Controllability and observability in the problem of stabilizing mechanical systems with cyclic coordinates

Analysis of modern modeling methods in problems of stabilization of motions of mechatronic systems with differential constraints

“…Since the method developed by the authors is oriented toward automating the process of studying the dynamics of complex systems, perhaps of a wider class, the P.V. Voronets equations in Routh variables were originally chosen to describe the system, in contrast to, for example, [13,40]. The choice of these variables is due to the fact that they use rather general and well established procedures.…”

“…In the method developed by the authors of this article, unlike [13,[39][40][41], the equations have a form that allows one to analyze in detail the structure of the linear and nonlinear terms of the perturbed equations of motion after replacing the theory of critical cases. Therefore, the use of the equations obtained in [34][35][36][37][38][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56] is not limited (compare [13,[39][40][41]) only for locating the roots of the characteristic equation or for studying controllability and observability (compare [13,40]), but also from the point of view of the theory of critical cases [28][29][30], the structure of nonlinear terms is analyzed. Since the method developed by the authors is oriented toward automating the process of studying the dynamics of complex systems, perhaps of a wider class, the P.V.…”

“…immediately have a normal form used in control theory. It should be emphasized that the developed form of the vectormatrix equations will allow us to consider stabilization problems for nonholonomic systems that differ significantly from known ones (for example, [13,40]). It is possible to consider the problem of ensuring in the general case of non-asymptotic stability of unperturbed motion by applying linear control with the maximum possible use of the properties (possibly, non-asymptotic and conditional) of the stability of the system's own motions to reduce the dimension of control, simplify its structure, and reduce the volume of measurement information.…”

“…Vector-matrix equations of disturbed motion are widely used [13, to consider the problems of stability and stabilization of motions of complex mechanical systems. It should be noted that the systematic application of such a form of equations for the study of the dynamics of nonholonomic systems began quite a long time [34][35][36][37][38] (compare [13,[39][40][41]). In the method developed by the authors of this article, unlike [13,[39][40][41], the equations have a form that allows one to analyze in detail the structure of the linear and nonlinear terms of the perturbed equations of motion after replacing the theory of critical cases.…”

“…It should be noted that the systematic application of such a form of equations for the study of the dynamics of nonholonomic systems began quite a long time [34][35][36][37][38] (compare [13,[39][40][41]). In the method developed by the authors of this article, unlike [13,[39][40][41], the equations have a form that allows one to analyze in detail the structure of the linear and nonlinear terms of the perturbed equations of motion after replacing the theory of critical cases. Therefore, the use of the equations obtained in [34][35][36][37][38][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56] is not limited (compare [13,[39][40][41]) only for locating the roots of the characteristic equation or for studying controllability and observability (compare [13,40]), but also from the point of view of the theory of critical cases [28][29][30], the structure of nonlinear terms is analyzed.…”