Multi-input Dynamical Systems Research Articles

Uncontrollability for Linear Autonomous Multi-input Dynamical Systems Depending on Parameters

Linear multi-input dynamical systems smoothly depending on parameters are considered. A set of parameter values corresponding to uncontrollable systems (an uncontrollability set) is studied. The typical (generic) structure of the uncontrollability set is described. A constructive method of perturbation analysis of the uncontrollability set is developed. Formulae of first-order approximations for the uncontrollability set and generalized eigenvalues (uncontrollable modes) are derived and used for numerical construction of the uncontrollability set. The method is based on the versal deformation theory for matrix pairs under feedback equivalence. As an example, the uncontrollability set is found for a three-parameter two-degree-of-freedom mechanical system.

Moving Sliding Surfaces for Fast Tracking Control of Second-Order Dynamical Systems

A new type of sliding surface for a variable structure control system is proposed to achieve fast and accurate path tracking in a class of nonlinear second-order multi-input dynamical systems. The surface is adaptable to arbitrary initial conditions, and movable towards a predetermined surface. The movement is executed in a stepwise manner according to the trajectory of representative points. We call it a moving sliding surface (MSS). Using the MSS favorable fast tracking is accomplished without increasing the magnitude of the discontinuous control gain. A two-degree-of-freedom robotic manipulator subjected to external disturbances is considered to demonstrate the efficacy of the proposed method.

A New Procedure For Multi-Input Dynamic Systems Identification

One of the major problem for the identification of industrial multi-input multi-output (MIMO) systems is the too small variance of some signals collected during several experiments. Usually, sufficient information exist but are often dispersed among many data-files. In this case, it is difficult to conciliate this information to build a single well adapted model. The ALS procedure (Alternate Least Squares) has been performed in order to solve this kind of problem. In the first part of this paper, the authors present the principle of the ALS procedure; the details of the complete algorithm are given in part two. Then, based on some examples, a comparison of the Prediction Error Method (PEM) with our new method is presented.

An Eclectic Approach to the State Feedback Control of Nonlinear Dynamical Systems

This paper examines the problem of robust state-feedback stabilization of a class of nonlinear multi-input dynamical systems. Four approaches to the problem are investigated: the variable structure control (VSC) method, the high-gain feedback technique, the feedback linearization algorithm, and finally the deterministic approach to the control of uncertain systems. It is shown that each design method can lead to a controller such that the closed-loop system exhibits a sliding mode property. The sliding mode is a desirable property since it results in a robust control. The analysis is illustrated by means of a simple numerical example.

Guaranteed robustness properties of multivariable nonlinear stochastic optimal regulators

We study the robustness of optimal regulators for nonlinear, deterministic and stochastic multiinput dynamical systems, under the assumption that all state variables can be measured. We show that, under mild assumptions, such nonlinear regulators have a guaranteed infinite gain margin; moreover, they have a guaranteed 50 percent gain reduction margin and a 60 degree phase margin in each feedback channel, provided that the system is linear in the control and the penalty to the control is quadratic, thus extending the well-known properties of LQ regulators to nonlinear optimal designs. These results are also valid for infinite horizon, average cost, stochastic optimal control problems.

Pole placement in multi-input systems via elementary transformations

This paper is concerned with the development of an algorithm for pole placement in multi-input dynamic systems. The algorithm which uses a series of elementary transformations is believed to be simpler, computationally more efficient and numerically stable when compared with earlier methods. In this paper two methods have been presented.