On the instability of equilibrium of a mechanical system with nonconservative forces

In this paper the stability of equilibrium of nonholonomic systems, on which dissipative and nonconservative positional forces act, is considered. We have proved the theorems on the instability of equilibrium under the assumptions that: the kinetic energy, the Rayleigh?s dissipation function and the positional forces are infinitely differentiable functions; the projection of the positional force component which represents the first nontrivial form of Maclaurin?s series of that positional force to the plane, which is normal to the vectors of nonholonomic constraints in the equilibrium position, is central and repulsive (with its centre of action in the equilibrium position). The suggested theorems are generalization of the results from [V.V. Kozlov, Prikl. Math. Mekh. (PMM), T58, V5, (1994), 31-36] and [M.M. Veskovic, Theoretical and Applied Mechanics, 24, (1998), 139-154]. The result obtained is analogous to the result from [D.R. Merkin, Introduction to theory of the stability of motion, Nauka, Moscow (1987)], which refers to the impossibility of equilibrium stabilization in a holonomic conservative system by dissipative and nonconservative positional forces in case when the potential energy in the equilibrium position has the maximum. The proving technique will be similar to that used in the paper [V.V. Kozlov, Prikl. Math. Mekh. (PMM), T58, V5, (1994), 31-36]. .

Design and Implementation of a Neural Network Controlled Electro-Hydraulic Drive

Hydraulic systems are commonly used in industry when large forces of torques are required. Increasing demands for positional, force and speed control from users have led to the use of closed-loop control techniques. While classical controllers are used successfully for many hydraulic applications, they cannot cope with the non-linearities inherent in hydraulic systems or the changes to system parameters over time. This paper considers these problems and proposes a solution in the form of a neural network-based controller in the forward path of the system directly controlling the hydraulic plant. A network-learning mechanism is also proposed to train the network to minimize the system error and examples are given of the implementation with comparisons against a PID controller. The examples illustrate the rapid convergence of the training algorithm and the robustness properties of a simple two-neuron, two-input network controlling a non-linear time-varying plant.