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IN THIS ISSUE

### Research Papers

J. Dyn. Sys., Meas., Control. 2018;141(4):041001-041001-11. doi:10.1115/1.4041757.

Motor speed synchronization is important in gear shifting of emerging clutchless automated manual transmissions (AMT) for electric vehicles and other kinds of parallel shaft-based powertrains for hybrid electric vehicles. This paper proposes a speed synchronization controller design for a kind of system integrating a traction motor and a dual clutch transmission (DCT), using optimal control and disturbances compensation. Based on the relativity between magnitudes of different system parameters, the optimal control law is simplified into the proportional (P) one to ease design and analysis. Relationship between the feedback gain and the duration of speed synchronization process is derived in an explicit way to facilitate model-based determination of controller parameters. To alleviate overshoot while maintaining predesigned performances, the explicit nominal speed trajectory rather than the fixed setpoint speed is chosen as the reference signal. To improve robustness of the controller, a time-domain disturbance observer (DO) is added to cancel effects from parameter drift, unmodeled dynamics, and other exogenous disturbances. As a result, the proposed controller possesses merits of few controller parameters to be determined, good transient response, and robustness. These features make it suitable for practical engineering use. Simulation and experiment results verify its effectiveness in attaining both a fast and small-overshoot speed synchronizing process.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2018;141(4):041002-041002-9. doi:10.1115/1.4041664.

In this paper, we present a method to accurately predict the wheel speed limits at which mobile robots can operate without significant slipping. The method is based on an asymptotic solution of the nonlinear equations of motion. Using this approach, we can predict wheel slipping limits of both the inside and outside wheel when the robot is in a constant circular motion of any radius. The analytical results are supported by experiments, which show that the inside wheel slipping limits for circular motions of various radii occur very close to the predicted values. The method is then applied to predict wheel speed profiles for general motion without slipping and experimentally verified for a sinusoidal path.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2018;141(4):041003-041003-11. doi:10.1115/1.4041703.

This paper deals with the problem of rigid formation control using directed graphs in both two-dimensional (2D) and three-dimensional (3D) spaces. Directed graphs reduce the number of communication, sensing, and/or control channels of the multi-agent system. We show that the directed version of the gradient descent control law asymptotically stabilizes the interagent distance error dynamics of minimally persistent formation graphs. The control analysis begins with a (possibly cyclic) primitive formation that is grown consecutively by Henneberg-type insertions, resulting at each step in two interconnected nonlinear systems, which are recursively analyzed using the stability of interconnected systems. Simulation and experimental results are presented for the directed formation controller in comparison to the standard undirected controller.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2018;141(4):041004-041004-7. doi:10.1115/1.4041812.

In this paper, a new aging detection method of a supercapacitor is proposed through the study of the charge process. Good indicators to describe this aging are equivalent series resistance (ESR) and capacitance evolution, which are online unmeasurable parameters of the component model. The proposed model belongs to the class of state and parameter affine nonlinear system. A new adaptive nonlinear observer is designed to estimate, under different aging phases, both states and parameters using measurements only available at each sampling instant. This unusual observer contains an adaptive gain, an unknown parameter into the measured output equation, and the control signal into state matrix. This discrete-continuous observer is proved to be globally exponentially convergent under some sufficient conditions. Theoretical results are implemented for two cases of study, the first one through some simulations and the second one applied on real data for different sampling times and different values of observer gain. Results highlight good performances of the observer in online parameter estimation; thus, the component aging is clearly shown.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2018;141(4):041005-041005-9. doi:10.1115/1.4041712.

This paper considers the observer design problem for a class of discrete-time system whose nonlinear time-varying terms satisfy incremental quadratic constraints. We first construct a circle criterion based full-order observer by injecting output estimation error into the observer nonlinear terms. We also construct a reduced-order observer to estimate the unmeasured system state. The proposed observers guarantee exponential convergence of the state estimation error to zero. The design of the proposed observers is reduced to solving a set of linear matrix inequalities. It is proved that the conditions under which a full-order observer exists also guarantee the existence of a reduced-order observer. Compared to some previous results in the literature, this work considers a larger class of nonlinearities and unifies some related observer designs for discrete-time nonlinear systems. Finally, a numerical example is included to illustrate the effectiveness of the proposed design.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2018;141(4):041006-041006-12. doi:10.1115/1.4041978.

This study deals with sliding-mode nonlinear observers for a flux-controlled active magnetic bearing (AMB) operated with zero-bias flux. The Lyapunov sliding-mode observer (LSMO) feedback designs are performed for the nonlinear AMB dynamics due to control voltage saturation. The nonlinear observers are designed to estimate the magnetic flux and rotor mass velocity. The observer designs are incorporated in equivalence implementation of the nonlinear state-feedback controller. The main design tools such as sliding-mode control, Lyapunov-based control are used in this framework. The proposed observers are verified by means of numerical simulations, and stability and effectiveness of the proposed observer-based feedback designs are shown.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2018;141(4):041007-041007-15. doi:10.1115/1.4042027.

To reduce the contouring errors in computer-numerical-control (CNC) contour-following tasks, the cross-coupling controller (CCC) is widely researched and used. However, most existing CCCs are well-designed for two-axis contouring and can hardly be generalized to compensate three-axis curved contour following errors. This paper proposes an equivalent-plane CCC scheme so that most of the two-axis CCCs or flexibly designed algorithms can be utilized for equal control of the three-axis contouring errors. An initial-value regeneration-based Newton method is first proposed to compute the foot point from the actual motion position to the desired contour with a high accuracy, so as to establish the equivalent plane where the estimated three-dimensional contouring-error vector is included. After that, the signed contouring error is computed in the equivalent plane, thus a typical two-axis proportional-integral-differential (PID)-based CCC is utilized for its control. Finally, the two-axis control commands generated by the typical CCC are coupled to three-axis control commands according to the geometry of the established equivalent plane. Experimental tests are conducted to verify the effectiveness of the presented method. The testing results illustrate that the proposed equivalent-plane CCC performs much better than conventional method in both error estimation and error control.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2018;141(4):041008-041008-10. doi:10.1115/1.4042028.

In this paper, a robust fixed-gain linear output pressure controller is designed for a double-rod electrohydrostatic actuator using quantitative feedback theory (QFT). First, the family of frequency responses of the system is identified by applying an advanced form of fast Fourier transform on the open-loop input–output experimental data. This approach results in realistic frequency responses of the system, which prevents the generation of unnecessary large QFT templates, and consequently contributes to the design of a low-order QFT controller. The designed controller provides desired transient responses, desired tracking bandwidth, robust stability, and disturbance rejection for the closed-loop system. Experimental results confirm the desired performance met by the QFT controller. Then, the nonlinear stability of the closed-loop system is analyzed considering the friction and leakage, and in the presence of parametric uncertainties. For this analysis, Takagi–Sugeno (T–S) fuzzy modeling and its stability theory are employed. The T–S fuzzy model is derived for the closed-loop system and the stability conditions are presented as linear matrix inequalities (LMIs). LMIs are found feasible and thus the stability of the closed-loop system is proven for a wide range of parametric uncertainties and in the presence of friction and leakages.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2018;141(4):041009-041009-9. doi:10.1115/1.4042029.

This paper presents a directional stability control based on robust tube-based model predictive control (RMPC) approach for an overactuated electric vehicle after tire blowout on curved expressway, in the presence of the exogenous disturbances, such as cross wind and road variation. To begin with, the vehicle dynamic simulation platform allowing for the tire vertical force redistribution after tire blowout is presented, and the reliability of the platform is further analyzed by comparing with the existing experimental test results. After that, a RMPC-based controller is designed to enhance the directional stability performance of the vehicle on curved expressway after tire burst. Also, a pseudo inverse switch control allocator is developed to realize the allocation of the desired resultant signal for the remained effective wheels at the last stage. In the end, the simulation results conducting on the depicted simulation platform demonstrate the favorable maneuverability of the proposed method over the conventional model predictive control (MPC) in enhancing directional stability performance of the vehicle after a tire blowout on curved expressway.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2018;141(4):041010-041010-7. doi:10.1115/1.4042030.

In this paper, we designed multiple control inputs for Rucklidge oscillator through sliding, adaptive, and backstepping control techniques. Dynamical stability through Lyapunov theory is discussed to check whether the above‐mentioned nonlinear dynamical system is stable or not for defined controller. Based on error dynamics, adaptive and sliding control techniques are used such that solution approaches to its stable state with time. Furthermore, simulation results of nonlinear Rucklidge system are included in this paper to confirm controlled results and to analyze applied techniques. A brief analysis of these techniques for considered dynamical system is an integral part of the paper.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2018;141(4):041011-041011-11. doi:10.1115/1.4042032.

This paper presents a convergence analysis and experimental validation of an iterative design optimization framework that fuses numerical simulations with experiments. At every iteration, a G-optimal design generates a set of simulations and experiments that are used to characterize response surfaces. A subset of the experiments termed as the training points are used to fit a combined numerical/experimental response. This numerical response is obtained as a result of numerical model correction via experiments. The quality of fit for this combined response is evaluated using the remaining validation points. Based on the quality of fit, the feasible design space is reduced for a given confidence interval using hypothesis testing. A convergence analysis of the framework quantifies the closeness of the corrected numerical model to the true system as a function of response estimation error. This design optimization framework, along with the convergence result, is validated through an airborne wind energy (AWE) application using a lab-scale water channel setup. The quality of flight is greatly improved by optimizing the center of mass location, pitch angle set point, horizontal and vertical stabilizer areas using an effective experimental infusion as compared to a pure numerically optimized design.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2018;141(4):041012-041012-10. doi:10.1115/1.4042033.

Uncertainty and disturbance are common in a planar snake robot model due to its structural complexity and variation in system parameters. To achieve efficient head angle and velocity tracking with least computational complexity and unknown uncertainty bounds, a time-delayed control (TDC) scheme has been presented in this paper. A Serpenoid gait function is being tracked by the joint angles utilizing virtual holonomic constraints (VHCs) method. The first layer of TDC has been proposed for stabilizing the VHC dynamics to the origin. Once the VHCs are satisfied, the system is said to be on the constraint manifold. The second layer of TDC has been applied to an output system defined over the reduced order dynamics on the constrained manifold. To establish the robustness of the control approach through simulation, uncertainty in the friction coefficients is considered to be time-varying emulating change in the ground conditions. Simulation results and Lyapunov stability analysis affirm the uniformly ultimately bounded stability of the robot employing the proposed approach.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2019;141(4):041013-041013-10. doi:10.1115/1.4042026.

Estimating residual unbalances of a flexible rotor that is fully levitated on active magnetic bearings (AMBs) are challenging tasks due to the modeling error of AMB rotordynamic parameters. In this work, an identification algorithm has been developed for the estimation of dynamic parameters of speed-dependent AMBs and residual unbalances in a high-speed flexible rotor-bearing system. Parameters are identified during an estimation process with the help of displacement and current information at AMB locations only. For reducing the finite element model to suit the measurement availability, an improved dynamic reduction scheme has been proposed, which considers the gyroscopic matrix also in the transformation matrix. For a numerical testing of the developed identification algorithm, a multidisk flexible-shaft rotor is considered, which is fully levitated on AMBs. Speed-dependent AMB parameters have been modeled by a cubic function. Proportional–integral–derivative (PID) controllers are used to control the supply current to AMBs. Displacements and currents are generated using the finite element method of the rotor-AMB numerical model. These responses have been used in the identification algorithm for the estimation of the AMB displacement and current stiffness as well as of residual unbalances, concurrently. The algorithm with the proposed reduction scheme has shown an excellent estimation agreement in the presence of noisy responses and bias errors in rotor model parameters.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2019;141(4):041014-041014-10. doi:10.1115/1.4042143.

Ammonia storage nonuniformity has a significant impact on the emission reduction performance of urea-based selective catalytic reduction (SCR) systems. In this paper, a unique SCR platform with two catalysts in a parallel configuration was created for investigating the impact of ammonia storage nonuniformity on the emission reduction performance in a simulation environment. The established two-cell SCR platform allows users to independently control the ammonia-to-NOx ratio (ANR) for each catalyst using two independent urea solution injectors. Simulation results over US06 cycle demonstrate that, compared to the case without ammonia storage nonuniformity, the tailpipe NOx and ammonia emissions can be increased by 6.73% and 22.0%, respectively, due to the nonuniform ammonia storage in the case of an ANR nonuniformity index (NUI) at 0.2. Furthermore, an innovative model-based method was proposed for estimating the ammonia coverage ratio nonuniformity (i.e., ammonia storage nonuniformity if storage capacity is known) by utilizing a control-oriented SCR model and the tailpipe NOx and ammonia measurements at the confluence point. Simulation results proved the effectiveness of the proposed method in estimating the ammonia coverage ratio nonuniformity.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2019;141(4):041015-041015-10. doi:10.1115/1.4042247.

Modeling of the soft-solid frictional interactions plays an important role in many robotic and mechatronic systems design. We present a new model that characterizes the two-dimensional (2D) soft-solid contact interactions. The new computational approach integrates the LuGre dynamic friction model with the beam network structure of the soft-solid contact. The LuGre dynamic friction model uses the bristle deformation to capture the friction characteristics and dynamics, while the beam network structure represents the elastic contact interactions. We also present a model simplification to facilitate analysis of model properties. The model prediction and validation results are demonstrated with the experiments. The experimental results confirm the effectiveness of the modeling development. We further use the model to compute the influence of the normal load and sliding velocity on the stick-slip interaction patterns and properties. These results explain and provide analytical foundation for the reported experiments in the literature.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Dyn. Sys., Meas., Control. 2018;141(4):044501-044501-8. doi:10.1115/1.4041977.

This paper studies the design and implementation of an interactive real-time cloud supervisory control and data acquisition (SCADA) platform. The platform relying on C# and client/server architecture provides full support for data supervision of the cloud control system (CCS). Users are allowed to design supervisory interfaces by dynamically creating and customizing virtual instruments, which are seamlessly integrated into the platform by reconstructing it. Both the scalar and matrix data from different cloud nodes are supported for supervising simultaneously in real-time through receiving data asynchronously. The user can tune the parameters of the CCS online via duplex channels based on the transmission control protocol/internet protocol (IP). To overcome the disturbance of network delays to data display, a stable data and real-time data communication scheme are proposed. All the supervised data can be stored in separate files for further analysis. Finally, the online simulation and experiment are provided to demonstrate the feasibility of the designed SCADA platform.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2018;141(4):044502-044502-5. doi:10.1115/1.4042091.

This paper presents a frequency domain analysis toward the robustness, convergence speed, and steady-state error for general linear time invariant (LTI) iterative learning control (ILC) for single-input-single-output (SISO) LTI systems and demonstrates the optimality of norm-optimal iterative learning control (NO-ILC) in terms of balancing the tradeoff between robustness, convergence speed, and steady-state error. The key part of designing LTI ILC updating laws is to choose the Q-filter and learning gain to achieve the desired robustness and performance, i.e., convergence speed and steady-state error. An analytical equation that characterizes these three terms for NO-ILC has been previously presented in the literature. For general LTI ILC updating laws, however, this relationship is still unknown. Adopting a frequency domain analysis approach, this paper characterizes this relationship for LTI ILC updating laws and, subsequently, demonstrates the optimality of NO-ILC in terms of balancing the tradeoff between robustness, convergence speed, and steady-state error.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2018;141(4):044503-044503-9. doi:10.1115/1.4042031.

In addition to the longitudinal dynamics, the lateral control of the platoon can significantly affect its performance on winding road. This paper presents a platoon control framework on winding road for electric vehicles subject to stochastic communication delay and interference. The intervehicle spacing errors (ISEs) in both longitudinal and lateral directions are transformed to an arc-length-based form first. Then, the relationship between single vehicle dynamics and the ISEs is created based on the feedback linearization of the nonlinear system and the arc-length parametric representation of the directed curve. In this way, the whole platoon can be represented by three decoupled linear single-input and single-output systems, i.e., the longitudinal, lateral, and yaw. To assure the steady-state stability of the platoon on a winding road, a robust controller based on the $H∞$ method is designed to suppress the affection of the communication delay and interference. Also, sufficient conditions that achieve the transient stability of the platoon are derived. Simulations are conducted to verify the effectiveness of the proposed method. Results show that the proposed platoon control can realize the stability of the platoon as well as the supernal road traceability.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2019;141(4):044504-044504-3. doi:10.1115/1.4042144.

In a series of papers, Chang et al. proved and experimentally demonstrated a phenomenon in underactuated mechanical systems, that they termed “damping-induced self-recovery.” This paper further investigates a few features observed in these demonstrated experiments and provides additional theoretical interpretation for the same. In particular, we present a model for the infinite-dimensional fluid–stool–wheel system, that approximates its dynamics to that of the better understood finite dimensional case, and comment on the effect of the intervening fluid on the large amplitude oscillations observed in the bicycle wheel–stool experiment.

Commentary by Dr. Valentin Fuster