An Updating Method for Finite Element Models of Flexible-Link Mechanisms Based on an Equivalent Rigid-Link System

This paper proposes a comprehensive methodology to update dynamic models of flexible-link mechanisms (FLMs) modeled through ordinary differential equations. The aim is to correct mass, stiffness, and damping matrices of dynamic models, usually based on nominal and uncertain parameters, to accurately represent the main vibrational modes within the bandwidth of interest. Indeed, the availability of accurate models is a fundamental step for the synthesis of effective controllers, state observers, and optimized motion profiles, as those employed in modern control schemes. The method takes advantage of the system dynamic model formulated through finite elements and through the representation of the total motion as the sum of a large rigid-body motion and the elastic deformation. Model updating is not straightforward since the resulting model is nonlinear and its coordinates cannot be directly measured. Hence, the nonlinear model is linearized about an equilibrium point to compute the eigenstructure and to compare it with the results of experimental modal analysis. Once consistency between the model coordinates and the experimental data is obtained through a suitable transformation, model updating has been performed solving a constrained convex optimization problem. Constraints also include results from static tests. Some tools to improve the problem conditioning are also proposed in the formulation adopted, to handle large dimensional models and achieve reliable results. The method has been experimentally applied to a challenging system: a planar six-bar linkage manipulator. The results prove their capability to improve the model accuracy in terms of eigenfrequencies and mode shapes

Multi-domain optimization of the eigenstructure of controlled underactuated vibrating systems

The paper proposes a multi-domain approach to the optimization of the dynamic response of an underactuated vibrating linear system through eigenstructure assignment, by exploiting the concurrent design of the mechanical properties, the regulator and state observers. The approach relies on handling simultaneously mechanical design and controller synthesis in order to enlarge the set of the achievable performances. The underlying novel idea is that structural properties of controlled mechanical systems should be designed considering the presence of the controller through a concurrent approach: this can considerably improve the optimization possibilities. The method is, first, developed theoretically. Starting from the definition of the set of feasible system responses, defined through the feasible mode shapes, an original formulation of the optimality criterion is proposed to properly shape the allowable subspace through the optimal modification of the design variables. A proper choice of the modifications of the elastic and inertial parameters, indeed, changes the space of the allowable eigenvectors that can be achieved through active control and allows obtaining the desired performances. The problem is then solved through a rank-minimization with constraints on the design variables: a convex optimization problem is formulated through the \u201csemidefinite embedding lemma\u201d and the \u201ctrace heuristics\u201d. Finally, experimental validation is provided through the assignment of a mode shape and of the related eigenfrequency to a cantilever beam controlled by a piezoelectric actuator, in order to obtain a region of the beam with negligible oscillations and the other one with large oscillations. The results prove the effectiveness of the proposed approach that outperforms active control and mechanical design when used alone

Pole assignment for active vibration control of linear vibrating systems through Linear Matrix Inequalities

This paper proposes a novel method for pole placement in linear vibrating systems through state feedback and rank-one control. Rather than assigning all the poles to the desired locations of the complex plane, the proposed method exactly assigns just the dominant poles, while the remaining ones are free to assume arbitrary positions within a pre-specified region in the complex plane. Therefore, the method can be referred to as "regional pole placement". A two-stage approach is proposed to accomplish both the tasks. In the first stage, the subset of dominant poles is assigned to exact locations by exploiting the receptance method, formulated for either symmetric or asymmetric systems. Then, in the second stage, a first-order model formulated with a reduced state, together with the theory of Linear Matrix Inequalities, are exploited to cluster the subset of the unassigned poles into some stable regions of the complex plane while keeping unchanged the poles assigned in the first stage. The additional degrees of freedom in the choice of the gains, i.e., the non-uniqueness of the solution, is exploited through a semidefinite programming problem to reduce the control gains. The method is validated by means of four meaningful and challenging test-cases, also borrowed from the literature. The results are also compared with those of classic partial pole placement, to show the benefits and the effectiveness of the proposed approach

Adaptive shaper-based filters for fast dynamic filtering of load cell measurements

This paper proposes a novel adaptive model-based filtering technique for dynamic mass measurement through load cells, named Adaptive Shaper-Based Filter (ASBF). Filtering is performed by convolving the oscillating load cell signal with a baseline of few impulses (usually 3) to rapidly compensate for its underdamped behaviour. The correct timings and amplitudes of the impulses are computed by means of a simplified dynamic model of the load cell (that requires the knowledge of the natural frequency and the damping ratio of the empty cell), and the filter output itself (i.e. the estimated mass). The load cell is modelled through the theory of systems with variable mass as a linear time-variant system and the variations of frequency and damping are predicted; in this way, the filter zeros track the load cell poles to cancel them. Robustness specifications are included in the filter design to account for the unavoidable uncertainty and estimation errors. Given the non-rational transfer function of the proposed Adaptive Shaper Based Filter, whose poles have an infinite and negative real part, rapid settling time is ensured. Experimental assessment is proposed by comparing the results with some benchmark filters

Energy optimal design of servo-actuated systems: A concurrent approach based on scaling rules

This paper addresses the issue of reducing the energy consumption of servo-actuated systems by means of the optimal selection of the electric motor and of the gearbox from catalogs of commercially available components. This idea overcomes a lack of literature: on the one hand, the energy efficiency of these systems is usually tackled through the improvement of the efficiency of each individual component rather than on focusing on a global efficiency goal; on the other one, the methods to select these components neglect the specific issue of energy consumption, being usually focused on cost reduction or minimum motor sizing. The aim of this paper is to propose a model-based design approach for the energy-optimal concurrent selection of motor, coupling and gearbox in servo-actuated systems. The method is based on the use of scaling rules, which are developed to condensate all the relevant characteristics of the system into just two parameters: the gearbox transmission ratio and the motor continuous torque at stall. Scaling rules summarize and reveal the complex relations between the system parameters and energy consumption, and hence are incorporated into the analytic formulation of the overall energy consumption. The use of these metamodels, that can be easily obtained from data provided in datasheets, allows casting the design problem as a constrained optimization problem with just two design variables. The outlined procedure is completely automatic and does not require any design iteration. The results, evaluated for two application examples, demonstrate the relevant energy savings provided by the proposed method

Optimization of the Energy Consumption Through Spring Balancing of Servo-Actuated Mechanisms

The ever-growing interest toward energy efficiency imposes the optimization of mechanism design under an energetic point of view. Even if the benefit of using spring balancing systems to reduce energy consumption is intuitive, the relation between spring design and electrical energy consumption has never been systematically addressed in the literature, which is mainly focused on static compensation of gravity forces. This paper tackles this novel and important issue and proposes an analytical method for model-based design of springs minimizing the energy required in rest-to-rest motion. The method relies on the model of energy dissipation that accountsfor the characteristics of the mechanical, electrical, and power electronic components of a servo-actuated mechanism. The theory is developed with reference to a single rotating beam. The proposed solution ensures significant energy saving compared with the traditional static balancing design of springs and is particularly suitable for repetitive (cyclic) motion tasks

Robust transient oscillation reduction for rest-to-rest motion of underactuated multibody systems

Conventional model-based design methods are often limited in their effectiveness by model-plant discrepancy. A solution to this problem is proposed in this work to enhance the robustness of motion planning solution for systems affected by parametric uncertainty. The method exploits a variational formulation in the form of a two-point boundary value problem (TPBVP) in which the robustness is achieved as a constraint enforced at the two boundaries. The formulation, which is specifically targeted at underactuated systems, aims at reducing both the transient and residual vibrations, as well as at mitigating the actuation effort. The development of the method is supported by its application to two numerical test-cases in the form of a double pendulum on a cart and a translating flexible beam

Active control of linear vibrating systems for antiresonance assignment with regional pole placement

This paper proposes a novel method for antiresonance assignment and regional pole placement in linear time-invariant vibrating systems, by means of state feedback control. The method also handles asymmetric systems and unstable ones too. Additionally, it works with both point and cross-receptances and handles the simultaneous assignment of more antiresonances in the same receptance. The method relies on two stages. In the first stage, the desired pairs of closed-loop zeros of a prescribed receptance are exactly assigned. In the second stage, all the closed-loop system poles are placed within the desired region of the complex plane. This feature allows the controller to impose the system stability and to feature the desired dynamic properties through a regional pole placement. Since the gain correction computed in the second stage is obtained as a solution of the homogeneous system related to the zero-assignment problem, it does not cause any spillover on the assigned zeros. The first step exploits the receptance method for gain computing, while the second step uses the first-order model formulation to exploit all the benefits of the Linear Matrix Inequality theory, by formulating a bilinear matrix problem solved as a semidefinite optimization aimed at reducing the control effort. The chief original contribution of the proposed method is that it embeds an a-priori imposition of both the closed-loop stability and the pole clustering in the desired regions, by overcoming the limitations of most of the methods appeared in the literature. The method effectiveness is demonstrated through five meaningful test cases