A variational approach to the analysis of non-conservative mechatronic systems (original) (raw)

A variational approach to the analysis of dissipative electromechanical systems

We develop a method for systematically constructing Lagrangian functions for dissipative mechanical, electrical and, electromechanical systems. We derive the equations of motion for some typical electromechanical systems using deterministic principles that are strictly variational. We do not use any ad hoc features that are added on after the analysis has been completed, such as the Rayleigh dissipation function.

Inverse Dynamics of Electromechanical Systems Using Lagrange-Based Modelling

Inverse problems of dynamics shall be understood as the task of determination of topology, kinematics and constitutive equations (force/torque laws) of a (mechatronic) system to fulfil given dynamic properties. Inverse dynamics is one subtask out of the complex variety of inverse problems. This paper shows a method to solve the task of inverse dynamics under special assumptions. Electromechanical systems (EMS) are characterized by interaction of electromagnetic fields with inertial bodies. These interactions can be described by so-called constitutive equations. EMS with a finite degree of freedom are called discrete EMS. Such systems can be modelled by coupling the dynamics of multibody systems and Kirchhoff’s theory. The development of tools for both analysis and synthesis of such systems needs a unified mathematical description. A Lagrange-based modelling proofs to be a suitable approach. In this paper, it is used to model optical micromirrors as mechatronic systems to carry out i...

A power-based description of standard mechanical systems

Systems & Control Letters, 2007

This paper is concerned with the construction of a power-based modeling framework for mechanical systems. Mathematically, this is formalized by proving that every standard mechanical system (with or without dissipation) can be written as a gradient vector field with respect to an indefinite metric. The form and existence of the corresponding potential function is shown to be the mechanical analog of Brayton and Moser's mixed-potential function as originally derived for nonlinear electrical networks in the early sixties. In this way, several recently proposed analysis and control methods that use the mixed-potential function as a starting point can also be applied to mechanical systems.

A power-based perspective of mechanical systems

Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, 2005

This paper is concerned with the construction of a power-based modeling framework for a large class of mechanical systems. Mathematically this is formalized by proving that every standard mechanical system (with or without dissipation) can be written as a gradient vector field with respect to an indefinite metric. The form and existence of the corresponding potential function is shown to be the mechanical analogue of Brayton and Moser's mixed-potential function as originally derived for nonlinear electrical networks in the early sixties. In this way, several recently proposed analysis and control methods that use the mixed-potential function as a starting point can also be applied to mechanical systems.

Modelling of Electromechanical Systems as a Basis for Inverse Dynamics

A unified, Lagrange-based mathematical approach is used to model the optical micromirrors as mechatronic systems. A method to solve a special task of inverse dynamics of such systems is shown: the calculation of electrical voltages in accordance with a given mechanical motion. This can be considered as a special case of the so-called Inverse Problems of dynamics. The method can be understood as one step on the way of the development of both methods and tools suitable for synthesis of mechatronic systems.

Energy Based Analysis of Mechanical System

2015

This paper is on Energy based Analysis of Mechanical Systems using Lagrangian and Hamiltonian approach. These approaches can be used to understand the non-linearity and further to control a dynamic system efficiently by using the Kinetic and Potential Energy of the system. Here, we choose an inverted Double Pendulum System as the mechanical system for our analysis. We determine the equations of motions for the double pendulum system using the Lagrangian and Hamiltonian Mechanics and further we implement these concepts to analyse the non-linear properties of the system and further simulate the system in MATLAB. L2 and mass m2. We can say there are two pendulums, first with mass m1 and length L1, second with mass m2 and length L2 and having a pivot point O. We will let the angle that the first bar makes with the vertical line drawn down from O be θ1 and that the second bar makes with a vertical line drawn from m1 be θ2 , where counter clockwise angles are positive. If we set this syst...

Dynamics of Electromechanical Systems

Electromechanical systems can be regarded as physical structures characterized by interaction of electromagnetic fields with inertial bodies. Constitutive equations describing the coupling of multibody dynamics with Kirchhoff's theory define discrete electromechanical systems. Based on the principle of virtual work the motion equations are Lagrange's equations of second kind. The automatic generation of these model equations based on a unique approach is presented.

Energy Methods in Dynamics

Springer Verlag, 2011

The aim of this textbook is to help students acquire both a good grasp of the first principles from which the governing equations can be derived, and the adequate mathematical methods for their solving. Its distinctive features, as seen from the title, lie in the systematic and intensive use of Hamilton’s variational principle and its generalizations for deriving the governing equations of conservative and dissipative mechanical systems, and also in providing the direct variational-asymptotic analysis, whenever available, of the energy and dissipation for the solution of these equations. It will be demonstrated that many well-known methods in dynamics like those of Lindstedt-Poincare, Bogoliubov-Mitropolsky, Kolmogorov-Arnold-Moser (KAM), and Whitham are derivable from this variational-asymptotic analysis.

Energy optimal trajectories for electro-mechanical systems

IOP Conference Series: Materials Science and Engineering, 2020

Electro-mechanical systems (EMS) efficiency improvement can result not only in significant energy savings but also can have positive impact on our environment. Progressive applications of EMS control as e.g. dynamical system of multi-parts robots are described by system of non-linear mutually coupled differential equations considering gravity, acceleration, Coriolis and centrifugal couplings together with parameter changes as a function of load. Using Euler-Lagrange optimization we discuss some results in decreasing energy demands for given electro-mechanical systems exploiting electric drives, which are typical for industrial and transportation applications e.g. robotic arm control, train movement control etc.