Control Constraint Realization Applied to Underactuated Aerospace Systems

2011 ◽  
Author(s):  
Pierangelo Masarati ◽  
Marco Morandini ◽  
Alessandro Fumagalli
Keyword(s):  
Position Control ◽  
Feedforward Control ◽  
Equations Of Motion ◽  
Vertical Plane ◽  
Differential Algebraic Equations ◽  
General Purpose ◽  
Point Of View ◽  
Theoretical Point ◽  
Algebraic Equations ◽  
Control Constraint

This paper discusses the problem of control constraint realization applied to the design of maneuvers of complex under-actuated systems modeled as multibody problems. Applications of interest in the area of aerospace engineering are presented and discussed. The tangent realization of the control constraint is discussed from a theoretical point of view and used to determine feedforward control of realistic under-actuated systems. The effectiveness of the computed feedforward input is subsequently verified by applying it to more detailed models of the problems, in presence of disturbances and uncertainties in combination with feedback control. The proposed applications consist in the position control of a complex closed chain mechanism representative of a robotic system, the control of a simplified model of a canard and a conventional air vehicle in the vertical plane, and the angular velocity control of a wind-turbine. In the aeromechanics examples, the tangent realization of the control relies on the availability of the Jacobian matrix of an aeroelastic model. All problems are solved using a free general-purpose multibody software that writes the constrained dynamics of multi-field problems in form of Differential-Algebraic Equations (DAE). The equations are integrated using A/L-stable algorithms. The essential extension to the multibody code consisted in the addition of the capability to write arbitrary constraint equations and apply the corresponding reaction multipliers to arbitrary equations of motion. This allowed to exploit the modeling capabilities of the formulation without any undue restriction on the modeling requirements.

Control Constraint of Underactuated Aerospace Systems

2014 ◽  
Vol 9 (2) ◽  
Author(s):  
Pierangelo Masarati ◽  
Marco Morandini ◽  
Alessandro Fumagalli
Keyword(s):  
Feedforward Control ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
General Purpose ◽  
Point Of View ◽  
Underactuated Systems ◽  
Theoretical Point ◽  
Algebraic Equations ◽  
Control Constraint ◽  
Multibody Problems

This paper discusses the problem of control constraint realization applied to the design of maneuvers of complex underactuated systems modeled as multibody problems. Applications of interest in the area of aerospace engineering are presented and discussed. The tangent realization of the control constraint is discussed from a theoretical point of view and is used to determine feedforward control of realistic underactuated systems. The effectiveness of the computed feedforward input is subsequently verified by applying it to more detailed models of the problems, in the presence of disturbances and uncertainties in combination with feedback control. The problems are solved using a free general-purpose multibody software that writes the constrained dynamics of multifield problems formulated as differential-algebraic equations. The equations are integrated using unconditionally stable algorithms with tunable dissipation. The essential extension to the multibody code consisted of the addition of the capability to write arbitrary constraint equations and apply the corresponding reaction multipliers to arbitrary equations of motion. The modeling capabilities of the formulation could be exploited without any undue restriction on the modeling requirements.

Trajectory Tracking of Underactuated Multibody Systems

2011 ◽  
Author(s):  
Stefan Reichl ◽  
Wolfgang Steiner
Keyword(s):  
Trajectory Tracking ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Feedforward Control ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Differential Algebraic Equations ◽  
State Variables ◽  
Algebraic Equations

This work presents three different approaches in inverse dynamics for the solution of trajectory tracking problems in underactuated multibody systems. Such systems are characterized by less control inputs than degrees of freedom. The first approach uses an extension of the equations of motion by geometric and control constraints. This results in index-five differential-algebraic equations. A projection method is used to reduce the systems index and the resulting equations are solved numerically. The second method is a flatness-based feedforward control design. Input and state variables can be parameterized by the flat outputs and their time derivatives up to a certain order. The third approach uses an optimal control algorithm which is based on the minimization of a cost functional including system outputs and desired trajectory. It has to be distinguished between direct and indirect methods. These specific methods are applied to an underactuated planar crane and a three-dimensional rotary crane.

A Computer-Aided Environment for Analysis and Design of Mechanical Systems

1991 ◽  
Author(s):  
Hamid M. Lankarani ◽  
Behnam Bahr ◽  
Saeid Motavalli
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
General Purpose ◽  
Design System ◽  
Integrated Analysis ◽  
Algebraic Equations ◽  
Efficient Design ◽  
Analysis And Design ◽  
Wide Range

Abstract This paper presents the description of an ideal tool for analysis and design of complex multibody mechanical systems. It is in the form of a general-purpose computer program, which can be used for simulation of many different systems. The generality of this computer-integrated environment allows a wide range of applications with significant engineering importance. No matter how complicated the mechanical system under consideration is, a numerical multibody model of the system is constructed. The governing mixed differential/algebraic equations of motion are automatically formulated and numerically generated. State-of-the-art numerical techniques and computational methods are employed and developed which produce in the response of the system at discrete time junctures. Postprocessing of the results in the form of graphical images or real-time animations provides an enormous aid in visualizing motion of the system. The analysis package may be merged with an efficient design optimization algorithm. The developed integrated analysis/design system is a valuable tool for researchers, design engineers, and analysts of mechanical systems. This computer-integrated tool provides an important bridge between the classical decision making process by an engineer and the emerging technology of computers.

Rotorcraft Trim Analysis Using a General-Purpose Multibody Code

2008 ◽  
Author(s):  
L. Federico ◽  
A. Russo
Keyword(s):  
Aerodynamic Force ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Original System ◽  
Differential Algebraic Equations ◽  
General Purpose ◽  
Integration Scheme ◽  
Algebraic Equations ◽  
Periodic Motions ◽  
Wide Range

Rotorcraft dynamics represents a major analytical challenge to aeronautical industry and research centres. Complexities arising from large rigid motions, body elasticity, aerodynamic loads and control systems have to be taken into account in order to ensure the accuracy of a comprehensive analysis. Architected for the nonlinearities associated with large motion in three-dimensional space, the ADAMS general-purpose multibody code allows to automatically formulate and integrate the equations of motion for a wide range of mechanisms, including rotary wing systems (once provided with an aerodynamic force field description). However, the ADAMS simulation system lacks the capability to calculate periodic motions, as required in the helicopter trim analysis and stability evaluation. The prediction of the trimmed periodic motions of the rotor system implies the numerical solution of differential-algebraic boundary value problem. In this work we present a new approach to perform this task inside the ADAMS numerical environment. Thia approach is based on the perturbation of the minimal set of Ordinary Differential Equations (ODEs), being equivalent to the original system of Differential Algebraic Equations (DAEs) which defines the rotorcraft equation of motion. The transformation of DAEs to ODEs is based on the linearization of the local constraint manifold defined by the algebraic constraint equations, as suggested by Maggi in his work [1–3]. The proposed method is quite general and can be used to drive the ADAMS integration scheme within the periodic motion analysis of mechanical systems. The algotithm is adopted to simulate the wind tunnel trim test of a ECD BO105 machscaled model (EU HeliNOVI project [4]). Comparisons between numerical and experimental results are provided.

Analytical Modelling of the Dynamics of the Four-Bar Mechanism: A Comparison of Some Methods

2018 ◽  
Author(s):  
J. P. Meijaard ◽  
V. van der Wijk
Keyword(s):  
Virtual Work ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Force Balance ◽  
Dynamic Force ◽  
Algebraic Equations ◽  
Principle Of Virtual Work ◽  
Principal Vector ◽  
Reaction Forces ◽  
Principal Points

Some thoughts about different ways of formulating the equations of motion of a four-bar mechanism are communicated. Four analytic methods to derive the equations of motion are compared. In the first method, Lagrange’s equations in the traditional form are used, and in a second method, the principle of virtual work is used, which leads to equivalent equations. In the third method, the loop is opened, principal points and a principal vector linkage are introduced, and the equations are formulated in terms of these principal vectors, which leads, with the introduced reaction forces, to a system of differential-algebraic equations. In the fourth method, equivalent masses are introduced, which leads to a simpler system of principal points and principal vectors. By considering the links as pseudorigid bodies that can have a uniform planar dilatation, a compact form of the equations of motion is obtained. The conditions for dynamic force balance become almost trivial. Also the equations for the resulting reaction moment are considered for all four methods.

scholarly journals Assessment of Linearization Approaches for Multibody Dynamics Formulations

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Francisco González ◽  
Pierangelo Masarati ◽  
Javier Cuadrado ◽  
Miguel A. Naya
Keyword(s):  
Mechanical System ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Practical Applications ◽  
Linearization Methods ◽  
Highly Nonlinear ◽  
Wide Range ◽  
The Way

Formulating the dynamics equations of a mechanical system following a multibody dynamics approach often leads to a set of highly nonlinear differential-algebraic equations (DAEs). While this form of the equations of motion is suitable for a wide range of practical applications, in some cases it is necessary to have access to the linearized system dynamics. This is the case when stability and modal analyses are to be carried out; the definition of plant and system models for certain control algorithms and state estimators also requires a linear expression of the dynamics. A number of methods for the linearization of multibody dynamics can be found in the literature. They differ in both the approach that they follow to handle the equations of motion and the way in which they deliver their results, which in turn are determined by the selection of the generalized coordinates used to describe the mechanical system. This selection is closely related to the way in which the kinematic constraints of the system are treated. Three major approaches can be distinguished and used to categorize most of the linearization methods published so far. In this work, we demonstrate the properties of each approach in the linearization of systems in static equilibrium, illustrating them with the study of two representative examples.

scholarly journals Numerical solution for consistent initial conditions of constrained mechanical systems

2003 ◽  
Vol 25 (3) ◽  
pp. 170-185
Author(s):  
Dinh Van Phong
Keyword(s):  
Numerical Solution ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Flexible Approach ◽  
Constrained Mechanical Systems ◽  
Consistent Initial Values

The article deals with the problem of consistent initial values of the system of equations of motion which has the form of the system of differential-algebraic equations. Direct treating the equations of mechanical systems with particular properties enables to study the system of DAE in a more flexible approach. Algorithms and examples are shown in order to illustrate the considered technique.

Automating the Derivation of the Equations of Motion of a Multibody Dynamic System With Uncertainty Using Polynomial Chaos Theory and Variational Work

2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Paul S. Ryan ◽  
Sarah C. Baxter ◽  
Philip A. Voglewede
Keyword(s):  
Chaos Theory ◽  
Polynomial Chaos ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Multibody Dynamic ◽  
Mass Spring ◽  
Polynomial Chaos Theory ◽  
Multibody Dynamic System ◽  
Crank Mechanism

Abstract Understanding how variation impacts a multibody dynamic (MBD) system's response is important to ensure the robustness of a system. However, how the variation propagates into the MBD system is complicated because MBD systems are typically governed by a system of large differential algebraic equations. This paper presents a novel process, variational work, along with the polynomial chaos multibody dynamics (PCMBoD) automation process for utilizing polynomial chaos theory (PCT) in the analysis of uncertainties in an MBD system. Variational work allows the complexity of the traditional PCT approach to be reduced. With variational work and the constrained Lagrangian formulation, the equations of motion of an MBD PCT system can be constructed using the PCMBoD automated process. To demonstrate the PCMBoD process, two examples, a mass-spring-damper and a two link slider–crank mechanism, are shown.

Control Constraint Realization for Multibody Systems

2009 ◽  
Author(s):  
Alessandro Fumagalli ◽  
Pierangelo Masarati ◽  
Marco Morandini ◽  
Paolo Mantegazza
Keyword(s):  
Linear Systems ◽  
Multibody Systems ◽  
Matrix Pencil ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Control Constraint ◽  
Practical Observation ◽  
Alternative Condition ◽  
Deformable Bodies

This paper discusses the problem of control constraint realization applied to generic under-actuated multibody systems. The conditions for the realization are presented. Focus is placed on the tangent realization of the control constraint. An alternative condition is formulated, based on the practical observation that Differential-Algebraic Equations (DAE) need to be integrated using implicit algorithms, thus naturally leading to the solution of the problem in form of matrix pencil. The analogy with the representation of linear systems in Laplace’s domain is also discussed. The formulation is applied to the solution of simple, yet illustrative problems, related to rigid and deformable bodies. Some implications of considering deformable continua are addressed.

scholarly journals The Pantelides algorithm for delay differential-algebraic equations

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Ines Ahrens ◽  
Benjamin Unger
Keyword(s):  
Differential Algebraic Equations ◽  
Equivalence Classes ◽  
Point Of View ◽  
Algebraic Equations ◽  
Sufficient Criterion ◽  
Differential Algebraic Equation ◽  
Graph Theoretical Approach ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Structural Point

Abstract We present a graph-theoretical approach that can detect which equations of a delay differential-algebraic equation (DDAE) need to be differentiated or shifted to construct a solution of the DDAE. Our approach exploits the observation that differentiation and shifting are very similar from a structural point of view, which allows us to generalize the Pantelides algorithm for differential-algebraic equations to the DDAE setting. The primary tool for the extension is the introduction of equivalence classes in the graph of the DDAE, which also allows us to derive a necessary and sufficient criterion for the termination of the new algorithm.

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