Adjoint-Based Optimization Procedure for Active Vibration Control of Nonlinear Mechanical Systems

Abstract

In this paper, a new computational algorithm for the numerical solution of the adjoint equations for the nonlinear optimal control problem is introduced. To this end, the main features of the optimal control theory are briefly reviewed and effectively employed to derive the adjoint equations for the active control of a mechanical system forced by external excitations. A general nonlinear formulation of the cost functional is assumed, and a feedforward (open-loop) control scheme is considered in the analytical structure of the control architecture. By doing so, the adjoint equations resulting from the optimal control theory enter into the formulation of a nonlinear differential-algebraic two-point boundary value problem, which mathematically describes the solution of the motion control problem under consideration. For the numerical solution of the problem at hand, an adjoint-based control optimization computational procedure is developed in this work to effectively and efficiently compute a nonlinear optimal control policy. A numerical example is provided in the paper to show the principal analytical aspects of the adjoint method. In particular, the feasibility and the effectiveness of the proposed adjoint-based numerical procedure are demonstrated for the reduction of the mechanical vibrations of a nonlinear two degrees-of-freedom dynamical system.

Development and implementation of a control system for a retrofitted CNC machine by using Arduino

“…The research areas of interest for the authors are multibody dynamics [16][17][18][19][20], system identification [21][22][23][24][25], and optimal control [26][27][28][29][30]. Therefore, the main research efforts of the authors are devoted to the development of new methods for performing accurate analytic modelling [31][32][33][34][35], numerical parameter identification using experimental data [36][37][38][39][40], and optimal control optimization for dynamic models of multibody mechanical systems [41][42][43][44][45][46].…”

Entropic Measure of Epistemic Uncertainties in Multibody System Models by Axiomatic Design

“…A ij DP j (8) In Equation (2), the diagonal matrix is a special case. The design matrix [A], in general, is a rectangular array of values.…”

“…Multibody systems represent a special class of mechanical systems made of rigid and/or flexible bodies, mutually interconnected by joint constraints, and subjected to external force fields [1][2][3][4][5][6][7][8][9][10]. Several examples of such complex systems can be found in industrial engineering applications [11][12][13][14][15][16][17][18][19][20].…”

System Identification Algorithm for Computing the Modal Parameters of Linear Mechanical Systems

“…In the case of the parametric identification problem, one needs to construct analytical expressions in terms of the desired parameters and correlate them with experimental data in order to identify the parameters of interest [62,63]. For this purpose, simple least-square methods, as well as more advanced gradient-based optimization techniques relying on the adjoint method can be used for minimizing the error between the time responses observed in experimental measurements and the time evolutions predicted by the mathematical model based on the unknown parameters [64][65][66][67][68][69]. On the other hand, in the case of the model identification problem in the time domain, one needs to find a linear dynamical model directly that embodies the best fit for an input and output dataset measured for a given mechanical system.…”