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IN THIS ISSUE

### Research Papers

J. Dyn. Sys., Meas., Control. 2018;141(3):031001-031001-14. doi:10.1115/1.4041606.

Axial piston pumps with variable volumetric displacement are often used to control flow and pressure in hydraulic systems. The displacement control mechanism in these pumps occupies significant space and accounts for significant cost in the pump design. Fixed displacement pumps have lower cost and a more compact design but suffer from a significant energy consumption disadvantage due to the need to control flow and pressure by throttling flow and bypassing unused flow to pressures below the discharge pressure. An inlet metering valve-controlled pump marks a recent development in pumping technology for hydraulic systems. In this design, an inlet metering valve restricts inlet flow reducing inlet pressure so that the specific volume of the fluid is increased as it enters a fixed displacement pump. By altering the specific volume of the working fluid, the inlet metering valve permits precise control over the pump discharge flow. This paper presents a theoretical model for inlet metered pump efficiency. The work considers additional sources of energy loss unique to the inlet metering system. Experimental results associated with inlet metered pump efficiency are presented. A comparison of the theoretical model and the experimental results is also included. It is determined that the current efficiency model accurately predicts efficiencies determined using experimental data.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2018;141(3):031002-031002-10. doi:10.1115/1.4041506.

In this paper, we develop the equations of motion at low-speed of a swimming robot for tank floor inspection. The proposed dynamic model incorporates a new friction drag force model for low-speed streamlined swimming robots. Based on a boundary layer theory analysis, we prove that for low-speed maneuvering case (Re from 103 to 105), the friction drag force component is nonlinear and is not insignificant, as previously considered. The proposed drag viscous model is derived based on hydrodynamic laws, validated via computational fluid dynamics (CFD) simulations, and then experimental tests. The model hydrodynamic coefficients are estimated through CFD tools. The robot wheels friction LuGre model is experimentally identified. Extensive experimental tests were conducted on the swimming robot in a circular water pool to validate the complete dynamic model. The dynamic model developed in this paper may be useful to design model-based advanced control laws required for accurate maneuverability of floor inspection swimming robots.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2018;141(3):031003-031003-14. doi:10.1115/1.4041505.

Linearization of the eigenvalue problem has been widely used in vibration-based damage detection utilizing the change of natural frequencies. However, the linearization method introduces bias in the estimation of damage parameters. Moreover, the commonly employed regularization method may render the estimation different from the true underlying solution. These issues may cause wrong estimation in the damage severities and even wrong damage locations. Limited work has been done to address these issues. It is found that particular combinations of natural frequencies will result in less biased estimation using linearization approach. In this paper, we propose a measurement selection algorithm to select an optimal set of natural frequencies for vibration-based damage identification. The proposed algorithm adopts $L1$-norm regularization with iterative matrix randomization for estimation of damage parameters. The selection is based on the estimated bias using the least square method. Comprehensive case analyses are conducted to validate the effectiveness of the method.

Topics: Algorithms , Damage
Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2018;141(3):031004-031004-11. doi:10.1115/1.4041446.

Bioinspired design of robotic systems can offer many potential advantages in comparison to traditional architectures including improved adaptability, maneuverability, or efficiency. Substantial progress has been made in the design and fabrication of bioinspired systems. While many of these systems are bioinspired at a system architecture level, the design of linkage connections often assumes that motion is well approximated by ideal joints subject to designer-specified box constraints. However, such constraints can allow a robot to achieve unnatural and potentially unstable configurations. In contrast, this paper develops a methodology, which identifies the set of admissible configurations from experimental observations and optimizes a compliant structure around the joint such that motions evolve on or close to the observed configuration set. This approach formulates an analytical-empirical (AE) potential energy field, which “pushes” system trajectories toward the set of observations. Then, the strain energy of a compliant structure is optimized to approximate this energy field. While our approach requires that kinematics of a joint be specified by a designer, the optimized compliant structure enforces constraints on joint motion without requiring an explicit definition of box-constraints. To validate our approach, we construct a single degree-of-freedom elbow joint, which closely matches the AE and optimal potential energy functions and admissible motions remain within the observation set.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2018;141(3):031005-031005-8. doi:10.1115/1.4041607.

This paper focuses on the stability analysis of linear fractional-order systems with fractional-order $0<α<2$, in the presence of time-varying uncertainty. To obtain a robust stability condition, we first derive a new upper bound for the norm of Mittag-Leffler function associated with the nominal fractional-order system matrix. Then, by finding an upper bound for the norm of the uncertain fractional-order system solution, a sufficient non-Lyapunov robust stability condition is proposed. Unlike the previous methods for robust stability analysis of uncertain fractional-order systems, the proposed stability condition is applicable to systems with time-varying uncertainty. Moreover, the proposed condition depends on the fractional-order of the system and the upper bound of the uncertainty matrix norm. Finally, the offered stability criteria are examined on numerical uncertain linear fractional-order systems with $0<α<1$ and $1<α<2$ to verify the applicability of the proposed condition. Furthermore, the stability of an uncertain fractional-order Sallen–Key filter is checked via the offered condition.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2018;141(3):031006-031006-6. doi:10.1115/1.4041605.

Linear proportional-integral-derivative (PID) controller stands for the most widespread technique in industrial applications due to its simple structure and easy tuning rules. Recently, considering fractional orders λ and μ, there has been studied the fractional-order PIλDμ (FPID) controller to provide salient advantages in comparison to the conventional integer-order PID, such as, a more flexible structure and a preciser performance. In addition, proportional and derivative (PD) and PID error manifolds have been classically proposed; however, there remains the question on how FPID-like error manifolds perform for the control of nonlinear plants, such as robots. In this paper, this problem is addressed by proposing a PD-IλDμ error manifold for novel vector saturated control. The stability analysis shows convergence into a small vicinity of the origin, wherein, such hybrid combination of integer- and fractional-order error manifolds provides further insights into the closed-loop response of the nonlinear plant. Simulations studies are carried out to illustrate the feasibility of the proposed scheme.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2018;141(3):031007-031007-12. doi:10.1115/1.4041604.

Previously, we proposed a multithread active vision system with virtual multiple pan-tilt tracking cameras by rapidly switching the viewpoints for the vibration sensing of large-scale structures. We also developed a system using a galvanometer mirror that can switch 500 different viewpoints in 1 s. However, the measurement rate of each observation point is low, and the time density is not always sufficient. In addition, strong multiple illuminations are required for the system owing to the retro reflective markers attached to the object being observed. In this study, we propose a multiple vibration distribution synthesis method for vibration analysis that increases the sampling rate of each observation point in the multi-thread active vision system, which is subsequently modified to a system that requires only one illumination by using corner cubes as markers. Several dynamics-based inspection experiments are conducted for a 4 m long truss-structure bridge model. The proposed method and system are verified via a high-order modal analysis, which was impossible to perform in the previous method and system.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2018;141(3):031008-031008-9. doi:10.1115/1.4041608.

The measurement of the motion of a small-scale wave energy device during wave tank tests is important for the evaluation of its response to waves and the assessment of power production. Usually, the motion of a small-scale wave energy converter (WEC) is measured using an optical motion tracking system with high precision and sampling rate. However, the cost for an optical motion tracking system can be considerably high and, therefore, the overall cost for tank testing is increased. This paper proposes a low-cost capture system composed of an inertial measurement unit and ultrasound sensors. The measurements from the ultrasound sensors are combined optimally with the measurements from the inertial measurement unit through an extended Kalman filter (EKF) in order to obtain an accurate estimation of the motion of a WEC.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Dyn. Sys., Meas., Control. 2018;141(3):034501-034501-6. doi:10.1115/1.4041609.

As an alternative to operational modal analysis and classical experimental modal analysis (EMA), a novel method was introduced previously, namely impact-synchronous modal analysis (ISMA). The effectiveness ISMA on rotor and structural dynamic systems has been proven in previous literature. More recently, an automated impact device (AID) was introduced which utilized tachometer pulse as initiation signal and its effectiveness on ISMA was proven. An attempt to further enhance this device in term of equipment and cost is then proposed by replacing the tachometer with the in-use tri-axial accelerometer through utilizing the filtered response of cyclic load component as an initiation signal to control the impact device, which is also the primary aim for this study. Prior to modal testing, accuracy of this device is illustrated at desired phase angles of 0 deg, 90 deg, 180 deg, and 270 deg. Subsequently, frequency response function (FRF) estimations obtained for ISMA using enhanced AID has demonstrated the suppression capabilities of this device on disturbances, i.e., reduction of 93.58% at 30 Hz and 57.78% at 60 Hz, resulting in a high correlation for signature assurance criterion (SAC) and cross signature assurance criterion (CSAC). Modal parameters extracted from the EMA and ISMA using impact device are presented and compared, for the first three natural modes of the test rig. It is found that natural frequencies are deviating by less than 6%, whereas modal assurance criterion (MAC) values between the mode shapes of the two tests are found to be above 0.9.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2018;141(3):034502-034502-6. doi:10.1115/1.4041610.

In this technical brief, we focus on solving trajectory optimization problems that have nonlinear system dynamics and that include high-order derivatives in the objective function. This type of problem comes up in robotics—for example, when computing minimum-snap reference trajectories for a quadrotor or computing minimum-jerk trajectories for a robot arm. DirCol5i is a transcription method that is specialized for solving this type of problem. It uses the fifth-order splines and analytic differentiation to compute higher-derivatives, rather than using a chain-integrator as would be required by traditional methods. We compare DirCol5i to traditional transcription methods. Although it is slower for some simple optimization problems, when solving problems with high-order derivatives DirCol5i is faster, more numerically robust, and does not require setting up a chain integrator.

Commentary by Dr. Valentin Fuster

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