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IN THIS ISSUE

### Research Papers

J. Dyn. Sys., Meas., Control. 2011;133(5):051001-051001-8. doi:10.1115/1.4004042.

A free-floating space robot with four linkages, two flexible arms and a rigid end-effector that are mounted on a rigid spacecraft; is studied in this paper. The governing equations are derived using Kane’s method. The powerful tools of Kane’s approach in incorporating motion constraints have been applied in the dynamic model. By including the motion constraints in the kinematic and dynamic equations, a two way coupling between the spacecraft motion and manipulator motion is achieved. The assumed mode method is employed to express elastic displacements, except that the associated admissible functions are supplanted by quasicomparison functions. By a perturbation approach, the resulting nonlinear problem is separated into two sets of equations: one for rigid-body maneuvering of the robot and the other for elastic vibrations suppression and rigid-body perturbation control. The kinematic redundancy of the manipulator system is removed by exploiting the conservation of angular momentum law that makes the rigid manipulator system nonholonimic. Nonholonomic constraints, resulted from the nonintegrability of angular momentum, in association with equations obtained from conservation of linear momentum and direct differential kinematics generate a set of ordinary differential equations that govern the motion tracking of the robot. The digitalized linear quadratic regulator (LQR) with prescribed degree of stability is used as the feedback control scheme to suppress vibrations. A numerical example is presented to show the numerical preferences of using Kane’s method in deriving the equations of motion and also the efficacy of the control scheme. Acquiring a zero magnitude for spacecraft attitude control moment approves the free-floating behavior of the space robot in which considerable amount of energy is saved.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2011;133(5):051002-051002-4. doi:10.1115/1.4004062.

Model parameters of a nonlinear mechanical system are identifiable if a unique relationship exists between its input–output behavior and the parameter values. The identifiability analysis of the parameters is one of the most important steps in the parametric model identification of nonlinear mechanical systems. The concept and two numerical approaches of analyzing the identifiability are presented in this paper. We propose that, via case studies, one had better check of the local identifiability of a parametric model at the identified parameter point using the numerical approach, when the parameter identification procedure has been finished.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2011;133(5):051003-051003-10. doi:10.1115/1.4003800.

The capability of over-actuated vehicles to maintain stability during limit handling is studied in this paper. A number of important differently actuated vehicles, equipped with hydraulic brakes toward more advanced chassis solutions, are presented. A virtual evaluation environment has specifically been developed to cover the complex interaction between the driver and the vehicle under control. In order to fully exploit the different actuators setup, and the hard nonconvex constraints they possess, the principle of control allocation by nonlinear optimization is successfully employed. The final evaluation is made by exposing the driver and the over-actuated vehicles to a safety-critical double lane change. Thereby, the differently actuated vehicles are ranked by a quantitative indicator of stability.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2011;133(5):051004-051004-6. doi:10.1115/1.4003383.

In this paper, the problem of disturbance attenuation with internal stability for a class of nonlinear singularly perturbed systems via nonlinear $H∞$ approach is studied. It is shown through a useful theorem that under appropriate assumptions, the problem of disturbance attenuation for the main system may be related to the problem of disturbance attenuation for the reduced-order system. This is carried out by a new approach in which we use the quasi-steady state of fast variables. Therefore, the problem of existence of a positive definite solution for the Hamilton–Jacobi–Isaacs (HJI) inequality related to the main system leads to the problem of existence of a solution of a simpler HJI inequality related to the reduced-order system.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2011;133(5):051005-051005-10. doi:10.1115/1.4004058.

Coherent phantom track generation through controlling a group of electronic combat air vehicles is currently an area of great interest to the defense agency for the purpose of deceiving a radar network. However, generating an optimal or even feasible coherent phantom trajectory in real-time is challenging due to the high dimensionality of the problem and severe geometric, as well as state, control, and control rate constraints. In this paper, the bio-inspired virtual motion camouflage based methodology, augmented with the derived early termination condition, is investigated to solve this constrained collaborative trajectory planning problem in two approaches: centralized (one optimization loop) and decentralized (two optimization loops). Specifically, in the decentralized approach, the first loop finds feasible phantom tracks based on the early termination condition and the equality and inequality constraints of the phantom track. The second loop uses the virtual motion camouflage method to solve for the optimal electronic combat air vehicle trajectories based on the feasible phantom tracks obtained in the first loop. Necessary conditions are proposed for both approaches so that the initial and final velocities of the phantom and electronic combat air vehicles are coherent. It is shown that the decentralized approach can solve the problem much faster than the centralized one, and when the decentralized approach is applied, the computational cost remains roughly the same for the cases when the number of nodes and/or the number of electronic combat air vehicles increases. It is concluded that the virtual motion camouflage based decentralized approach has promising potential for usage in real-time implementation.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2011;133(5):051006-051006-8. doi:10.1115/1.4004061.

This paper investigates the design of spacecraft attitude stabilization controllers that are robust against actuator faults and external disturbances. A nominal controller is developed initially, using the adaptive backstepping technique, to stabilize asymptotically the spacecraft attitude when the actuators are fault-free. Additive faults and the partial loss of actuator effectiveness are considered simultaneously and an auxiliary controller is designed in addition to the nominal controller to compensate for the system faults. This auxiliary controller does not use any fault detection and isolation mechanism to detect, separate, and identify the actuator faults online. The attitude orientation and angular velocity of the closed-loop system asymptotically converge to zero despite actuator faults providing the nominal attitude system is asymptotically stable. Numerical simulation results are presented that demonstrate the closed-loop performance benefits of the proposed control law and illustrate its robustness to external disturbances and actuator faults.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2011;133(5):051007-051007-12. doi:10.1115/1.4004065.

We present a control design method for nonlinear partial differential equations (PDEs) based on a combination of gain scheduling and backstepping theory for linear PDEs. A benchmark first-order hyperbolic system with an in-domain nonlinearity is considered first. For this system a nonlinear feedback law, based on gain scheduling, is derived explicitly, and a proof of local exponential stability, with an estimate of the region of attraction, is presented for the closed-loop system. Control designs (without proofs) are then presented for a string PDE and a shear beam PDE, both with Kelvin–Voigt (KV) damping and free-end nonlinearities of a potentially destabilizing kind. String and beam simulation results illustrate the merits of the gain scheduling approach over the linearization based design.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2011;133(5):051008-051008-7. doi:10.1115/1.4004041.

Presented is the model based diagnostics of a three-way catalyst (TWC). The proposed TWC model relates measurable engine inputs (engine air mass (AM) and catalyst temperature) to a metric that quantifies TWC oxygen storage capacity. The TWC model structure is based on the dynamics of the TWC and identified using orthogonal least squares (OLS). The model coefficients are estimated using an instrumental variables four step (IV4) approach. TWC diagnostics is realized by means of an information synthesis (IS) technique where changes in the adapted TWC model coefficients are utilized to estimate TWC health. The approach is experimentally validated on a federal test procedure (FTP) drive cycle for healthy (full useful life, FUL) and failed (threshold) TWCs. The results will show that a 100% accurate classification in TWC health estimation (FUL or threshold) is produced for the catalysts tested.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2011;133(5):051009-051009-10. doi:10.1115/1.4004072.

The focus of this work is on the development of a framework permitting the unification of generalized polynomial chaos (gPC) with the linear moment propagation equations, to accurately characterize the state distribution for linear systems subject to initial condition uncertainty, Gaussian white noise excitation and parametric uncertainty which is not required to be Gaussian. For a fixed value of parameters, an ensemble of moment propagation equations characterize the distribution of the state vector resulting from Gaussian initial conditions and stochastic forcing, which is modeled as Gaussian white noise. These moment equations exploit the gPC approach to describe the propagation of a combination of uncertainties in model parameters, initial conditions and forcing terms. Sampling the uncertain parameters according to the gPC approach, and integrating via quadrature, the distribution for the state vector can be obtained. Similarly, for a fixed realization of the stochastic forcing process, the gPC approach provides an output distribution resulting from parametric uncertainty. This approach can be further combined with moment propagation equations to describe the propagation of the state distribution, which encapsulates uncertainties in model parameters, initial conditions and forcing terms. The proposed techniques are illustrated on two benchmark problems to demonstrate the techniques’ potential in characterizing the non-Gaussian distribution of the state vector.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2011;133(5):051010-051010-7. doi:10.1115/1.4003802.

This paper presents a simple analysis evaluating the stability threshold for magnetically levitated flexible structures using dissipative colocated controllers. It is shown that with such a control structure, the controller that stabilizes a rigid levitated mass can also stabilize a simple flexible structure with the same overall mass and electrodynamics. Experimental and simulation results are presented to validate this conclusion.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2011;133(5):051011-051011-8. doi:10.1115/1.4003095.

As engine designers look for ways to improve efficiency and reduce emissions, piezoelectric actuated fuel injectors for common rail diesel engines have shown to have improved response characteristics over solenoid actuated injectors and may allow for enhanced control of combustion through multipulse, closely spaced injections or rate shaping. This paper outlines the development of an 11 state simulation model for a piezoelectric fuel injector and associated driver that can be used for injector design and control system verification. Nonmeasureable states of the model are plotted and analyzed, while measurable quantities including injection rate, piezo stack voltage, and piezo stack current are validated against experimental injector rig data for two different rail pressures.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2011;133(5):051012-051012-11. doi:10.1115/1.4004063.

This article models the dynamics of cilia-based devices (soft cantilever-type, vibrating devices that are excited by external vibrations) for mixing and manipulating liquids in microfluidic applications. The main contribution of this article is to develop a model, which shows that liquid sloshing and the added-mass effect play substantial roles in generating large-amplitude motion of the cilia. Additionally, experimental mixing results, with and without cilia, are comparatively evaluated to show more than one order-of-magnitude reduction in the mixing time with the use of cilia.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2011;133(5):051013-051013-10. doi:10.1115/1.4004040.

In this paper, a new approach to estimation of unknown inputs and faults in a class of nonlinear systems is presented. The approach is based on the design of a cascade connection of two sliding mode observers. The first observer is used for the estimation of state and unknown inputs and the second is used for the fault detection and isolation. An important feature of the proposed approach is that the state trajectories do not leave the sliding manifold even in the presence of unknown inputs and faults. This allows for faults and unknown inputs to be completely reconstructed based on the information retrieved from the equivalent output injection signals. The proposed approach is tested on a nonlinear model of single link flexible joint robot system.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2011;133(5):051014-051014-10. doi:10.1115/1.4004059.

In this paper, the fractionalized differentiating method is implemented to reduce commensurate fractional order models complexity. The prominent properties of this method are its simplicity and guarantee of preserving the stability of a specific class of fractional order models in their reduced counterparts. The presented reduction method is employed in simplifying complicated fractional order controllers to a fractional order PID (FOPID) controller and proposing tuning rules for its parameters adjustment. Finally, the efficiency of the FOPID tuning rule obtained based on the proposed reduction method is shown in the temperature control of a cutting process.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J. Dyn. Sys., Meas., Control. 2011;133(5):054501-054501-6. doi:10.1115/1.4004039.

The modular model assembly method (MMAM) is an energy based model distribution and assembly algorithm that distributes and assembles model information through computer networks. Using the MMAM linear and affine physical system, models can be distributed and assembled using dynamic matrices. Though the MMAM procedure can be used for a large class of systems, linear model dynamic matrices cannot be used to represent nonlinear behavior. This work is an extension of the MMAM to assemble nonlinear physical models described through Volterra expansions. Volterra expansions are models representations of smooth nonlinearities. Using the approach proposed here, complex assemblies of nonlinear physical models can be executed recursively while hiding the topology and characteristics of their structural model subassemblies.

Topics: Manufacturing
Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2011;133(5):054502-054502-5. doi:10.1115/1.4003798.

In this paper, we consider the control of time delay system by first order controller. By Using the Hermite-Biehler theorem, which is applicable to quasipolynomials, we seek a stability region of the controller for first order delay systems.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2011;133(5):054503-054503-9. doi:10.1115/1.4003797.

Clutch to clutch shift control technology, which is the key enabler for a compact and low cost transmission design, is important for both automatic and hybrid transmissions. To ensure a smooth clutch to clutch shift, precise synchronization between the on-coming and off-going clutches is critical. This further requires the on-coming clutch to be filled and ready for engagement at the predetermined time. Due to the compact design, currently there is no pressure sensor inside the clutch chamber, and therefore the clutch fill can only be controlled in an open loop fashion. The traditional clutch fill approach, by which the clutch fill input pressure command is manually calibrated, has a couple of limitations. First, the pressure profile is not optimized to reduce the peak flow demand during clutch fill. Moreover, it is not systematically designed to account for uncertainties in the system, such as variations of solenoid valve delay and parameters of the clutch assembly. In this paper, we present a systematic approach to evaluate the clutch fill dynamics and synthesize the optimal pressure profile. First, a clutch fill dynamic model, which captures the key dynamics in the clutch fill process, is constructed and analyzed. Second, the applicability of the conventional numerical dynamic programming (DP) method to the clutch fill control problem, which has a stiff dynamic model, is explored and shown to be ineffective. Thus, we proposed a customized DP method to obtain the optimal and robust pressure profile subject to specified constraints. The customized DP method not only reduces the computational burden significantly, but also improves the accuracy of the result by eliminating the interpolation errors. To validate the proposed method, a transmission clutch fixture has been designed and built in the laboratory. Both simulation and experimental results demonstrate that the proposed customized DP approach is effective, efficient and robust for solving the clutch fill optimal control problem.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2011;133(5):054504-054504-6. doi:10.1115/1.4003096.

Iterative learning control algorithms have been shown to offer a high level of performance both theoretically and when applied to practical applications. However, the trial-to-trial convergence of the error is generally highly dependent on the initial choice of input applied to the plant. Techniques are therefore developed, which generate an optimal initial input selection, and the effect this has on the error over subsequent trials is examined. Experimental benchmarking is undertaken using a gantry robot test facility.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2011;133(5):054505-054505-6. doi:10.1115/1.4004055.

This paper presents a new predictive greedy control law for the control of electropneumatic systems using solenoid valves. The method is based on a predictive model of the mass flow rate of the valves. For this strategy, a control vector, depending on the number of possible configurations for the solenoid valves, is defined. In order to evaluate the new approach, a comparison has been performed with a classical PWM control for a force tracking problem. The experimental results show that not only the accuracy in steady state but also the dynamic behavior of the pressures is better in the case of greedy control than PWM control.

Commentary by Dr. Valentin Fuster