Research Papers

J. Dyn. Sys., Meas., Control. 2019;141(8):081001-081001-10. doi:10.1115/1.4043026.

This paper investigates the applicability of two state feedback controllers for a class of uniformly controllable and observable nonlinear systems. The first one is based on an appropriate high gain control principle that has been developed by duality from the high gain observer principle. The state feedback control gain is particularly provided by a synthesis function satisfying a well-defined condition, leading thereby to a unification of the high gain control designs. The second one is a backstepping controller that has been developed from a suitable combination of the backstepping control approach bearing in mind the high gain control principle pursued for the first controller design. A common engineering design feature that is worth to be mentioned consists in properly formulating their underlying control problems as a regulation problem involving a suitable reference model with respect to the structure of the system as well as the control design principle under consideration. Of fundamental interest, the involved reference model is systematically derived thanks to the flatness and backstepping principles using an appropriate Lyapunov approach. An experimental evaluation is carried out to illustrate the efficiency of the proposed nonlinear controllers.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2019;141(8):081002-081002-9. doi:10.1115/1.4042948.

This paper analyzes how a multisegment, articulated serpentine tail can enhance the maneuvering and stability of a quadrupedal robot. A persistent challenge in legged robots is the need to account for propulsion, maneuvering, and stabilization considerations when generating control inputs for multidegree-of-freedom spatial legs. Looking to nature, many animals offset some of this required functionality to their tails to reduce the required action by their legs. By including a robotic tail on-board a legged robot, the gravitational and inertial loading of the tail can be utilized to provide for the robot's maneuverability and stability, while the legs primarily provide the robot's propulsion. System designs for the articulated serpentine tail and quadrupedal platform are presented, along with the dynamic models used to represent these systems. Outer-loop controllers that implement the desired maneuvering and stabilizing behaviors are discussed, along with an inner-loop controller that maps the desired tail trajectory into motor torque commands for the tail. Case studies showing the tail's ability to modify yaw-angle heading during locomotion (maneuvering) and to reject a destabilizing external disturbance in the roll direction (stabilization) are considered. Simulation results utilizing the tail's dynamic model and experimental results utilizing the tail prototype, in conjunction with the simulated quadrupedal platform, are generated. Successful maneuvering and stabilization are demonstrated by the simulated results and validated through experimentation.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2019;141(8):081003-081003-12. doi:10.1115/1.4042741.

This paper presents a nonlinear disturbance observer (NDOB) for active disturbance rejection in the attitude control loop for quadrotors. An optimization framework is developed for tuning the parameter in the NDOB structure, which includes the infinity-norm minimization of the weighted sum of noise-to-output transfer function and load disturbance sensitivity function. Subsequently, the minimization generates an optimal value of the parameter based on the tradeoff between disturbance rejection and noise propagation in the system. The proposed structure is implemented on PIXHAWK, a real-time embedded flight control unit. Simulation tests are carried out on a custom built, high-fidelity simulator providing physically accurate simulations. Furthermore, experimental flight tests are conducted to demonstrate the performance of the proposed approach. The system is injected with step, sinusoidal, and square wave disturbances, and the corresponding system tracking performance is recorded. Experimental results show that the proposed algorithm attenuates the disturbances better compared to just a baseline controller implementation. The proposed algorithm is computationally cheap, an active disturbance rejection technique and robust to exogenous disturbances.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2019;141(8):081004-081004-10. doi:10.1115/1.4042952.

During twin-roll steel strip casting, molten steel is poured onto the surface of two casting rolls where it solidifies to form a steel strip. The solidification process introduces a two-phase region of steel known as mushy steel which has a significant effect on the resulting quality of the manufactured steel strip. Therefore, an accurate model of the growth of mushy steel within the steel pool is imperative for ultimately improving strip quality. In this paper, we derive a reduced-order model of the twin-roll casting process that captures the dynamics of the mushy region of the steel pool and describes the effect that the casting roll speed and gap distance have on the solidification dynamics. We propose a switched-mode description that leverages a lumped parameter moving boundary approach, coupled with a thermal resistance network analogy, to model both the steel pool and roll dynamics. The integration of these models and simulation of the combined model are nontrivial and discussed in detail. The proposed reduced-order model accurately describes the dominant dynamics of the process while using approximately one-tenth of the number of states used in previously published models.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2019;141(8):081005-081005-13. doi:10.1115/1.4042880.

Driver-machine shared control scheme opens up a new frontier for the design of driver assistance system, especially for improving active safety in emergency scenario. However, the driver's stress response to steering assistance and strong tire nonlinearity are main challenges suffered by controller designing for collision avoidance. These unfavorable factors are particularly pronounced during emergency steering maneuvers and sharply degrade shared control performance. This paper proposes a fuzzy-linear quadratic regulator (LQR) game-based control scheme to simultaneously enhance vehicle stability while compensating driver's inappropriate steering reaction in emergency avoidance. A piecewise linear-based Takagi–Sugeno (T–S) fuzzy structure is presented to mimic driver's knowledge about vehicle lateral nonlinearity, and the control authority is shared between driver and emergency steering assistance (ESA) system through steer-by-wire (SBW) assembly. An identical piecewise internal model is chosen for ESA and the shared lane-keeping problem is modeled as a fuzzy linear quadratic (LQ) problem, where the symmetrical fuzzy structure further enhances vehicle's ability to handle extreme driving conditions. In particular, the feedback Stackelberg equilibrium solutions of the fuzzy-LQ problem are derived to describe the interactive steering behavior of both agents, which enables the ESA to compensate driver's irrational steering reaction. Hardware-in-the-loop (HIL) experiment demonstrates the ESA's capability in compensating driver's aggressive steering behavior, as well as the copiloting system's excellent tracking and stabilizing performance in emergency collision avoidance.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2019;141(8):081006-081006-10. doi:10.1115/1.4042879.

The tracking performance of piezoelectric nanopositioning stages is vital in many applications, such as scanning probe microscopes (SPMs). Although modified repetitive control (MRC) can improve tracking performance for commonly used periodic reference input, it is sensitive to unexpected disturbances that deteriorate tracking precision, especially for high-speed motion. In order to achieve high-speed and precision motion, in this paper, a new composite control scheme by integrating MRC with disturbance observer (DOB) is developed. To simplify controller implementation, the hysteresis nonlinearity is treated as external disturbance and the proposed method is designed in frequency domain. The stability and robust stability are analyzed, and an optimization procedure to calculate the controller parameters is employed to enhance the performance to the maximum extent. To validate the effectiveness of the proposed method, comparative experiments are performed on a piezoelectric nanopositioning stage. Experimental results indicate that the hysteresis is suppressed effectively and the proposed method achieves high-speed and precision tracking with triangular waves references up to 25 Hz and improves the disturbance rejection ability with disturbances under different frequencies and robustness to model uncertainty through comparing with feedback controllers and MRC, respectively.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2019;141(8):081007-081007-11. doi:10.1115/1.4042953.

In this work, we study the dynamic response of the most popular unstable control problem, the inverted pendulum in terms of classical control theory. The theoretical and experimental results presented here explore the relationship between changes in the indirect tuning parameters from the linear quadratic regulator (LQR) design, and the final system performance effected using the feedback gains specified as the LQR weight constraints are changed. First, we review the development of the modern control approach using full state-feedback for stabilization and regulation, and present simulation and experimental comparisons as we change the optimization targets for the overall system and as we change one important system parameter, the length of the pendulum. Second, we explore the trends in the response by developing the generalized root locus for the system using incremental changes in the LQR weights. Next, we present a family of curves showing the local root locus and develop relationships between the weight changes and the system performance. We describe how these locus trends provide insight that is useful to the control designer during the effort to optimize the system performance. Finally, we use our general results to design an effective feedback controller for a new system with a longer pendulum and present experiment results that demonstrate the effectiveness of our analysis.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2019;141(8):081008-081008-9. doi:10.1115/1.4042954.

In this paper, the nonlinear model predictive control (NMPC) for the energy management of a power-split hybrid electric vehicle (HEV) has been studied to improve battery aging while maintaining the fuel economy at a reasonable level. A first principle battery model is built with simulation capacity of the battery aging features. The built battery model is integrated with an HEV model from autonomie software to investigate the vehicle and battery performance under control strategies. The NMPC has simplified battery models to predict the state of charge (SOC) change, the fuel consumption of the engine, and the battery aging index over the predicted horizon. The purpose of the NMPC is to find an optimized control sequence over the prediction horizon, which minimizes the designed cost function. The proposed control strategy is compared with that of an NMPC, which does not consider the battery aging. It is found that, with the optimized weighting factor selection, the NMPC with the consideration of battery aging has better battery aging performance and similar fuel economy performance comparing with the NMPC without the consideration of battery aging.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2019;141(8):081009-081009-9. doi:10.1115/1.4042949.

The effectiveness of a network's response to external stimuli depends on rapid distortion-free information transfer across the network. However, the rate of information transfer, when each agent aligns with information from its network neighbors, is limited by the update rate at which each individual can sense and process information. Moreover, such neighbor-based, diffusion-type information transfer does not predict the superfluid-like information transfer during swarming maneuvers observed in nature. The main contribution of this paper is to propose a novel model that uses self-reinforcement, where each individual augments its neighbor-averaged information update using its previous update to (i) increase the information-transfer rate without requiring an increased, individual update-rate and (ii) enable superfluid-like information transfer. Simulations results of example systems show substantial improvement, more than an order of magnitude increase, in the information transfer rate, without the need to increase the update rate. Moreover, the results show that the delayed self-reinforcement (DSR) approach's ability to enable superfluid-like, distortion-free information transfer results in maneuvers with smaller turn radius and improved cohesiveness. Such faster response rate with limited individual update rate can enable better understanding of cohesiveness of flocking in nature, as well as improve the performance of engineered swarms such as unmanned mobile systems.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2019;141(8):081010-081010-12. doi:10.1115/1.4042881.

This paper presents a new recursive forwarding method to design control laws that globally asymptotically stabilize strict-feedforward systems, of which Jacobian linearization at the origin might not be stabilizable. At each step, a Lyapunov function is constructed based on a solution of a linear partial differential equation (PDE) or a system of globally asymptotically stable (GAS) ordinary differential equations (ODEs). Optimal and bounded control designs are also addressed. The flexibility of the proposed design is illustrated via five examples.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2019;141(8):081011-081011-9. doi:10.1115/1.4042950.

As demonstrated by the 2014 MV Sewol incident, the prevention of top heavy ship capsize is necessary to protect life and property aboard a ship. The goal of this paper is to prevent the capsize of ships, which lack a restoring torque about the roll axis, by using a feedback-controlled pendulum actuator. A seven degrees-of-freedom (7DOF) model is developed for a ship equipped with a pendulum actuator. The model is used to conduct parameter analyses on the pendulum length, pendulum mast height, pendulum mass, ship center of mass (COM) height, and the pendulum controller's proportional feedback gain. The results of these analyses are depicted via time responses and phase plots. Key points for designing a pendulum actuator summarize simulation results, stating that the pendulum mass should be 3–7% of the total ship mass, and the pendulum moment of inertia should be 0.5–1.0 times the roll moment of inertia of the ship.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2019;141(8):081012-081012-10. doi:10.1115/1.4042951.

This paper presents a computationally efficient sensor-fusion algorithm for visual inertial odometry (VIO). The paper utilizes trifocal tensor geometry (TTG) for visual measurement model and a nonlinear deterministic-sampling-based filter known as cubature Kalman filter (CKF) to handle the system nonlinearity. The TTG-based approach is developed to replace the computationally expensive three-dimensional-feature-point reconstruction in the conventional VIO system. This replacement has simplified the system architecture and reduced the processing time significantly. The CKF is formulated for the VIO problem, which helps to achieve a better estimation accuracy and robust performance than the conventional extended Kalman filter (EKF). This paper also addresses the computationally efficient issue associated with Kalman filtering structure using cubature information filter (CIF), the CKF version on information domain. The CIF execution avoids the inverse computation of the high-dimensional innovation covariance matrix, which in turn further improves the computational efficiency of the VIO system. Several experiments use the publicly available datasets for validation and comparing against many other VIO algorithms available in the recent literature. Overall, this proposed algorithm can be implemented as a fast VIO solution for high-speed autonomous robotic systems.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2019;141(8):081013-081013-8. doi:10.1115/1.4042947.

This paper deals with the robust stabilization of a class of linear parameter varying (LPV) systems in the sampled data control case. Instead of using a state observer or searching for a dynamic output feedback, the considered controller is based on output derivatives estimation. This allows the stabilization of the plant with very large parameter variations or uncertainties. The proof of stability is based on the polytopic representation of the closed-loop under Lyapunov conditions and system transformations. The result is a control structure with only one parameter tuned via very simple conditions. Finally, the effectiveness of the proposed method is verified via a numerical example of a second-order LPV system.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2019;141(8):081014-081014-12. doi:10.1115/1.4043104.

This paper presents a rigid multibody dynamic model to simulate the dynamic response of a spar floating offshore wind turbine (FOWT). The system consists of a spar floating platform, the moorings, the wind turbine tower, nacelle, and the rotor. The spar platform is modeled as a six degrees-of-freedom (6DOFs) rigid body subject to buoyancy, hydrodynamic and moorings loads. The wind turbine tower supports rigid nacelle and rotor at the tip. The rigid rotor is modeled as a disk spinning around its axis and subject to the aerodynamic load. The generator torque control law is incorporated into the system dynamics to capture the rotor spinning speed response when the turbine is operating below the rated wind speed. The equations of motions are derived using Lagrange's equation in terms of the platform quasi-coordinates and rotor spin speed. The external loads due to hydrostatics, hydrodynamics, and aerodynamics are formulated and incorporated into the equations of motion. The dynamic simulations of the spar FOWT are performed for three load cases to examine the system eigen frequencies, free decay response, and response to a combined wave and wind load. The results obtained from the present model are validated against their counterparts obtained from other simulation tools, namely, FAST, HAWC2, and Bladed, with excellent agreement. Finally, the influence of the rotor gyroscopic moment on the system dynamics is investigated.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2019;141(8):081015-081015-10. doi:10.1115/1.4043223.

This paper presents an accurate and computationally efficient time-domain design method for the stability region determination and optimal parameter tuning of delayed feedback control of a flying robot carrying a suspended load. This work first utilizes a first-order time-delay (FOTD) equation to describe the performance of the flying robot, and the suspended load is treated as a flying pendulum. Thereafter, a typical delayed feedback controller is implemented, and the state-space equation of the whole system is derived and described as a periodic time-delay system. On this basis, the differential quadrature method is adopted to estimate the time-derivative of the state vector at concerned sampling grid point. In such a case, the transition matrix between adjacent time-delay duration can be obtained explicitly. The stability region of the feedback system is thereby within the unit circle of spectral radius of this transition matrix, and the minimum spectral radius within the unit circle guarantees fast tracking error decay. The proposed approach is also further illustrated to be able to be applied to some more sophisticated delayed feedback system, such as the input shaping with feedback control. To enhance the efficiency and robustness of parameter optimization, the derivatives of the spectral radius regarding the parameters are also presented explicitly. Finally, extensive numeric simulations and experiments are conducted to verify the effectiveness of the proposed method, and the results show that the proposed strategy efficiently estimates the optimal control parameters as well as the stability region. On this basis, the suspended load can effectively track the pre-assigned trajectory without large oscillations.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Dyn. Sys., Meas., Control. 2019;141(8):084501-084501-7. doi:10.1115/1.4043102.

Various practical applications use filtered backstepping technique, which follows the same procedure as backstepping design but uses high gain filters to circumvent the analytical computation of derivatives. As a result, there exists a time-scale separation between the system dynamics and the fast filter dynamics. This paper proposes a new contraction theory-based technique to design a high gain disturbance observer-based filtered backstepping controller and to quantify the convergence bounds in terms of design parameters. The quantification of the bounds explicitly shows the dependency of the closed-loop performance on various parameters, which in turn provide more ways to tune the performance apart from reducing the magnitude of filter parameter. Unlike the existing results, the proposed approach relaxes the conservative restriction, required on the filter parameter to achieve a satisfactory closed loop performance. The efficacy of the proposed method is verified through simulation examples.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2019;141(8):084502-084502-6. doi:10.1115/1.4043153.

In this technical brief, we provide an asynchronous modified repetitive controller design to address the periodic trajectory tracking problem for switched systems with time-varying switching delays between plant modes and controllers. In the feedback channel, a dynamic output feedback mechanism is adopted. By utilizing the lifting technique, the dynamic output feedback-based switched repetitive control system is transformed into a continuous-discrete two-dimensional (2D) model to differentiate the control and learning actions involved in the repetitive controller. For the transformed 2D model, by constructing a piecewise Lyapunov functional and utilizing a matrix decomposition approach, sufficient conditions in terms of linear matrix inequalities (LMIs) and the average dwell time are developed to guarantee closed-loop exponential stability. The performance of the proposed approach is illustrated via a switched RLC series circuit example and numerical simulations are provided.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2019;141(8):084503-084503-6. doi:10.1115/1.4043121.

This study investigates a passive controller for a coupled two degrees-of-freedom (DOFs) oscillator to suppress friction-induced mode-coupling instability. The primary system is acted upon by a friction force of a moving belt and static coupling of the oscillator provided with an oblique spring. The combined system, original system plus absorber, response is governed by two sets of differential equations to include contact and loss of contact between the mass and the belt. Therefore, the model accounts for two sources of nonlinearity in the system: (1) discontinuity in the friction force and (2) intermittent loss of contact. Friction coefficient and absorber orientation are used to define planar parameter space for stability analysis. For various mass ratios, the parameter space is divided into stable and unstable zones by defining stability boundaries. In general, an absorber expands the stability region and provides a significant reduction in transient response overshoot and settling time. Incorporation of the absorber also prevents mass-belt separation, thereby suppressing the belt-speed-overtake by the primary mass.

Commentary by Dr. Valentin Fuster

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