beam system. >

Abstract: Ball and plate system is the extension of traditional ball and beam system. In this paper, a trajectory planning and tracking problem of ball and plate system is put forward to proof-test diverse control schemes. Firstly, we derive the mathematical model of the ball and plate system in detail. Then a hierarchical fuzzy control scheme is proposed to deal with this problem. Our scheme is composed of three levels. The lowest level is a TS type fuzzy tacking controller; the middle level is a fuzzy supervision controller that takes actions in extreme situations; and the top level is a fuzzy planning controller that determines the desired trajectory. In order to optimize the ball's moving trajectory, the genetic algorithm is introduced to adjust the output membership functions of the fuzzy planning controller. Simulation results have shown that the hierarchical fuzzy control scheme can control the ball from a point to another without hitting the obstacles and in the least time.