Control Of Flexible Multibody Systems Research Articles

Control design and experimental validation for flexible multi-body systems pre-compensated by inverse shapers

A complex methodology for control of flexible multi-body systems is proposed with the objective to achieve a favorable distribution of system motion so that the oscillatory mode of the flexible part is not excited. As the key element, the recently proposed concept of a feedback loop with an inverse distributed delay shaper is adopted. Unlike in existing works, the mutual coupling between the primary (controlled) structure and secondary (flexible) structure of oscillatory nature is explicitly taken into account in the controller design. First, an easy to apply method to isolate the flexible mode to be targeted in the shaper design is proposed. Secondly, the interconnection of the system, shaper and the controller is formulated as a set of delay differential algebraic equations. Then the spectral optimization control design technique is applied to achieve fast dynamics of the infinite dimensional system. The viability of the overall methodology is validated by both simulations and experiments in an extensive case study example.

Experimental studies of control concepts for a parallel manipulator with flexible links

Control of flexible multibody systems, such as flexible manipulators, is a challenging task. This is especially true if end-effector trajectory tracking is aspired. On the one hand, these systems require a large number of generalized coordinates to describe their dynamical behavior accurately. On the other hand, only a small subset of these values can be measured or reconstructed on-the-fly. Hence, it is difficult, if not nearly impossible, to use a state controller. In addition, flexible systems are underactuated, i.e. they possess less control inputs than generalized coordinates. In case of a non-collocated output controller, which is the case for end-effector trajectory tracking, the closed loop of the system might lose passivity and is non-minimum phase. In order to achieve end-effector trajectory tracking, exact and approximate feed-forward controls can be applied. In this work, two different versions of such concepts are compared experimentally. These model-based concepts are computed off-line and they supply, next to the required input values, a C1-continuous solution of the complete state vector which can be used for feedback control. If the system is non-minimum phase, a two-sided boundary value problem has to be solved and the solution includes a pre-actuation as well as a post-actuation phase. While the exact method incorporates all dynamical effects of the flexible multibody system, the approximate concepts neglect certain implications, for example the dynamical effects due to the flexibility. In addition to the presentation of the theoretical basics of the control approaches and the underlying models, this contribution addresses some of the crucial obstacles, which have to be overcome for the operation of the test bench, e.g., signal conditioning, state reconstruction and friction compensation. Since the installed sensors do not allow the direct measurement of the endeffector position, image tracking is used to judge the quality of the different control approaches.

Modeling and Control of Flexible Multibody Systems: Application to Elastic Vehicles

A new reduced-order modeling method for flexible multibody systems is proposed in this paper. This model is designed using the property of mode shapes, natural frequencies and modal mass, as well as real mass, real moment of inertia and center of gravity instead of material properties such as mass density, module of elasticity and volume. To represent elastic deformation during large translational motion and large rotational motion, the momentum and angular momentum of each vibration mode are considered. Because state differential equations are obtained from the equations of motion of multibody systems, all coupling terms are included. Therefore, a highly accurate state-space model can be obtained. As an example of this approach, the application to elastic vehicles to suppress vibration of a car body is studied.

Dynamics and control of flexible multibody systems: Part II: simulation code and parametric studies with nonlinear control

This paper describes a rather general numerical simulation code newly developed for studying dynamics and control of flexible multibody systems. It accounts for an arbitrary level of topological branching, character of the structural members, slewing, deployment, orbital perturbations, etc. The program is based on a recursive order n formulation whose details are given in Part I. Versatility and validity of the code are illustrated through parametric studies of several distinctively different systems. The dynamical analysis indicates that critical situations can lead to an undesirable system response. To establish specified performance, feasibility of a nonlinear control strategy based on the feedback linearization technique (FLT) in conjunction with the order n algorithm is explored. The FLT can control both the rigid and flexible degrees of freedom. The effectiveness of the control is assessed through numerical simulation.

Passivity and Noncollocation in the Control of Flexible Multibody Systems

Collocation of actuation and sensing in flexible structures leads to the desirable input-output property of passivity which greatly simplifies the stabilization problem. However, many control problems of interest such as robotic manipulation are noncollocated in nature. This paper examines the possibility of combining collocated and noncollocated outputs so as to achieve passivity. An appropriate combination is shown to depend on the interplay between collocated and noncollocated mass properties. Tracking problems are also studied and a controller with adaptive feedforward elements is introduced. An experimental study using a simple flexible apparatus with one rigid degree of freedom and two vibration modes is used to validate the analysis. [S0022-0434(00)01701-9]

Adaptive control of flexible-link manipulators with piezoelectric ceramic sensors and actuators

Active control of flexible multi-body systems and structures through utilization of smart materials is considered in this paper. Specifically, utilization of piezoceramics for sensing and actuation is investigated. Experimental setups have been developed at CRRL to study modeling issues and control design approaches for flexible structures with embedded (or surface-mounted) piezoceramics. In this paper, experimental results on vibration suppression for a flexible manipulator with surface mounted piezoceramics are presented. It will be shown that piezoceramics substantially improve the performance of the systems under consideration. The advocated approaches for control designs are decentralized frequency shaping and self-tuning adaptive controllers. The self-tuning controller is based on identification of the system dynamics in frequency domain utilizing Fast Fourier Transform (FFT). Addition of a self-tuning regulator enhances the performance and the robustness of the controlled system to parameter variations.

New approach to the maneuvering and control of flexible multibody systems

A mathematical formulation capable of treating the problem of maneuvering and control of flexible multibody systems is developed. The formulation is based on equations of motion in terms of quasicoordina tes derived independently for the individual substructures and on a consistent kinematical synthesis causing the substructures to act as a single structure. A perturbation approach permits the separation of the nonlinear high-dimensional system of equations into a zero-order, low-dimensional problem for the rigid-body maneuvering and a first-order, high-dimensional, time-varying problem for the elastic motions and the perturbations from the rigid-body motions. The formulation lends itself to ready computer implementation. A numerical example involving a three-beam system demonstrates the effectiveness of the new algorithm. OR a number of years there has been a persistent interest in the dynamics of flexible multibody systems. This type of system is encountered in flexible robots, rotorcraft, and spacecraft. Equations of motion for flexible multibody systems have been derived by a variety of approaches. 1'9 Recently, the interest has broadened so as to include maneuvering and control. This narrows the choice of formulations significantly, as the formulation must be consistent with the control task. A set of equations of motion suited for the control task can be formulated by means of Lagrangian equations for flexible bodies in terms of quasicoordina tes.10 The advantage of this approach is that it yields equations in terms of body axes, which are the same axes as those used to express control forces and torques. In using the approach of Ref. 10 to derive equations of motion for a chain of flexible multibody systems, it is convenient to adopt a kinematic procedure permitting the expression of the velocity vector of a nominal point in a typical body in terms of the velocity vector of the preceding body in the chain. The resulting differential equations are nonlinear and hybrid,11 where the term implies that the equations for the rigid-body translations and rotations are ordinary differential equations and those for the elastic motions are partial differential equations. Because maneuvering and control design in terms of hybrid equations is not feasible, the partial differential equations must be transformed into sets of ordinary differential equations by means of a discretizationin-space procedure, such as the finite element method12 or a Rayleigh-Ritz-based substructure synthesis.13 The resulting formulation consists of a high-order set of nonlinear ordinary differential equations. A common approach to control design requires the solution of a two-point boundary-value problem. However, this is not feasible for high-order systems; hence, a different approach is advisable. The nonlinearity enters into the differential equations through the rigid-body motions. Indeed, the elastic motions tend to be small. In view of this, it appears natural to conceive of a perturbation approach whereby the rigid-body motions

Hybrid control of flexible multi-body systems

In constrained systems of rigid and flexible bodies, the gross rigid body motion and elastic deformation cannot be controlled independently because of the coupling between these two motions. A hybrid control method for suppressing the vibration of a geometrically nonlinear flexible multi-body system is proposed in this paper. This method utilizes both the passive and active control concepts. In the passive control strategy, flexible components in the system are manufactured from fiber-reinforced composite laminates which have high strength-to-weight and stiffness-to-weight ratios. On the other hand, the active control scheme used in this paper utilizes measurable velocity and acceleration signals to produce the command signals required to activate the actuator forces. A small number of sensors and controllers with constant gain factors are used in order to obtain a low-cost and simple control system. The generalized active control forces associated with the system generalized coordinates are developed using the virtual work and are written in terms of the coupled set of reference and elastic coordinates. The system differential equations of motion are developed using Lagrange's equation and the Jacobian matrix of the nonlinear algebraic constraint equations describing mechanical joints in the system is used to identify a set of independent generalized coordinates. The associated independent differential equations are identified and are written in the state space formulation. The characteristics of the proposed hybrid control are evaluated through computer simulations of a seven-body flexible vehicle. The performance characteristics of the hybrid control are also compared to the performance characteristics of the passive and active controls.

Pulse control of flexible multibody systems

An active pulse control method is developed to reduce the vibrations of multibody systems resulting from impact loadings. The pulse, which is a function of system generalized coordinates and velocities, is determined analytically using energy and momentum balance equations of the impacting bodies. Elastic components in the multibody system are discretized using the finite element method. The system equations of motions and nonlinear algebraic constraint equations describing mechanical joints between different components are written in the Lagrangian formulation using a finite set of coupled reference position and local elastic generalized coordinates. A set of independent differential equations are identified by the generalized coordinate partitioning of the constraint Jacobian matrix. These equations are written in the state space formulation and integrated forward in time using a direct numerical integration method. Dependent coordinates are then determined using the constraint kinematic relations. Points in time at which impact occurs are monitored by an impact predictor function, which controls the integration algorithms and forces for the solution of the momentum relation, to define the jump discontinuities in the composite velocity vector as well as the system reaction forces. The effectiveness of the active pulse control in reducing the vibration of flexible multibody aircraft during the touchdown impact is investigated and numerical results are presented.