Showing papers on "Ball and beam published in 2000"

Neurocontroller alternatives for "fuzzy" ball-and-beam systems with nonuniform nonlinear friction

Abstract: The ball-and-beam problem is a benchmark for testing control algorithms. Zadeh proposed (1994) a twist to the problem, which, he suggested, would require a fuzzy logic controller. This experiment uses a beam, partially covered with a sticky substance, increasing the difficulty of predicting the ball's motion. We complicated this problem even more by not using any information concerning the ball's velocity. Although it is common to use the first differences of the ball's consecutive positions as a measure of velocity and explicit input to the controller, we preferred to exploit recurrent neural networks, inputting only consecutive positions instead. We have used truncated backpropagation through time with the node-decoupled extended Kalman filter (NDEKF) algorithm to update the weights in the networks. Our best neurocontroller uses a form of approximate dynamic programming called an adaptive critic design. A hierarchy of such designs exists. Our system uses dual heuristic programming (DHP), an upper-level design. To our best knowledge, our results are the first use of DHP to control a physical system. It is also the first system we know of to respond to Zadeh's challenge. We do not claim this neural network control algorithm is the best approach to this problem, nor do we claim it is better than a fuzzy controller. It is instead a contribution to the scientific dialogue about the boundary between the two overlapping disciplines.

A state observer for nonlinear systems and its application to ball and beam system

Abstract: In this paper, we present a state observer for single-input/single-output nonlinear systems which fail to have well defined relative degree. It is shown that there exists a local state observer for a nonlinear system if it has robust relative degree n. The proposed observer utilizes the coordinate change which transforms a system into an approximate normal form. The proposed method is applied to a ball and beam system, and simulation results show that substantial improvement in the performance was achieved compared with other local observers.

Matching, linear systems, and the ball and beam

Abstract: A recent approach to the control of underactuated systems is to look for control laws which will induce some specified structure on the closed loop system. This basic idea is used in several papers already. In this paper, we will describe one matching condition and an approach for finding all control laws that fit the condition. After an analysis of the resulting control laws for linear systems, we will present the results from an experiment on a ball and beam system.

On the control of the "ball and beam" system: a trajectory planning approach

Abstract: An approximate linearization, in combination with a suitable off-line trajectory planning, is proposed for the equilibrium to equilibrium regulation of the popular "ball and beam" system. The results are illustrated by means of digital computer simulations.

Stabilization and equilibrium control of super articulated ball and beam system

Abstract: Deals with the stabilization and equilibrium control of a super-articulated ball and beam system. On the basis of establishing a mathematical model of the plant, we put forward two kinds of design methods of the controller. The state controller is realized via state feedback, where the unmeasurable states are estimated by a Luenberger reduced order observer. Different to the state control, a cascade structure is used for the fuzzy controller, the more simple definition of fuzzy variables and rules as well as a short execution time are the advantages of this structure. We consider disturbance compensation in the controller designing. Experimental studies are presented at the end of the paper. From the result, we can conclude that the algorithms have high control precision and good stability.

Stabilization and Equilibrium Control of Super Articulated Ball and Beam System

Abstract: Ibis paper deals with the stabilization and equilibrium control of super-articulated ball and beam system. On the basis of establishing mathematical model of the plant, we put forward two kinks of design methods of the controller. The state controller is realized via state feedback, where the "able stat= are estimated by a Luenberger reduced order observa. Different to the state control, a cascade stn~cture is used for the fuzzy controller, the more simple definition of fuzzy variables and rules as well as a shod execution time are the advantages of this structure. We consider disturbance compensation in the controller designing. Experiment studies are presented in the end of this paper. From the result, we can conclude that the algorithms have high control precision and good stability.

Matching control laws for a ball and beam system

Abstract: This note describes a method for generating an infinite-dimensional family of nonlinear control laws for underactuated systems. For a ball and beam system, the entire family is found explicitly.

Robust motion control algorithm for brushless direct drive motor

Abstract: Brushless direct drive motors became very popular among robot designers due to the simple mechanical structure which avoids the use of a speed reducer. Speed reducers introduce undesired nonlinear phenomena in the motion transmission, thus imposing positioning errors and uncertain control stability. With the use of the direct drive motor backlash flexibility, and friction are diminished or eliminated, while highly nonlinear load variation affecting the motor axis is not reduced. Therefore, an advanced motion control algorithm has to be applied in a control scheme. The paper introduces a robust motion control algorithm, which is derived from a sliding manifold definition and Lyapunov design introducing the perturbation estimator. The control algorithm was tested using a highly nonlinear direct driven ball and beam system. Experimental results are presented and discussed.

Approximate methods for nonlinear output regulation problem

Abstract: One of the important control problems is to design a control law for a plant such that the output of the plant can asymptotically track a class of reference trajectories and/or reject a class of external disturbances. When the reference trajectories and the disturbance are generated by an autonomous differential equation, the problem is called output regulation, or servomechanism problem. Output regulation is becoming more and more challenging and interesting because of its ability of coping with uncertainties and dealing with a large class of complex systems. For the class of linear systems, the output regulation problem was thoroughly studied in the 1970s and 1980s. For the class of nonlinear systems, the output regulation problem has attracted extensive attention since the 1990s. So far, many fruitful theoretical results have been obtained. However, the key issue of the practical computation of the control law has not been well addressed because the control law based on output regulation theory relies on the solution of a set of mixed nonlinear partial differential and algebraic equations known as the regulator equations. Since it is almost impossible to obtain the closed form solution for the regulator equations due to the nonlinearity and complexity, it is necessary to develop effective approximation methods to solve the output regulation problem in order to make the output regulation theory a practical design tool. This thesis will propose two approximation methods for solving the output regulation problem as described below: (1) We will present an approximation method for solving the regulator equations based on a class of feedforward neural networks. We will show that a three layer neural network can solve the regulator equations up to a prescribed arbitrarily small error, and this small error can be translated into a guaranteed steady state tracking error for the closed-loop system. The method will lead to an effective control strategy to solving the nonlinear output regulation problem approximately and practically. (2) We will also present an approximation method that does not rely on the solution of the regulator equations. This approach will approximately solve the output regulation problem by directly approximating a feedforward function using a class of artificial neural networks. Further, a control configuration is developed that allows the reduction of the tracking error by the on-line adjustment of the parameters of the neural networks. A strength of the output regulation theory is its capability of handling a large class of nonlinear systems that cannot be controlled by other methods. We will apply the above two approaches to some benchmark nonlinear control problems such as the asymptotic tracking of the inverted pendulum on a cart system, the ball and beam system and the disturbance rejection problem for rotational/translational actuator (RTAC). These designs will be thoroughly evaluated and compared.

An interactive environment for design, simulation and real-time control of nonlinear systems

Abstract: General features of an interactive environment for linear/nonlinear optimal and robust control design, simulation and real-time implementation of a class of nonlinear systems are described. The motivation for development of the environment is explained and its utility demonstrated through a case study using the popular ball and beam system.