Research Papers

J. Dyn. Sys., Meas., Control. 2012;134(3):031001-031001-11. doi:10.1115/1.4005496.

A necessary condition for the existence of the solution of the Riccati differential equation for both linear, time varying systems and nonlinear systems is introduced. First, a necessary condition for the existence of the solution of the Riccati differential equation for linear, time varying systems is proposed. Then, the sufficient conditions to satisfy the necessary condition are given. After that, the existence of the solution of the Riccati differential equation is generalized for nonlinear systems.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2012;134(3):031002-031002-8. doi:10.1115/1.4005499.

This paper proposes a new modeling approach which is experimentally validated on piezo-electric systems in order to provide a robust Black-box model for complex systems control. Industrial applications such as vibration control in machining and active suspension in transportation should be concerned by the results presented here. Generally one uses physical based approaches. These are interesting as long as the user cares about the nature of the system. However, sometimes complex phenomena occur in the system while there is not sufficient expertise to explain them. Therefore, we adopt identification methods to achieve the modeling task. Since the microdisplacements of the piezo-system sometimes generate corrupted data named observation outliers leading to large estimation errors, we propose a parameterized robust estimation criterion based on a mixed L2 – L1 norm with an extended range of a scaling factor to tackle efficiently these outliers. This choice is motivated by the high sensitivity of least-squares methods to the large estimation errors. Therefore, the role of the L1 -norm is to make the L2 -estimator more robust. Experimental results are presented and discussed.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2012;134(3):031003-031003-6. doi:10.1115/1.4005502.

Terrain topology is the principal source of vertical excitation into the vehicle system and must be accurately represented in order to correctly predict the vehicle response. It is desirable to evaluate vehicle models over a wide range of terrain, but it is computationally impractical to simulate long distances of every terrain type. A method to parsimoniously characterize terrain topology is developed in this work so that terrain can be grouped into meaningful sets with similar topological characteristics. Specifically, measured terrain profiles are considered realizations of an underlying stochastic process; an autoregressive model and a residual process provide the mathematical framework to describe this process. A statistical test is developed to determine if the residual process is independent and identically distributed (IID) and, therefore, stationary. A reference joint probability distribution of the residuals is constructed based on the assumption that the data are realizations of an IID stochastic process. The distribution of the residuals is then compared to this reference distribution via the Kolmogorov–Smirnov “goodness of fit” test to determine whether the IID assumption is valid. If the residual process is IID, a single probability distribution can be used to generate residuals and synthetic terrain of any desired length. This modeling method and statistical test are applied to a set of U.S. highway profile data and show that the residual process can be assumed to be IID in virtually all of these cases of nondeformable terrain surfaces.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2012;134(3):031004-031004-8. doi:10.1115/1.4005504.

In this paper, a new methodology for robust controller design in nonlinear multivariable systems is suggested to guarantee asymptotic output tracking. The systems under consideration are perturbed by functionally bounded matched and unmatched uncertainties/perturbations and assumed to be described in the strict-feedback form. The main idea of the methodology is based on the combination of conventional sliding mode control and backstepping algorithm. The proposed controller called nested sliding mode controller that is obtained through a stepwise algorithm. It has the ability of rejecting nonvanishing perturbations by using dynamic switches, unlike conventional and other hierarchical sliding mode design methods. Performance is studied through theorems and verified by two numerical examples.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2012;134(3):031005-031005-13. doi:10.1115/1.4005505.

The partial differential equation describing one-dimensional flow in a hydraulic pipeline with linear resistance can be approximated and solved numerically using different modal approaches. Modal models can be obtained either by using rational transfer functions (RTF) in the Laplace domain solution or by using separation of variables (SOV) techniques. The pipeline models have four possible input–output configurations: pressure inputs at both ends, flow rate inputs at both ends, and the two cases of mixed inputs. In this paper, modal bond graph representations for pipeline sections are reviewed, and new bond graphs are proposed for combinations of solution method and input–output configurations not yet presented in the literature. This includes bond graph representations for the two mixed input cases developed using the SOV technique, and bond graphs for the other two cases, pressure inputs or flow rate inputs, constructed on the basis of RTF solutions. Through numerical simulations of hydraulic single lines, the obtained models are compared to alternative models already established in the literature. It is shown that the modal models developed by the RTF and SOV methods have the same accuracy when the same number of modes is used. For both of these approaches, correction methods to maintain a high accuracy when truncating high-order modes are described, and also adapted to the bond graph form. Finally, simulation results for various line configurations are illustrated.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2012;134(3):031006-031006-15. doi:10.1115/1.4005512.

This paper investigates a passive fault tolerant control to aircraft that suffers from vertical tail damage. A novel notion of damage degree is introduced to parameterize the damaged flight dynamics model. It is applied to seek the maximum allowable damage degree (tolerance capacity) stabilizable by the proposed passive fault tolerant and backup control under a linearized model. The design algorithms are presented and illustrated through numerical simulations on a Boeing-747 100/200 model. Furthermore, the impact of potential control saturation is taken into account in the proposed design and a set of design parameters are tuned such that the maximum allowable damage degree is bounded, represented as the so-called critical damage degree.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2012;134(3):031007-031007-11. doi:10.1115/1.4005511.

In this paper, a recently introduced model-based method for precedent-free fault detection and isolation (FDI) is modified to deal with multiple input, multiple output (MIMO) systems and is applied to an automotive engine with exhaust gas recirculation (EGR) system. Using normal behavior data generated by a high fidelity engine simulation, the growing structure multiple model system (GSMMS) approach is used to construct dynamic models of normal behavior for the EGR system and its constituent subsystems. Using the GSMMS models as a foundation, anomalous behavior is detected whenever statistically significant departures of the most recent modeling residuals away from the modeling residuals displayed during normal behavior are observed. By reconnecting the anomaly detectors (ADs) to the constituent subsystems, EGR valve, cooler, and valve controller faults are isolated without the need for prior training using data corresponding to particular faulty system behaviors.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2012;134(3):031008-031008-10. doi:10.1115/1.4005508.

Due to the chemical reactions occurring inside the diesel oxidation catalysts (DOCs) and diesel particulate filters (DPFs) that are commonly equipped on diesel engines, the exhaust gas oxygen concentrations considerably vary through the aftertreatment systems. Oxygen concentration in exhaust gas is important for the performance of catalysts such as the NOx conversion efficiencies of the selective catalytic reduction systems and lean NOx traps. Moreover, in the presence of a low-pressure loop exhaust gas recirculation, the exhaust gas oxygen concentration after DPF also influences the in-cylinder combustion. From system control, estimation, and analysis viewpoints, it is thus imperative to have a control-oriented model to describe the oxygen concentration dynamics across the DOC and DPF. In this paper, a physics-based, lumped-parameter, control-oriented DOC–DPF oxygen concentration dynamic model was developed with a multi-objective optimization method and validated with the experimental data obtained on a medium-duty diesel engine equipped with a full suite of aftertreatment systems. Experimental results show that the model can well capture the oxygen dynamics across the diesel engine aftertreatment systems. As an application of the experimentally validated model, an observer was designed to estimate the DOC-out and DPF-out oxygen concentrations in real time. Experimental results show that the estimated states from the proposed observer can converge to the measured signals fastly and accurately.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2012;134(3):031009-031009-7. doi:10.1115/1.4005507.

This paper presents a novel robust controller design for formation control of autonomous underwater vehicles (AUVs). We consider a nonlinear three-degree-of-freedom dynamic model for the horizontal motion of each AUV. By using the Jacobi transform, the horizontal dynamics of AUVs are explicitly expressed as dynamics for formation shape and formation center, and are further decoupled by feedback control. We treat the coupling terms as perturbations to the decoupled system. An H-infinity state feedback controller is designed to achieve robust stability of the closed loop formation and translation dynamics. By incorporating an orientation controller, the formation shape under control converges and the formation center tracks a desired trajectory simultaneously. Simulation results demonstrate the effectiveness of the controllers.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2012;134(3):031010-031010-9. doi:10.1115/1.4005493.

A dynamic model to describe the effect of compliance in a transmission system is presented. Analysis of this model shows that it is desirable to use feedback from driver-side of the transmission system. This model is extended to include the effects of both compliance and backlash in a mechanical transmission system. The proposed model considers compliance (which may be either due to the elasticity of the shafts or belt in a belt-pulley transmission system) and backlash appearing in series in a drive system. In contrast to the classical backlash model which considers both input and output to the backlash as displacements, the proposed model considers (torque) force as input to the backlash and (angular velocity) velocity of the driven member as the output of the backlash. Thus, the proposed model does not assume that the load is stationary when contact is lost due to backlash width, i.e., momentum of the load is taken into account. Using the proposed model, a bound on the speed error due to the presence of backlash is derived. Experiments were conducted on a rectilinear mass-spring system platform, which has a provision to change the backlash width by a known value. Experiments were conducted with different backlash widths and a velocity error bound was computed. The error bound obtained from the experimental results agrees with the theoretically computed bound.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2012;134(3):031011-031011-6. doi:10.1115/1.4005495.

Vibration control is an effective alternative to conventional feedback and feedforward control. Motivated by its important application in physical systems and few results on general oscillatory tracking control, we consider tracking control of a class of nonlinear systems using oscillation in the paper. We propose a new oscillatory control design using general averaging analysis for the tracking problem. Based on the oscillation functions associated with accessible vibrating components of the system, oscillatory control is designed to track a desired trajectory. Comparing to existing oscillatory tracking control, our approach is robust to initial conditions. We show the effectiveness of the proposed method by two simulation examples, which include a second-order nonholonomic integrator and the inverted pendulum system. For the inverted pendulum system, we show that our designed oscillatory control does not need state feedback to track a desired trajectory, which is desirable for systems where state measurement is not feasible.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2012;134(3):031012-031012-12. doi:10.1115/1.4005513.

A multi-input-multi-output (MIMO) sliding mode control scheme was developed with guaranteed stability to simultaneously control air-to-fuel ratio (AFR) and fuel ratios to desired levels under various air flow disturbances by regulating the mass flow rates of engine port-fuel-injection (PFI) and direct injection (DI) systems. The sliding mode control performance was compared with a baseline multiloop proportional integral differential (PID) controller through simulations and showed improvements. A four cylinder mean value engine model and the proposed sliding mode controller were implemented into a hardware-in-the-loop (HIL) simulator and a target engine control module, and HIL simulations were conducted to validate the developed controller for potential implementation in an automotive engine.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2012;134(3):031013-031013-15. doi:10.1115/1.4005500.

This paper is concerned with the design of a robust, state-feedback, delay-dependent H∞ controller for an active vibration control of seismic-excited structural systems having actuator delay, norm bounded uncertainties, and L2 disturbances. The norm bounded uncertainties are assumed to exist in variations of structural stiffness and damping coefficients. Based on the selection of Lyapunov–Krasovskii functional, first a bounded real lemma (BRL) is obtained in terms of linear matrix inequalities (LMIs) such that the nominal, time-delay system is guaranteed to be globally asymptotically stable with minimum allowable disturbance attenuation level. Extending BRL, sufficient delay-dependent criteria are developed for a stabilizing H∞ controller synthesis involving a matrix inequality for which a nonlinear optimization algorithm with LMIs is proposed to get feasible solution to the problem. Moreover, for the case of existence of norm-bounded uncertainties, both the BRL and H∞ stabilization criteria are easily extended by employing a well-known bounding technique. Then, a cone complementary algorithm is also utilized to solve the nonconvex optimization problem. By use of the proposed method, a suboptimal controller with maximum allowable delay bound, uncertainty bound and minimum allowable disturbance attenuation level can be easily obtained by solving the proposed convex optimization technique. A four-degree-of-freedom uncertain structural system subject to seismic excitations is used to illustrate the effectiveness of the approach through simulations. Simulation results, obtained by using real time-history data of Kobe and Kocaeli earthquakes show that the proposed controller is very effective in reducing vibration amplitudes of storeys and guarantees stability at maximum actuator delay and parametric uncertainty bound.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2012;134(3):031014-031014-7. doi:10.1115/1.4005509.

In nuclear power plants (NPPs), according to current regulations, the response time of capacitive pressure transmitters is used as an index for surveillance. Such measurement can be carried out in situ applying the noise analysis techniques to the sensor output signal. The method is well established, and it is based on the autoregressive (AR) fitting optimized by the Akaike criterion (AIC). The sensor response is influenced by the sensing line, and its length is different in each plant. Recent empirical research has proved that the sensor inner structure can be modeled with a two real poles transfer function. In the present work, it has been proved that the noise analysis applied to the simulated response of a transmitter, modeled with two poles coupled with a sensing line, gives erroneous values for the ramp time delay when the sensing line is long. Specifically, the order of the AR model supplied by the Akaike criterion is not appropriate. Therefore, a Monte Carlo method is proposed to be applied in order to establish a new criterion, based on the statistical analysis of the repeatability of the ramp time delay obtained with the AR model.

Commentary by Dr. Valentin Fuster

Technical Briefs

J. Dyn. Sys., Meas., Control. 2012;134(3):034501-034501-5. doi:10.1115/1.4005506.

The objective of this paper is to experimentally investigate the significance of the pressure transient flow force acting on hydraulic spool valves. In the past, this flow force effect has been routinely neglected due to its assumed small size. Through analytical and experimental methods, this research shows that flow forces due to pressure transient effects can be comparable in magnitude to the steady flow forces acting on the valve and that the past tradition of neglecting this effect may not always be justified. The paper also shows that the traditional steady flow force model does a fairly good job predicting the steady flow forces on the valve, but more research must be done to develop a good model for pressure transient flow forces.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2012;134(3):034502-034502-8. doi:10.1115/1.4005503.

It is well known that the positional proportional-integral-derivative (PID) control of a servo mechanism with stiction always leads to a limit cycle. Related to this fact, two basic questions have still remained unanswered. The first question is, if the limit cycle occurs, how large it becomes for a given value of stiction force. The second question, which is of more practical importance, is how we should modify the PID controller to avoid this limit cycle with minimal sacrifice of the servo performance. This paper presents a rigorous analysis to provide particular answers to these two questions, which turn out to be closely related to each other. More specifically, it is shown that, by exploiting algebraic properties of the state trajectory, a simple bisection algorithm can be devised to compute the exact magnitude of the periodic solution for a given value of stiction. Through the geometric analysis of the impact map, this result is then used to find the minimum value of the integrator leakage to avoid the limit cycle. The work in this paper will be useful as a specific reference in designing servo mechanisms with stiction free from limit cycle.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2012;134(3):034503-034503-7. doi:10.1115/1.4005494.

In the paper, we show that for a class of linear plants, although the common linear control can be used to stabilize them, the step responses of the resulting closed-loop systems must have overshoot; however, a simple switching between them may avoid the overshoot. This indicates that switching control may overcome the performance limitation of linear feedback control in the overshoot-avoidance respect. A simple switching control scheme with such a quality is exploited and the conditions for its existence are presented. In the scheme, two common controllers are needed and they are only required to guarantee no overshoot on the time intervals [0, ts ) and [ts , ), respectively, where ts denotes the switching time. For actual implementation, a state-dependent version of the switching control law is developed. Two examples are presented to show its effectiveness.

Commentary by Dr. Valentin Fuster

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